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LARDNER'S  NATURAL  PHILOSOPHY. 

NOW    COMPLETE. 


HAND-BOOKS 
NATURAL  PHILOSOPHY  AND  ASTRONOMY. 

BY  DIONYSIDS  LARDNEB,  D.C.L., 

FoniwTij  PioftHDr  <J<  NUDnl  nidoiil^r  ud  AttrDBDnr  In  nninniLr  CqIIii^,  LfindviL 

lUi  nluUi  work  li  BOW  esDplata,  eauMiag  ct  Urn*  inrlM  «  aumw,  m  (iillawi  i 
FIKSIOOUBSB 

MMhuletf  HrdrotlatlOi  HrdranllcPi  Pneannticii,  Sonnd,  and 
Optic*. 

lBaMlut*Kir>lIlDW.Taliuu,i>f7fiDp*fai,irIUi  tU  Dlutntloiu. 
8KXn4]>  OODBSB. 

HcM,  Mat*eti*att  Common  Eloetriclty,  and  Tottaic  Eteelricity. 

In  0B4  Tolua*,  nj*!  lino.,  of  UO  pagu.  irKb  3*t  UlnMntioiu, 
THIRD  C0UB8&. 

Ailrouowr  and  npteorologr. 

Im  OB*  folou,  njal  l2mD.,  of  umtij  BOO  pagHi  with  S?  pUtH  uid  oto  300  lUuibAlloiu 


TIhh  TotinnM  can  br  Ii>d  dthsr 


lA-  tapuat«lr  or  In  unUbrin  istf,  oiulmlnlniE  Ln  111  i 
onatiioiuiiDdninil»iloni,oiiwDaduii)itMt.    Toi 
VOOM*  llua*  WHO  ooon  ■ep*ru*  tmtlvs  on  the  l«*dlTi|t  drpHTtmcutA  of  Nfelun]  Pli 
phj,  tha  tint  Oram  nuj  ■!»  ha  had  dlTldod  la  thna  pDrUDDa,  ai  fbllowi : 
rut  I^-KXOHAinOB. 
«  IL— HTSBOSTATIOB,  HYDBADLIOS,  PtfECUATICa,  u>  SOUND. 

•■iii/-opncs. 

It  wm  thu  tn  mh  that  tfab  miTk  tanliha  •llhrr  a  ooDplFla  mm 
thwa  niljacla,  or  atpinta  tTaaUrca  on  all  tbi  dUtanot  hraDcbn  of  Nalnnl  Bdtni 

Ooaof  thatHit  poffllaraciaBLiNi  wgckaihat  luarMappaarti!. — EmrtiakJeurwal  af  EdwM 


^tafnil fcboir  <o  ba'a.  rnm  inch  a •'•"bi.  cnmplau  wdanUtlq  minDili.  Thna  hii 
wiIGmi  iZnU  Battataatical  diUila.   WMIaUiwdiMBWiirpaii  Iba  J^  forThiicau 

1hli<I&^Aa>t,-lhaD,iiahiiiHataMiIlantaaiirKlaiiUllcInaTalnn.  KiiiiMth 
iaaiim  tt  ■  wm  who  baa  baao  AlnBtnK  Iba  anifcer  af  Iba  pool,  aad  Kanrini  ibi  ban 
■laat.  bn  tba  uiUnd  ptadHUea  af  an  aeoinnliabad  aaaibaaaucliB.  wbo  lua  denitHl  h 
andr  af  abi^iw.  wha  baa  anatad  bWi  aid  dind  daah  wbo  haa  UaTanad  iba  nmb  plic 
iSmiJSft^  than  wban  Ibaia  saa  ba  na  mfa  iH  man  JattlUiaal  faUa  Uinai  thi 


u 


JS5S- 


THIBD   CO&-asE.' 
HKTKOROLOGY— ASyijoirdM?;.. 


WITH  THIBTT-9EVBH  PLATK9,  AND  UPWAEDfl  0»  TWO 
HinrDRKD  ILLDSTRATIONS  OH  WOOD. 


PHILADELPHIA: 
BLANCHARD    AND    LEA. 

1858. 


PDELIc'liBRARY- 

I        TILO--.N    F     ■J.JOill-J*  { 


EDt«r«d,  Moordiag  to  Aot  of  CoDgnsa,  In  the  jMr  1864,  hj 

BLAHOHABD  AND  LEA, 

In  tlw  Clark'a  OffiM  of  the  IMatriot  Conrt  of  the  Uoited  State*  for  lh« 

Eastern  Dialriet  of  PeniiBjlTuiU. 


AMERICAN  PUBLISHERS'  NOTICE. 

In  reproduciog,  in  this  oonntiy,  the  ^'  I^hird  Course"  of  this 
excellent  Hand-book  of  Natural  Philosopht  and  Astronomy, 
cue  has  been  taken  to  oorreet.Bach  errors  as  had  escaped  the  atten- 
tion of  the  Author.  Additions  have  also  been  made  wherever  they 
appeared  necessary,  either  to  the  foller  elucidation  of  the  subject, 
or  to  bring  it  completely  on  a  level  with  the  existing  state  of  science. 

PnLADix<p»A|  Jamnmj,  1854. 


(») 


AUTHOR'S  PREFACE. 


To  SQpply  the  meaDs  of  aoquiring  a  competent  knowledge  of  the 
methods  and  results  of  the  physical  sciences,  without  any  unusual 
acquaintance  with  mathematics,  has  heen  the  purpose  of  the  Author 
in  the  composition  of  this  series  of  treatises.  The  methods  of  de- 
monstration and  illustration  have  heen  adopted  with  this  view.  It 
is,  however,  neither  possible  nor  desirable  invariably  to  exclude  the 
use  of  mathematical  nfmhoU. 

Some  of  these,  expressing  mere  arithmetical  operations  effected 
upon  numbers,  are  easily  understood  by  all  persons  to  whom  such  a 
work  as  the  present  is  addressed,  and,  as  they  express  in  many  cases 
the  relations  of  quantities  and  t|ie  laws  which  govern  them  with 
greater  brevity  and  clearness  than  ordinary  language,  to  exclude  the 
use  of  them  altogether  would  be  to  deprive  the  reader  of  one  of 
the  most  powerful  aids  to  the  comprehension  of  the  laws  of  nature. 

Nevertheless  such  symbols  are  used  sparingly,  and  never  without 
ample  explanation  of  their  signification.  The  principles  of  the 
sciences  are  in  the  main  developed  and  demonstrated  in  ordinary  and 
popular  language.  The  series  has  been  compiled  with  the  view  of 
affording  that  amount  of  information  on  the  several  subjects  com- 
prised in  it  which  is  demanded  by  the  student  in  law  and  in  medi- 
cine, by  the  engineer  and  artisan,  by  the  superior  classes  in  schools, 
and  by  those  who,  having  already  entered  on  the  active  business  of 
Hfe,  are  still  desirous  to  sustain  and  extend  their  knowledge  of  the 
general  truths  of  physics,  and  of  those  laws  by  which  the  order  and 
stability  of  the  material  world  are  maintained. 

It  18  well  known  ihat  msmy  Btadenta  who  enter  the  XJniverevticB 

/a:  1  (vii*) 


TIU  PREFACB. 

pass  through  them  without  aoquiring  even  so  much  as  a  superficial 
knowledge  of  geometry  and  algebra.  To  all  such  persons  mathe- 
matical treatises  on  physics  and  astronomy  must  be  sealed  books. 
They  may,  however,  by  these  volumes  acquire  with  great  facility  a 
considerable  acquaintance  with  these  sciences ;  and  although  such 
knowledge  be  not  in  all  cases  based  on  rigorous  mathematical  de- 
monstratiou;  it  is  founded  on  reasoning  sufficiently  satisfactory  and 
conclusive. 

Great  pains  have  been  taken  to  render  the  present  series  complete 
in  all  respects,  and  as  nearly  co-eztensive  with  the  actual  state  of 
the  sciences  as  the  objects  to  which  it  is  directed  admit.  Each  of 
the  classes  of  readers  for  whose  more  especial  use  it  is  designed 
will  doubtless  find  in  it  something  which,  for  their  purpose,  is  su- 
perfluous ;  but  it  must  be  considered  that  the  parts  which  are  thus 
superfluous  for  one  are  precisely  those  which  are  most  essential  for 
another.  It  is  hoped  that  no  student  will  find  that  anything  im- 
portant for  his  objects  has  been  omitted. 

The  rapid  succession  of  discoveries  by  which  astronomy  has  of 
late  years  been  extended,  has  rendered  elementary  works  in  that 
science  previously  published  to  a  certain  extent  obsolete,  while  the 
increasing  taste  for  its  cultivation  and  the  multiplication  of  private 
observatories  and  amateur  observers,  have  created  a  demand  for 
treatises  upon  it  which,  without  being  less  elementary  in  their  style, 
shall  comprise  a  greater  amount  of  that  vast  mass  of  knowledge 
which  has  hitherto  been  shut  up  in  the  transactions  of  learned  socie- 
ties and  other  forms  of  publication  equally  inaccessible  to  the 
student  and  aspirant. 

'A  large  space  has  therefore  been  assigned  to  this  science  in  the 
present  series.  The  results  of  the  researches  of  original  inquirers 
and  of  the  labour  of  observers  have  been  carefully  reviewed,  and 
large  selections  made  from  them  are  now  for  the  first  time  presented 
to  the  student  in  an  elementary  form.  In  cases  where  the  subject 
required  for  its  better  elucidation  graphic  illustrations,  and  where 
such  representations  could  be  obtained  from  original  and  authentic 
sources,  they  have  been  unsparingly  supplied. 

As  examples  of  this,  we  may  refer  among  the  planetary  objects 
to  the  beautiful  delineations  of  the  Moon  and  Mars  by  MM.  Beer 
and  Madler,  those  of  Jupiter  by  MM.  Madler  and  ^frschcl,  and 


PBSVAOB.  ix 

Uion  of  SatoiB  by  MM.  Dawes  and  Schmidt;  among  cometary 
ulgecto  to  the  magnificent  drawings  of  Enckes  comet  by  Strove, 
and  thofie  of  Halley's  comet  by  MM.  Struve,  Maclear,  and  Smith ; 
and  among  stellar  objects  to  the  splendid  selection  of  stellar  clusters 
and  nebalss  which  are  reproduced  from  the  originals  of  the  Earl  of 
Kosse  and  Sir  John  HersoheL  In  fine^  among  the  illustrations 
now  produced  for  the  first  time  in  an  elementary  work,  the  remark- 
able drawings  of  solar  spots  by  Pastorff  and  Capocci  ought  not  to 
be  paned  without  notice. 

To  have  entered  into  the  details  of  the  business  of  the  observa- 
tory,  beyond  those  explanations  which  are  necessary  and  sufficient 
to  ^ve  the  reader  a  general  notion  of  the  processes  by  which  the 
principal  astronomical  data  are  obtained,  would  not  have  been  com- 
patible with  the  popular  character  and  limited  dimensions  of  such 
a  treatise  as  the  present 

It  has,  nevertheless,  been  thought  advisable  to  append  to  this 
volume  a  short  notice  of  the  most  remarkable  instruments  of  ob- 
servation, accompanied  by  well  executed  drawings  of  them,  the 
ori^nals  for  some  of  which  have  been  either  supplied  by  or  made 
under  the  superintendence  of  the  eminent  astronomers  under  whose 
direction  the  instruments  are  placed. 

In  the  composition  of  this  part  of  the  series,  it  has  been  the 
good  fortune  of  the  author  to  detect  several  errors  of  considerable 
importance  which  have  been  hitherto  almost  universally  disseminated 
in  elementary  works  and  under  the  authority  of  the  most  eminent 
names.  Several  examples  of  this  will  be  noticed  by  the  reader, 
among  which  we  may  refer  more  particularly  to  the  Uranograpby 
of  Saturn,  a  subject  which  has  been  hitherto  completely  misappre- 
hended, phenomena  being  described  as  manifested  on  that  planet 
which  are  demonstrably  impossible.*  The  correction  of  other  errors 
less  striking,  though  of  great  scientific  importance,  will  be  found  in 
the  chapter  on  Perturbations,  and  in  other  parts  of  the  treatise. 

This  series  of  elementary  treatises  consists  of  three  courses,  which 
are  saleable  separately,  and  are  as  independent  each  of  the  others  as 
the  nature  of  the  subject  allows. 

•  See  a  Memoir,  by  the  Author,  on  the  Uranography  of  Saturn,  in  Vol. 
UJL  of  the  Memoirs  of  the  Royal  Astronomical  Society,  London,  Sept. 
1868. 


X  PBEFAOB. 

The  first  course  consists  of  Mechanics — ^HydroetatioB — ^Hydraulics 
^-Pneumatics — Sound  and  Optics ;  the  second  of  Heat — dommon 
Electricity — Magnetism  and  Voltaic  Electricity;  and  the  third  of 
Meteorology  and  Astronomy. 

The  Index  which  is  given  in  the  present  volume;  and  which  will 
be  found  extremely  copious  and  useful  for  the  puposes  of  general 
reference,  is  intended  to  serve  in  common  for  all  the  three  courses. 
The  references  in  it  are  made  to  the  numbers  of  the  paragraphsi 
and  not  to  those  of  the  pages,  and  it  will  be  found  convenient  to 
observe  that  the  first  paragraph  of  the  second  course  is  1304,  and 
that  of  the  third  2160.  The  paragraphs  being  numbered  continii- 
ously  throughout  the  three  courses,  it  has  not  been  necessary  in  the 
Index  to  make  any  reference  to  the  courses  or  volumes. 

It  will  be  found  that  this  Index^  combined  with  the  analy&dl 
Table  of  Contents,  will  give  to  the  entire  series  all  the  usefhlneai 
of  a  compendious  Encyclopssdia  of  Natural  Philosophy  -and  Aa- 
tronomy. 


TABLE  OF  CONTENTS 


THIRD  COURSE. 


BOOK   I. 


METXOROLOOT. 


CHAP.  L 


ns»   iBvofldeo^  of  tiiennal  ohBtrttt 


P^^ 


25 

Local  Twialioiu  oftempenitiirt ...  26 
Ofumal  tbermometrie  period ......  S0 

Anniul  tbennoroetrie  period 20 

Meon  diomal  tempermtnre 26 

Meon  tempentore  <tf  the  month  »  27 
Mean  tempermtore  of  the  year  .....  27 
Mcmth  of  meao  temperature  .......  27 


leothermal  lines 28 

iK^hermal  lonee  ^ 28 

The  first  thermal  or  torrid  aono ...  29 

Thermal  equator 29 

The  Moond  thermal  lone  ............  29 

The  thhd  thomal  sone 29 

The  fourth  thermal  sone  ............  29 

The  fifth  Uiermal  tone 80 

The  sixth  thermal  sone 80 

The  polar  regions 80 

Climat«  ▼aries  on  the  same  isother- 
mal line 80 

S179.  Cocutant,  Tariahle,  and  extreme 

cHmatf 80 

Kxamples  of  the  dassffloatlon  of 

dimatet 80 

CUmatologleal  oonditSons 81 

2193.  Table  of  Paris  temperatures 81 

2288.  Extreme   temperature   in   torrid 

sone 82 

Sxtreme  tnnperature  in  polar  r»* 

rkms... 82 

'Ae  Tarlatlon  of  the  temperature 
depending  on  the  deration  of  the 

obeerrer  abore  lerel  of  sea 82 

2185.  XleTatfcm  of  the  limit  of  perpetual 


2109. 
2170. 
ATI. 
2172. 
2173. 
2174. 
2175. 
2176. 
2176. 

2in. 

2178, 


S180. 
21 SL 


2184. 
S185. 


83 
2I«L  Conditions  which  alfect  it 83 

2187.  Table  of  heights  of  snow  line  *ob- 

eerred 83 

2188.  Further  results  of  Humboldt's  and 

Pentland's  researches 84 

21tt.  Thermal   phenomena   below   the 

snrftee 35 

2190.  Stratum  of  inTariable  temperature  35 
Sm.  Its  depth  Taries  with  the  latitude  35 
2191  ludqpth  and  temperature  at  Paris  36 
tm.  lUteB... 86 


2191 


2196. 

210A. 
2197. 

2197. 

2198. 
2199. 
2200. 

2201. 


2202. 

2208. 

2204. 

2205. 
2206. 

2207. 

2208. 
2209. 
2210. 

2211. 
2212. 
2213. 
2214. 

2215. 

2216. 

2217. 


2218. 
2219. 


2220. 


Page 
IlMnBal  phenomena  between  the 
sttrihee  and  the  stratum  of  inva- 

riahle  temperature 36 

Thermal  phenomena  bdow  the 
stratum  of  nnii>tm  temperature  87 

Tanperatnre(rfq>rings 37 

Thennal  eondition  (rf  ssas   and 

lakes 38 

Temperature  and  congelation  of 

rivers 3'.> 

Thermal  eondition  of  a  frosen  sea  iO 

Process  of  thawing 40 

Depth  of  stratum  of  constant  tem- 
perature In  oceans  and  Mas 41 

SITect  of  superficial  agitation  of 
the  sea  extends  to  only  a  small 

depth  « 41 

DestmetiTe  efEscts  whidilwould  be 
produced  if  water  had  not  a  point 
of  maximum  density  above  it« 

point  of  congelation 41 

variations  of  the  temperature  at 

sea  and  on  land 42 

Interchange  of  equatorial  and  po- 
lar waters 42 

Polar  ice 43 

Extent  and  character  of  the  ice 

IMdB 43 

Production  of  Ice-bergs  by  their 

fi'aeture 43 

Their  forms  and  magnitude 44 

Sunken  ice-bergs  44 

Angular  effects  of  thtdr  superficial 

fusion 44 

Depth  of  polar  seas 44 

Cold  of  the  polar  regions 45 

Solar  and  celestial  heat 45 

Quantity  of  beat  emitted  by  the 

sun 46 

Solar  heat  at  the  earth  would  melt  a 

nhetl  of  ioe  100  feet  thick  in  a  year  47 
Calculation  of  the  actual  quantity 

of  hcnt  emitted  by  the  sun 47 

lleat  at  sun's  surftoe  seven  times 
an  intense  as  that  of  a  blast  fur- 

nsce 47 

Temperature  of  the  celestial  spaces  47 
Heat  received  by  earth  from  celes- 
tial spare  would  melt  in  a  year 

85  ft»et  thick  of  ice -  48 

Summary  of  thermal  effects ~  49 

(xl) 


Xll 


C0NTBNT8. 


CHAP.  n. 

TKI  AIB  AMD   AtMOCPBBIO  TAPOUU. 

VHJb 

222L  Perfodieal  diaasgM  in   the  stmo- 

•pberio  preMuiv 40 

2222.  Mesa  anniul  height  of  bsronMter  49 

2223.  Sffeet  of  windB  on  the  bezometzio 

oolnmn 60 

2224.  IMamal  TmrUtkmi  of  the  baro- 

meter ~ 60 

2226.  The  winds 60 

2226w  Wind*  by  eompreaiion  and  rare* 

fMstion 60 

2227.  Effect  of  sodden  eondeneation  of 

▼aponr 61 

2228.  Hurricanes — 62 

2229.  The  probable  caxues  explained  .....  62 

2230.  Water  sponts  and  land  spoots 68 

228L  BraporaUon  ttom  the  surftceof 

water.. 68 

2282.  Air  may  be  saturated  with  Taponr  64 
2238.  If  the  temperatore  of  saturated  air 

ftll,  oondensatSon  will  take  place  64 

2284.  Atmosphere  rarely  satorated 64 

2286.  May  become  SO  by  reduced  tempe- 

pawtare  or  intermingling  strata  64 
228<li.  Air  and  Taponr  intermingle  though 
of  different  spedfle  grarlties 66 

2237.  The  preraore  of  air  retards  but 

does  not  diminish  eraporalion  ...  66 

2238.  When  Taponr  intermixes  with  air 

it  renders  it  specifically  lighter ...  66 


2239. 
2240. 
2241. 


2242. 

2243. 
2244. 

2246. 
2240. 
2247. 
8247. 

2248. 
2249. 
2260. 
2251. 
2262. 
2268. 


CHAP.  m. 

BTaROMRBT. 

Hygrometry 66 

The  dew  point 66 

Method  of  determining  the  pres- 
sure and  deniity  of  the.Tsponr 

suspended  in  the  air  ...m.^ 66 

Table  of  pressures  and  densities  of 

saturanng  rapours 57 

Example  of  such  a  calculation  .....  58 
Method  of  ascertaining  the  dew 

point 69 

Daniel's  hygrometer » 69 

August's  psfchrometer 60 

Saussure's  hygrometer 00 

General  consideration  of  hygrome- 
ters   61 

Sew M.  66 

Hoarfrost 68 

Fabrication  of  ice  in  hot  climates  68 

Fogs  and  douds 69 

Rain 70 

Bain-guage 70 


2264.  Quantity  of  rain  ftUSiif  la  railoas 

22(5w  Snow  ••••••••■•••••m** ••• ••••••  Tl 

2256l  Hafl  - Tl 

2267.  The  phenomena  attending   liaU> 

stones  .......................... .....M.M  i8 

2268.  Extraordinary  examples  of  hail- 

stones  M -  T4 

2268.  Disastrous   hailstorm  In   Prases 

and  Holland  in  1788  ..~ 76 


CHAP.  IV. 
ATMOSPHIXIO  XLSCTuarr. 


with 


2269.  The  air  generally  diarged 

poeitiTe  tltcMdtj 

2200.  This  state  sul^jeet  to  variation* 
and  exceptions 

2261.  Diurnal  TariatloDS  of  eleetrieal  fat- 

tensity  ~. 

2262.  Obserrations  of  Quetolet ...~.. 

2263.  Irregular  and  local  Tariati<ms  and 

exceptions.. ~ 

2264.  Methods  of  obserring  atmoqthflrio 

electricity  «... ~* 

2266.  Methods  of  ascertaining  the  elee- 
trieal condition  of  the  hli^ier 
strata ~ ».... 

2266.  Bemarkable  experiments  of  Ro- 

mans, 1757 

2267.  Electrical  diarge  of  doud  Tarles  ... 

2268.  Thunder  and  lightnings 

2260.  Form  and  extent  of  the  ilash  of 

lightning 

2270.  Causes  of  the  rolling  of  thunder 

2271.  Affected  by  the  sigsag  ftmn  of  the 

lightning 

2272.  Affected  by  the  TaiyingdlatanBe  of 

different  parts  of  the  flash  v— — 
2278.  Affected  by  edio  and  interlSnvDea 
2274.  Indnetire  action  of  douds  on  the 

earth 

2276.  Formation  of  fulgurites  explained 
2276.  Accidents  of  the  surfiice  whidi  at- 
tract lightning  .'. ~ » 

Ughtaing  follows  oondoctora  hf 
prrftoence.  —  Its  effiBots  on  build- 
ings   ....•• ....M.... M... 

2278.  Conductors  or  paratonnerres  Ibr 

the  protection  of  buildings  ......... 

2279.  Effects  of  lightning  on  bodies  whidi 

it  strikes 

2280.  The  Aurora  Borealls.  —  The  phe- 

nomenon unexplained 

22H1.  General  character  of  the  meteor ... 
2282.  Description  of  aurora  seen  in  the 

polar  regions  by  M.  Lottin 


n 
n 

re 

7« 
77 

n 

n 
n 

78 
79 

78 
79 


81 
81 

81 

81 


2277. 


n 

85 
86 


BOOK   II. 


ASTBONOMT. 


CHAP.  I. 


or  nrrwrioAnoir  ahd  muss  or 
oanBTAsnoN. 
8«st  Page 

2888.  The  solar  system 92 

SB84.  The  stellar  uaiTorse 92 


Sect  Page 

2285.  Sul^ect  of  Astronomy. — Origia  of 

the  name  - 92 

2286.  It  treats  of  inaooeaslble  ol«)eeti 98 

2287.  Hence  arise  peculiar  methods  of 

investigation  and  peculiar  iastm* 
meatsofobserya.ioa 93 


C0NTBNT8. 


••• 

XIU 


twi. 


2310. 


Page 
«Dd  bauing  of  Tbible 

Th0j  rapply  the  mMiit  of  tmeet' 
taJwing  tb«  dtoteaew  and  poai- 
tflona  dTlnaeoeHibto  oU«eta OS 

Angular  magnitude  —  fta  lmpor> 

DlTisioti  of  tba  drde.— Its  nonen- 
datare ~ - ^    M 

RoIsUto  magnitnda  of  aica  of  1^ 
VV  and  the  radiaa 94 

nie  Unaar  and  apgnlar  Taloe  of 
an  are ~ 86 

or  tba  thrao  ft)Uowing  qnantitiei. 
— Tb«  linear  value  of  an  are,  its 
angnlarTalue,  and  the  length  of 
the  radlna. — Any  tvo  being  giT- 
en,  the  third  maj  be  computed.    06 

The  are^  the  eofd,  and  the  dne^ 
may  be  eonddered  as  equal  when 
the  angle  le  email -    06 

Tb  aeeCTtain  the  dietance  of  an 
InarweilWe  oljeet  from  two  ao- 
emrible  etatione ^    06 

Gaae  in  whieh  the  dirtanee  of  an 
ol^feet  ie  great  relatiTely  to  the 
dletanee  between  the  aUUione....    07 

IHren,  the  apparent  dletanee  be- 
tween two  dietant  otdeeta,  ench 
dietanee  being  at  right  angles, 
or  nearly  so,  to  their  tIsusI  di- 
reetions,  and  their  distance  from 
the  oheerrer,  to  find  the  actual 
distance  between  than 06 

Oiren,  the  apparent  diameter  of 
a  spherical  o^eet,  and  its  die- 
tanee from  the  obeerrer,  to  find 
its  real  diameter 06 

Methods  of  ascertaining  the  direc- 
tion of  a  visible  and  distant  ob- 
j^^  ....^ 08 

Use  of  *iiit»!^!"!!!!!J!..*.L*!!!!l*.*'"."  o6 

AppUeatton  of  the  tdcsoope  to  in> 
dicate  the  visual  direction  oS  mi- 

crometrio  wirM«>«««.»« •••••*•••••    00 

line  of  ooUimatlon 00 

ApplleatSon  of  tiie  teleeoope  to  a 

graduated  instrument. 00 

Expedients  fbr  meeeuring  the  frac- 
tion of  a  division 101 

By  aTemier 102 

By  a  compound  microecope  and 

mierometric  screw 192 

Obe^rration  and  measnremcot  of 

minate  angles 102 

The  parallel  wire  micrometer 102 

Mmunrement  of  the  appansot  di- 
ameter of  an  object 103 


CHAP.  n. 
TBI  uxinauL  BOTuiroiTT  Ain>  nnczimoHi  or 

THB  lASTB. 

2311.  The  earth  a  station  from  which 

the  universe  is  observed 103 

2312L  Neeessarr  to  ascertain  its  fonai 

dimensions,  and  motions 104 

2813.  Form  globular 104 

S14  This  conclusion  corroborated  by 

dreumnavigation 106 

BU.  OoRoborated  by  lunar  edipees....  100 


Beet  Page 

2310.  Various    eObets    indicating    the 

earth's  rotundity 106 

2317.  Dimensions  of  the  earth.— Method 

of  measuring  a  degree 107 

281S.  Length  of  a  degree 108 

2810.  Length  of  a  second  of  the  earth ..  lOS 

2820.  Change  of  direction  of  plumb-line 
in  passing  over  a  given  distance  108 

2821.  To  find  the  earth's  diameter 108 

Superficial    Inequalities   of    the 

earth  relativdy  insignificant 109 

Relative  dimenrions  <^  the  atmo- 
sphere   110 

If  the  earth  moved,  how  could  its 

motion  be  perceived? Ill 

2825.  Parallax 113 

2326.  Apparent  and  true  place  of  an  ob- 

jwet^Dlumal  parallax 113 

2877.  Horisontal  parallax 114 

2328.  Given,  the  horisontal  parallax 
and  the  earth's  semiHiiametcr, 
to  compute  the  distance  of  the 
object 115 

CHAP.  m. 
ArrABBfT  roKM  Ain>  motior  or  thx 

FlRMAMIWr. 

2820.  Aspect  of  the  firmament 115 

2330.  The  celestial  hemisphere 115 

2S31.  Horixon  and  senith llu 

Apparent  rotation  of  the  firma- 
ment   116 

2333.  The  pole  star lid 

2884.  Rotation  proved  by  instrumental 

observation 117 

2336.  Exact  direction  of  the  axis  and 

position  of  the  pole 117 

2886.  Eqaatorial  instniment 117 

2337.  Rotation  of  firmament  proved  by 

eqaatorial 110 

2338.  Sidereal  time 120 

2830.  The  same  apparent  motion  ob- 
served by  day 121 

2840.  Certain  fixed  points  and  drrles 
necessary  to  exprass  the  podtion 

of  objects  on  the  heavens 121 

2341.  TerUcal  dreles,  lenltb,  and  nadir  121 
2842.  The  cdeetial  meridian  and  prime 

vertical 122 

2343.  Cardinal  points 122 

2344.  The  azimuth 122 

2345.  Zenith  distance  and  altitude 122 

2346.  Celestial  equator 122 

2847.  Apparent  motion  of  the  celestial 

sphere 123 

CHAP.  IV. 

nXURIIAL  BOTATIOir  OF  TRV  XARTil. 

2848.  Apparent  diurnal  rotation  of  the 

heavens— its  possible  nauvee a24 

2840.  Supposition  of  the  reel  motion  of 

the  universe  inadmiosible 124 

2860.  Simplicity  and    intrinfic  proba- 

bility  of  the  rotation  of  the  earth  125 

2351.  Direct  proofr  of  the  earth's  rota- 
tion  125 

2362.  Proof  by  the  descent  of  a  body 

from  a  great  height 125 

2868.  M.  Leon  Foucault's  mode  of  de- 

BonitmUon \^ 


-■i. 


SS7S.  nrnn  el  Ui 


b7  emtrlfViml  fone,.p..^-'.,w......  T3T 

nri.  Ldh  ot  wnlfbl  U  Dttaar  UUtadM  ua 
an*.  Sfftet  of  BDlrlTaial  fcm  oa  tba 


(HfnpMcal  oBndltloD 
(otAC*  of  (bo  iIoIk..— 


:3n  it>  •iiipttdv' 
zsa.  vupUi/tj  iB*y 


nilpUdl;  alsolikM.... 


CXAT.  ¥L 


t¥tl.  TfaaMBnKHdo.... 


ito 

Mil. 

tbohori- 

m 

Mil. 

Mrtbod  or  obieriiDR 
tloo  or  Uh  »)•  ud 

in  did*  i^iiodtiiu 

.ItltadM 

m 

ttoport- 

IM 

■""ssEsasKSr; 

IM 

MIT.  AppmntpodtionotoalotUlob- 


S«13.  OentnltffKtortliob* 


CONTENTS. 


XT 


CHAP.  Tin. 
Anvil  wmoir  or  tn  BiavB. 


usa. 


Apparent  motion  of  tho  ran  in 
th«  hoovono  ~ "••  '.•'»•:•— 

^Mft  AMRtaln«d  I7  th«  tnnait  bunro* 
mcnt  and  muni  drdo 

M».  The  •dlntlo  «.... 

2490.  The  eqniaoenal 

MSI.  The  vemoi 


Page 


••••••»•••••• 


pointo 
antomnal 


•  •••••«  ••• 


leo 

109 
170 
170 


•qui- 


•  •»•••••••••  —** 


» «•••«•••«  •••  •••  ••••••  •••  ••• 


)l3S.The 

S483.  The  aolBtioM .. 

tl4&4.  Th»  sodiee..... 

24S5.  The  ligne  of  the  lodlao  «........~»' 

jUWb  ThetxoplflB  ~ -^ 

9U7.  Oriartlanotltade  and  kmgitode ... 

«4^*  /^law*!  motion  of  the  earth ~ 

Sm.  MoCkm  of  light  proree  the  annoal 

iBotlcm  of  the  earth - 

S4ML  Iklwi  ntV>n  of  Ught 

J44L  Axgunent  from  analogj 

MiSL  Aff— '*^  paraUaz ••••••• 

24IS.  Iti  eflbete  upon  the  bodlea  of  the 

aolar  «yitcm  apparent .............. 

9Mi.  Bat  errooeoiuly  explained  by  the 

aadenta. — ^Ptolemaic  ^fftem  ..... 

21411^  YaadtM  of  annual  pandlaz  id  the 


170 
171 
171 
171 
172 
172 
172 
172 


174 
174 
170 

in 
in 

177 
177 

179 


MC7. 
IMS. 


179 


.»  179 


180 
182 
182 

183 


Ckwe  memblanee  of  theae  to 

aberration ........... 

Tet  aberration  oanaot  ariae  from 

3U9.  Oeoenl  abeenoe  of  paraUaz  ex- 

plained  by  great  distance 180 

3460.  Ttkt  dinmal  and  annual  pheno- 
mena «cplained  by  the  two  mo- 
tione  of  the  earth 

2151.  Mean  volttr  or  dvil  time 

2152.  Ctril  day— noon  and  midnight ... 
94U.*Dilhrenoe  between  mean  lolar 

and  sidereal  time... 

24M.  DUfcrenee  between  apparent  noon 

end  mean  noon •"•—  JJJ 

2455w  Mean  aolar  time— equation  of  time  iw 
2l5flu  IMatanee  of  the  tun "•...  184 

2467.  linear  Talue  of  T  at  the  ran*a 

dirtanoe "^ 

2468.  Daily  and  hourly  Mparent  mo- 

tion of  the  ran  and  real  motion 

of  the  earth 1^ 

9469.  OrMt  of  the  earth  elllptioal 180 

2100.  Method  of  deecrlbing  •n^UPff—  ,_ 

Ita  toAt  axel,  and  eooentridty  ...  vsi 
2461.  leeentridty  of  the  earth's  orbit ..  187 
2402.  Perihelion  and  aphelion  of  the 

MTth 1» 

24A.  Tariatlona  of  temperature  through 

the  year 188 

24M.  Why  the  longeetday  is  not  al«> 

the  hottest^Oog^ajs 180 

CHAP.  IZ. 


2Mg.  The  moon  an  oldeet  of  popular 

tnterast - 

2IM.  Ita diitanee 

2MT.  linear  Talue  of  l**  on  it 

2MB.  Its  apparent  and  ml  diameter  «. 

2400.  Apparmt  and  real  motion IW 

2«0i  Hourly  motion  apparent  and  real  IW 
2in.  OrMt  tU^MimJ "" 


Seet.  Page 

247i  Moon's  apsidea— apogee  and  peri- 

gee — progreseion  of  the  apsides  194 

2473.  Moon's  nodeo— aaootding  and  de- 

scending node— their  retrogres- 
sion   1<»5 

2474.  RoUtion  on  its  axis 1V*6 

2475.  Inclination  of  axis  of  rotation i9o 

2476*  Librationin  latitude -  1»6 

2477.  Llbration  in  longitude -  10« 

2478.  Diurnal  libration Jw 

2479.  Phases  of  the  moon  ■•  1»7 

2480.  Synodic  period  or  common  month  j8» 

2481.  Mass  and  density  JW 

24S2.  No  air  upon  the  moon iv« 

2483.  Absence  of  air  indicated  *V  »*>" 

sence  of  refraction  ~ ...•..••  ^ 

2484.  Moonlight  not  sensibly  calorific  202 
2386.  No  liquids  on  the  moon 202 

2486.  Absence  of  air  deprives  solar  Ught 

and  beat  of  their  utUity  203 

2487.  As  seen  from  the  moon^ppearance 

of  the  earth  and  the  flrmament  204 

2488.  Why  the  fOll  disk  of  the  moon  is 

&intly  visible  at  new  moon 205 

2189.  Physical  condition  of  the  moon's 

surftce  ;•  205 

2490.  General  deeeription  of  the  moon  s 
surface  » ^08 

2491.  ObeerrationsofHerscbel 213 

2492.  Obeerrations  of  the  Earl  of  Uosse  i\i 
2193.  Suppoeed  Influence  of  the  moon 

on  the  weather 213 

2401.  Other  supposed  lunar  influences  2i5 
2496.  The  red  moon ..•.. ^VJ 

2496.  Supposd  influence  on  timber iSio 

2497.  Supposed  lunar  influence  on  Teg»- 
tables  « ;■  — 

2498.  Supposed  lunar  influence  on  wine- 
making  •••• 

2499.  Supposed  lunar  influence  on  toe 
complexion 

2600.  Supposed  lunar  influence  on  pu- 
trefiiction  —  supposed  lunar  in- 
flucnce  on  shell-flsh  21i 

2801.  Supposed  lunar  influence  on  the 

marrow  of  animals 218 

2502.  Supposed  lunar  Influence  00  the 
weight  ofthe  human  body  ....^.  2lS 

2503.  Supposed  lunar  influence  on  births  -ii» 

2504.  Supposed  lunar  influence  on  in- 
oubation  ^^ 

2606.  Supposed  lunar  influence  on  men- 
tal derangement  and  other  bu- 

manmaladiee ;•— ••'v 'a 

2506.  Examples  produced  by  Paber  and 

Remauini • ••• ^^ 

2607.  Examples  of  Vallisnleri  and  Bacon  220 
2506.  Supposed  influence  on  cutaneous 

affections :v""*:"v""CT«*r 

2600.  Bemarkableoaje  adduced  by  Hoff- 
man   ; 

2510.  Cases  of  nerrous  diseases .— 

2611.  Obeerrations  of  Dr.  Gibers  on  In- 

eane  paUents '''"Z""^»i"'^ll 

2812.  Influence  not  to  be  hastily  re- 

Jected ^^ 


216 
217 
217 


220 

221 
221 


192 
102 
198 
198 


CHAP.  X. 

THI  »n>M  AHl)  TEADX  wnn)8. 

2618.  Correspondence  between  the  re- 
Wenoe  of  the  tides,  and  ttioA*- 
nniAl  appearanoa  of  tht  mooti  xa 


XVI    . 


OONTEVia. 


Page 
2614.  Xnonaom  notioni  of  the  lunar 

Infltttnoe  ~ 223 

2516.  The  moon's  attraction  alone  wiU 

not  explain  the  tidee 223 

2610.  Tides  caused  by  the  difference  of 

the  attraction  on  different  parts 

the  earth 234 

8517.  Effects  of  sun's  attracUon 226 

2518.  Cause  of  spring  and  neap  tides  ...  226 

2519.  Why  the  tides  are  not  produced 

directly  under  moon  227 

2620.  PriminR  and  laiqcing  of  the  tides  227 
2521.  Kenearches  of  Whewell  and  Lub- 
bock   227 

2622.  Vulgar  and  corrected  establish- 

ment   228 

2623.  IMunuU  inequality 228 

2624.  Loral  effects  of  the  land  upon  the 

tides 228 

2626.  Velocity  of  tidal  wave 228 

2520.  lUnge  of  the  tides 220 

2627.  Tides  affected  by  the  atmosphere  230 

2628.  The  trade  winds  „ 230 

CHAP.  XI. 

THE  SOX. 

2629.  Apparent  and  real  mafrnitude  ....  233 

2630.  Magnitude  of  the  sun  illustrated  233 

2631.  Bur&oe  and  rolume 234 

2632.  Its  mass  and  density 234 

2688.  Form  and  rotation — axis  of  rotar 

tion 234 

2634.  Bpots 235 

2685.  Cause  of  the  spots— physical  state 

of  the  sun's  surfiftce  ~  236 

2686.  Sun  invested  by  two  atmospheres, 

one  luminous  and  the  other  non* 
luminous 237 

2687.  Bpots  may  not  be  black  237 

2638.  Spots  Taziable -  237 

8639.  Prevail  generally  in  two  parallel 

sones  .M 238 

2640.  Obserrations  and  drawings  of  BI. 

Capood  238 

2541.  Obserrations  and  drawings  of  Dr. 

Pastorffinl826 239 

2642.  Obserrations   and   drawings   of 

Pastorff  in  182H 239 

8643.  Obserrations  of  Sir  John  Herachel 

in  1837  241 

8644.  Boundary  of  ftingos  distinctly  de- 

fined    241 

8646.  Solar  fitcules  and  lucnles 241 

8640.  Inoandeeoent  coating  of  sun  gase- 

ous    242 

2547.  Test  of  this  proposed  by  Arago  ...  242 

2648.  Its  result 242 

2649.  The  sun  probably  inrested  with  a 

douUe  gaseous  coating ~  243 

8660.  A  Uiird  gaseous  atmosphere  pro- 

bable ..!. 243 

8661.  Its  existenoe  indicated  by  solar 

eclipses 244 

8662.  Sir  John  Ilerscbcl's   hypothesis 

to  explain  the  solar  spots 244 

8663.  Calorific  power  of  solar  rays 246 

3664.  Pmbable  physical  cause  of  solar 

heat -.  246 

CHAP.  xn. 

nne  aoLAK  srsmi. 

8656.  Perception  of  the  motion  and  po- 
sition of  surrounding  olgects  de- 


8560. 

2667. 
2558. 

2669. 
2600. 

260L 


2602. 

2603. 
2604. 
2505. 
2600. 

2507. 

2508. 

2609. 
2570. 

2571. 
2572. 
2573. 
2574. 
2575. 
2570. 
2677. 

2678. 

2579. 
2680. 

2681. 
2682. 

2583. 
2684. 

2685. 


2586. 
2587. 

2688. 

25ft9. 
2590. 

2501. 


2692. 
2698. 

2594. 
2506. 
2590. 
2697. 

2598. 

8509. 

8000. 


pcfDfdi  upon  tha  ■taUon  of  11m 
obserrsF ...... •...~>........*M..M«.«»  an 

Peculiar  difflenltisapreientad  bj 

the  solar  systein ~ —  MT 

Two  metliods  of  exporitkm MS 

General  arrangement  of  bodka 
eompodng  the  solar  syiteoi  ...^  Sll 
Planets  primary  and  seeondaiy^  Ml 
Primary  carry  with  tbam  the  i^ 

oondary  round  tha  sun ~..  Stf 

Planetary  motions  to  be  first  n-      . 

garded  as  dreular,  unllbrm,  and       1 

in  a  common  plane ~«  Ml 

This  method  fidlows  the  order  of 

discovery -»  Ml 

Inferior  and  superior  plaiwta....^  Ml 

Periods ...—>  91 

Synodic  motion .»«  Ml 

Geocentric  and  hellooentrle  bkh 

tiens M >.  Ml 

Heliocentric     motion    dedudUa 

flt>m  geooentrie —  Ml 

Relation  between  the  dally  h«Ho- 

centrlc  motion  and  the  period  ^  SH 

I^ily  synodic  motion....^ «.  Ml 

Relation  between  the  synodic  mo- 
tion and  the  period 261 

Elongation ~  261 

Conjunction Ml 

Opposition —  Ml 

Quadrature 

Synodic  period 

Inferior  and  superior  ooqjunctfcm 
Relation    between    the   perlodio 

time  and  the  synodio  period 

The  apparent  motion  of  an  infl»> 

rior  planet Ml 

Direct  and  retrograde  motion..... 
Apparent  motion  as  prqjeeted  on 

theediptio 

Origin  of  the  term  *<  planet**..^.. 
Apparent  motion  of  a  superior 

planet 

Direct  and  retrograde  motion...... 

Apparent  motion  prqjected  on  tha 

ecliptic .- 

Conditions  under  which  a  planet 

is  visible  in  the  absence  of  the 

sun 201 

Morning  and  evening  star 881 

Appearance  of  superior  planets  at 

various  elongations 201 

To  find  the  periodic  time  of  the 

planet 2tt 

l^.  By  means  ofthe  synodic  period  268 
2°.  By  observing  the  transit  thro^ 

the  nodes ~ 

3P.  Br  comparing  oppositions  or 

oonjunctions  having  the  sama 

sidereal  plane .- 

4^'.  By  the  daily  angular  motion.. 
To  find  the  distances  ofthe  planets 

from  the  sun 20 

Phases  of  a  planet 26S 

Phases  of  an  inferior  planet 206 

Phases  of  a  superior  planet.........  206 

The  planets  are  suluect  to  a  cen- 
tral attraction 266 

What  is  the  centre  to  which  this 

attraction  is  directed? 266 

General  prindplee  of  the  onntre 

of  equal  areas  demonstrated......  806 

Linear,  angulari  and  area!  velo- 

dty 


COKTBNTS. 


XTU 


Puge      Sect. 
9S01.  R«UtSoB   betwwn   u^olar  and  SMO. 

•iwl  TttioeltlM 288 

aaoSL  CsM  of  tb«  motion  of  the  Mrth..  269      9641. 

1808.  Cue  of  tbo  ikUiwU 209      2612. 

MM.  OrhttM  of  the  plmoti  aUipMt 209      2643. 

PeiilMlioB,  aphoUoQ,  niMa  die- 

Uiwe.. 2fl9 

Mmiw  MBd  minor  azli  «Dd  eoom-  9644. 

Mdty  of  ibe  orUt 2T0      9645. 

9Kfl.  AnMm,  aacMnalr »  270 

9S0S.  PtMeofpOTiheUon 971      9646^ 

9609.  ■etntrldtlMof  orUtcimaU 9X1 

9610.  Utm  of  attnotlon  dodncwl  from  9617. 

dUptleorbit « 971 

96U.  The  orbit  mli^t  bo  •  parabola  or  9648. 

bupari)ola.M....M............M.M.....  271      9649. 

ObB&tloBS  which  dotvmtaM  the  2660. 

■pMlea  of  the  orbit 971 

Law  of  gnrritation,  goneral 272 

9814.  Matbod  at  ealcnlatlnf  the  onitral  96(1 

fBrea  bj  the  Taloeitj  and  onrra-  9662. 

tmw 272 

181ft.  Law  of  graTttatlon  thown  in  tlie 

eaaa  of  the  moon 278 

9816i  Bon'f  attraction  on  planeti  com- 

parad  —  law  of  grarltation  fkil- 

ffiled -  274 

9817.  The  law  (rf  graTltatloD  uniTenal  274 

9818.  Ita  analogy  to  the  general  law  of 

radiating  Inflnenoee 276 

9619.  Not,  howerer.tobe  Identified  with 

them 276 

The  harmonlclaw 275 

FoUiUed  bj  the  planeti.— Method 

of  eompnting  the  dictanoe  of  a 

planet  from  the  ran,  when  its 

jparlodle  time  If  known 276 

Harmonic  law  deduced  from  the 

law  of  graritatfam 277 

Kepler's  laws 277 

9684.  Inclination  of  the  orbits—  nodes  278 
Nodes  ascending  and  descending  278 

The  Bodiae 278 

Methods  of  determining  a  planet's 

distance  flrom  the  enn 278 

l^.  Bt  theelongation  and  synodic 

BOtMo....^ 278 

99.  By  the  greatest  elongation  for 
an  Inlinlor  planet 278 

9680.  8P.  By  the  greatest  and  least  ap* 
pacrent  magnitudes 279 

9681.  4fi.  By  the  harmonlclaw...... 270 

Tb  determine  the  real  diameters 

and  Tolnmes  of  the  bodies  of  the 
system 279 

Methods  for  determining  the 
msssws  of  tha  bodies  of  the  solar 
system 280 

Method  of  estimatinK  central 
messes  round  which  bodies  r»* 
▼oItc 281 

Method  of  determininp  tha  ratio 
of  the  masses  of  all  plants  which 
haTS  satellites  to  the  mass  of 
the  sun 982 

Tb  determine  the  ratio  of  the  mass 
of  tlie  earth  to  that  of  the  sun..  282 

Tb  determine  the  masses  of  planets 
whidi  have  no  satellites 2S2 

Mass  of  Mars  estimat<Kl  by  its 
attrition  upon  the  earth 283 

Maasaa  of  ITenns  and  Mercarjr.....  283  / 


Page 
Methods  of  determining  the  mass 

of  the  moon 284 

1°.  By  nutation 284 

20.  By  the  tides 284 

3^.  By  the  common    centre   of 

grarity  of  the  moon  and  the 

earth 284 

40.  By  terrestrial  gravity 286 

To  determine  the  masses  of  Uie 

satellites 285 

To  determine  the  densities  of  the 

bodies  of  the  system 285 

The  method  of  determining  the 

superficial  grarity  on  a  body 286 

Superficial  gravity  on  the  sun....  286 
Superficial  gravity  on  the  moon..  286 
Clasriftration  of  the  planets  in 

three  groups.— First  group,  the 

terrestrial  planets 287 

Second  group,  the  planetoids 287 

Third  group,  the  major  planets...  287 


CHAP.  xm. 

YHl  TKRRXSniAL  PLAITXTS. 

L  MncuET. 

9668.  Period 287 

2654.  Heliocentric  and  synodic  motions  288 
9666.  Distance  determined  by  greatest 

elongation 288 

9866.  Bf  the  harmonic  law 288 

2667.  Mean  and  extreme  distances  from 
the  earth 288 

9668.  Scale  of  the  orbit  relatively  to 

that  of  the  earth 289 

2669.  Apparent  motion  of  the  planet...  289 

2660.  Conditions  which  favour  tho  f>b- 

servation  of  an  inferior  planet...  290 

966L  Apparent  diameter — its  mean  and 

extreme  values 291 

2662.  Real  diameter 291 

2668.  Tolume 2'.4 

2664.  Mass  and  density 'JlH 

2665.  Superficial  gravity 2«»2 

2666.  Solar  light  and  heat '2Sri 

2667.  Method  of  ascertaininirthediurDa] 
rotation  of  the  planets 20i 

2668.  Difficulty  of  this  question  in  the 
case  of  Mercury 294 

2669.  Alleged  discovery  of  mountains...  294 

n.  Tnrus 

2670.  Period 295 

2671.  Heliocentric  and  synodic  motions  29.*^ 

2672.  Distance  by  |;^at«)it  elongation...  295 

2673.  By  the  harmonic  law 295 

2674.  Mean  and  extreme  distanecii  frum 
the  sun 295 

2075.  Scale  of  the  orbit  relative  to  that 

of  the  earth 296 

2676.  Apparent  motion 29A 

2677.  Stations  and  retrogression 297 

2678.  Conditions  which  favour  the  (>l>- 
servation  of  Tenus 297 

2679.  Evening  and  morning  star. — Lu- 
cifer and  Hesperus 2^7 

2680.  Apparent  diameter '297 

9681.  Difficulties    attending    the    tol»- 

scupic  observations  of  Vonun....  298 

2682.  Real  diameter 'i'.ws 

30S3,  Mass  and  density 2SM 


COKIENTB. 

."s 


aan.  obHrriUDm  or 

ud  BehrOIw.. 
Mas.  01»mUi!iu  01 


D.  T^^i,." 


aioa.  ssiu  i^t  ud  bait.... 


mi.  fltwnu  ftpd  cUdi 
S71Z.  OliHmtloiu   u 


CHAP.  XIV. 

IHI  PLAllEtOlM. 

,Dt  plan  In  tbe  pluiatuj 


17^,  DlKDTirT  or  tba  othar  planctoMi  SIS 
3IU.  CiUa  aboiring  tha  nnmbar  of 
planatolda  dlaeorarad  bafbre  lut 

lUMditoairrUirirdiscon^. 3U 

fnO.  ThadlM?arjoftli«aeBialnjf  Joa 

irr.  TbriiraiDtrkaMau»Tdaiioa'iritb 

Dr.  Olbar'i  hTpothnii -  SIS 

trSS.  Jbta  ofgnritj  oo  Cb«  pluwtoidi  SIS 


ara 

iln 

HeLlMUitrlc  and  tfliiidic  mo 

lo„ 

wa. 

Balmllie  !«]>  of  Iha  orUta  of  Jn- 

2734. 

ADDOal  panllu  of  Jupiter 
TuUUan  of   dllUnca   thHB 

'Oa 

9738.  lu  prsdlglaiu  ottdUl  Talod^.^.  til 


Z74X.  JnplleriaiB^lcu 

of  Jnpltor  and  U 
Hits.  Sorflice  and  Tolvn 
•BU.  Solar  tlgbl  and  ba 


niD.  MiEIilhlni  pimen  nimuaiT  lo 

■how  tha  (aatuns  of  Iba  dlak—  SM 
97MK  Balla — tbair  anan^Eatnt  and  ap- 

zrtL  iKh  naai  the  polaa  mon  fidat-  IK 


S.  Bolta  not  aeDOEnpbleal  ftatoraa, 

but  atmoflphaild K 

*.  IcItwoplodrairlnpDrjupItarlir 


3IS7.  Jujrit^T'i  aaMIIIM S» 

27A8.  Rapid  cbani^  and  graat  Taiielj 


.  Appatmt   t 


KTS-rhdriBotDBlpart 

rUUoi 

» 

2774.  Muaaa^Mid 

daoalUaaoftl) 

aiatal- 

377fi.  SaparAdat 
me.  Onlrihipd 

p^r 

Vi 

arttai 

CONTENTS. 


bet 

777.  Tmrtatkm  of  ■optriklal  gnritj 

firom  eqnator  to  pol* 

2778.  Dcnatty  moat  ineriaie  from  rar- 

ter^to  emtn...»»««>» .mm>*«>  889 

SnU  UtUlly  oT  tlM  JofTlan  ■ystom  m 

an  moBtCTtloii  of  the  toUr  ^y»tem  310 

n.  Satubv. 


by  the  planet 


354 
866 
857 
357 


860 


302 


..802 


2780.  Beliivului  ijrtwiiii— »«—»»»»— »—««»»««  Mi 
2(7el.  Period.  •....••.••. ....••^••■••••••••••••m  jmx 

270.  HeUoeentrie  motion....,^... ^.  841 

S7tl8.  Synodic  mffttA** 842 

284.  DManoe ^. ^~  842 

2785.  BeietiTe  icmle  of  orbit  and  die- 

tenee  n^w*  the  earth...  m.  .«••••••••  <H^ 

2700L  Annoal  panllaz  of  Saturn 842 

'JJfff.  Oieat  eeele  of  the  orbital  motion  848 

27 88L  DiTMon  of  eynodie  period 343 

rrW.  Ko  phases 848 

2790.  TariatSoos  of  the  planet's  distance 

Ikom  the  earth —  848 

2701.  Stations  and  retrofreesions 844 

2i92.  Apparesit  and  real  diameter 844 

STOS.  Snrfiwe  sod  Tolnme 845 

2704.  Dlnmal  roUtion 845 

2705.  Inclination  oftbe  axis  to  the  orbit  845 
27M.  Satumian  days  and  nights— year  345 

r07.  Belts  and  atmnsphtpre 340 

27«0.  Solar  light  and  heat 340 

27».  KiniDi  - 840 

flOO.  l*osition  of  nodes  of  rings,  and  in- 
clination to  ecliptic 348 

2M)L  Obllqaity  of  ring  to  the  planet's 

orbit  - 848 

2101.  Conditions  which  determine  the 

phases  of  the  ring » 840 

908k  Apparent  and  real  dimenMons  of 

the  rfngs  - 852 

9*04.  ThickncMi  of  the  rings 853 

2Mk&.  IHnminatkm  of  the  rings— helio- 
centric phsses  854 

Shadow  projected  on  the  planet 

by  the  rings  

Shadow  projected 
on  the  rings 

2800.  TIm  shadows  partially  Tiaible  from 
the  earth 

ttOO.  Conditions  under  which  the  ring 
becomes  inTisiblefhim  the  earth 

mo.  SchmidCs  obeerratlons  and  draw- 
ings of  Saturn,  with  the  ring  seen 

edgeways  

2111.  ObMrrationsofHenchel  ~ 361 

2912.  Snppoeed  multiplicity  of  rings ....  301 
2118.  Ring  probably  triple^  —  Obferrsr 

tlons  of  MM.  Lassell  and  Dawes 
2n4.  Bcsearehes  of  Bessel  corroborate 

these  conjectures  ... 
205.  Alleged  dlsoorery  of  obscure  rings 

by  MM.  Lassell  and  Bond 308 

2naL  Drawing  of  the  planet  and  rings, 

as  seen  by  Mr.  Dawes  ...............  808 

2817.  Bewei's  calculation  of  the  mass 

of  the  rings  804 

2818.  BUbility  of  the  rings  - 804 

2810.  Ctase  aalgned  for  this  sUbUity...  304 

28901  Rotation  of  the  rings 366 

282L  Beeentridty  of  the  rings 360 

282L  Arc nmenta  tor  the  stability  found- 
ed on  the  eeoentridty  ~. 360 

pm  SatelUtea 867 

W2L  Their  nomenclature -  887  J 

Ordmr  of  their  diteorMj 3iff 

III  2 


2828.  Their  distanees  and  periods ........  808 

2827.  Harmonic  law  observed  868 

2828.  Blongationsand  relatlTedfaitances  868 
2820.  Tarions  phases  and  appearances 

of  the  satellites,  to  obeenrers  on 

the  planet 369 

2880.  Magnitudes  of  the  satellites (360 

288L  Apparent  magnitudet  as  leen  from 

Saturn 370 

2882.  Horisontal  parallax  of  the  natellitcs  oTU 

2838.  Apparent  magnitudes  of  ifstum 

seen  from  the  satellites 371 

2834.  Satellites  not  risible  in  thedrcum- 

polar  regions  of  the  planet  371 

2836.  Remarkable  relation  between  the 

periods 371 

2880.  Rotation  on  their  axes 371 

2837.  Mass  of  Saturn  872 

2S38.  Dousity 372 

2839.  Superficial  graTity  872 

2840.  Centrifugal  force  at  Saturn's  equa- 

tor    372 

2S4L  Variation  of  grarity  fit>m  equator 

to  pole 373 

2842.  PrcTsiling  errors  respecting  the 

Umnogmphy  of  Saturn 373 

2843.  Tiewsof  i!(ir  Jobn  Ilerschd 374 

2844.  Theory  of  Midler  374 

2845.  Correction  of  the  preceding  Tiews  375 

2846.  rhcnomena  prefiouted  to  an  obMr- 

Tur  stationed  at  Saturn's  equa- 
tor.— Zone  of  the  firmament.ooT- 
ered  by  the  ring  376 

2847.  Solar  evlipfXM  at  Saturn's  equator  377 

2848.  Kclipnefl  of  the  Mat«llite8 377 

2849.  Phenomena  prwcnted  to  an  obrcr^ 

Ter  at  other  Satumian  latituiles  378 

2850.  Bdiies  of  the  rings  seen  at  Tariable 

dif>tanoes  frt)m  ceWnial  equator  378 

2851.  ParallKlR  of  declination  therefore 

intersect  them 378 

2852.  £dges  placiKl  symmetrically  in  re- 

lation to  meridian  end  borixon  379 

2853.  Form  of  the  projection  at  different 

laUtudes 379 

2854.  Rings  InTiiilble  aboTO  lat.  C30  20' 

38"  381 

2855.  Appearance  at  lat  &90  ItSf  25" 381 

2866.  Appearance  at  lat.  SSOsy  20" 381 

2857.  Appearan«atlat470  33'5r' 382 

2858.  Appearance  at  lower  latitudes  ....  382 

2859.  OcculUtions  of  celestial  oloects  by 

the  rings 384 

2860.  Zone  risible  between  the  rings  ...  385 
2801.  Effect  of  the  thickness  of  the  rings 

on  this  tone" ^^ 

2862.  Solar  eclipses  by  the  rings 386 

2868.  Eclipses  of  the  satellites 3^6 

2804.  Sfttumian  seasons  - 387 

in.  USAKUB. 

2866.  Disoorery ^ 

2866.  Period  by  synodic  motion oo» 

2807.  By  the  apparent  motion  in  quad- 

rature JJJ 

2868.  Heliocentric  motions  -  J^J 

2869.  Synodic  motion  8J» 

2870.  DisUnco  ••"—  «* 

2871.  Relatire  orbit  and  distance  from 

the  earth ^ 

2872.  Annual  parallax • 3W 

2ffiS.  \»^  scale  of  the  orbital  molion...  Aw 

mi.  Apparent  and  real  diameters ^Wi 


mt. 

DlarulntatlaD 
HsUr  of  lurbe 

SollI  light  HHllu 

sm. 

Ml 

MMt  ud  dmHV 

UnfiplllDtddlJt 
•d  In  Ih<  motlnu 

A  plinetaittrkii 
pnduu  ■  llkt  tt 

UdphH.. 

««i 

Of  Dniiiu 

3$U. 

JlDiMmwoiid 

KM. 

LlVUTlUUld 

»BT 

iL^ui?^. 

UBbtpluXtM- 

nsa 

ry™  Dr.  aJU 

Ksg 

COSTBNTS. 


mu  uid  pnd]ct«d  plftD«ti  4< 

L  No  uKTl  of  tbfl  merit  of  thb  dAft- 

»..rT  usrlli.U.  U,  dumc M 

L  Pwlod  41 


Mn*  Apnnnt  Hod  n«l  dUmvta 

»M.  BUdllta  of  KtBtiua 

3Ha.  Uww  ■■»■  daoill;  

MM.  Appunnt  mignltiuit  of  Ui 


sm  BiupMod  rlofofNapInn* 406 

CHAP.  XTI. 
MOZ.  TiitnT«ltloii  of  nlotl^  olijceta  (W 


T.  ODotrlcul  laUrpoilUQii  of  l«Hr 

dlik 4M 

8.  ComplttataUrpoitUan MS 


Wll.  Xnul  Hilt  octipH «» 

niS.  Anniul  odlpm 409 

mil  Bolu-  ooUpaei  cud  only  ippou  at 

or  mar  Ibt  «pocti  of  nflv  muoiu  410 
snt.  MttmlMBrpinilmx (ID 


me.  Toul  u>d  wttel  bUt  od^M 

uplalDHl  br  tha  lunar  lOndM  <U 
mo.  Annular  ti^^mt   Bxplatnad  ^ 

2M1.  powiibiiitf' "of'"*^rf»"i;iiiii 

iHa.  Boi'vediptk'iimiii" :'.'.'.'.'.'.'.!!!!"  Z  u: 


lueaof 


Bojal.. 

iam*** 

lionila 

stalornluacllpaaa.^.  4M 

"flh 

Lunar  etlVptk'iti 

<3r«l«l  dnratkii 
RalatlTa  DnmbaT 

™ 

nllpn 
faolu 

SMS. 

SS. 

2WT 

nalnurdlikTlaniledDrlnjtDlil 

L  Xquheb,  tiASmt,  akh  Occvuatioi* 


^llaatihlUt^Itha 


IMI.  KITectiinf  InlsTpcullkm 

IMl  1°.£dlpH>orthawlotlll«-.. 
aU3.  2°.  Xrllpnsi  of  tha  plauat  b^ 


! 


CONTENTS. 


mi.  |3.  Tnaarito  of  tho  mMUIm  OT«r 

Cbr  pluet 438 

29NL  UJ  tkmt  pheDomena  *»•"<*■■♦  "* 

iAqoadiBtara  ^^.^ 430 

flS*.  JUhcU  BKMlificd  at  other  «I<nig»- 

tioo$ ^ 440 

Mi.  PbcfMoienA  prtdieted  in  NaatiaJ 

Al—n«rfr  441 

ftSiL  MockNi  oTU^t  di«x»T«r«d  and  iu 
velodty  Bcasared  bj  meani  of 
tk«ewUpMi «  441 

MQ.  Edi|Ma  of  Saturn's  catelUtea  not 


IT.  TkAnnn  <»  ni  Ihtebiob  PLAanexB. 

0SL  Cbadltkma   which  datcrmina   a 

feraaidt 448 

SMB.  latcnrala  of  tha  oenurtnee  of 

traaidU 444 

M3^  Tba  mik>  ifiatanca  drtenninod  by 

tbatraiuitof  Veniu 445 

9M.  OecnlUtkau  deflncd 448 

3M&.  OecvItatioDa  bj  tha  moon 448 

SML  Determination  of  longitiidM  by 

lanar  ocraltatlonji 460 

WE.  OeenltatlDni  indieata  tha  prpMnoe 
or  ahMoee  of  an  atmospbera 
aroond  the  ooraltlng  body........  4S0 

mB.  Blncnlar  TLdbility  of  a  ttar  after 
tha  eommanoMnent  of  oecoltar 

tkm 4S0 

ftiUfintiwI  api^leation  of  lunar  o(v 
cultationa  to  raeolre  double  start  460 
ro.  Oeeultalions  by  Saturn's  rings 451 


CHAP.  XVIL 

■mUHU  Of  TIS  MLAK  SIRUL 

-  451 


Ti 

Ml, 


L  BtfA  wnoi  MTBumn  thi  Fobm,  Maa- 
irmi.  ASi>  PoBnoM  or  thx  Okbrs  or  thi 
PLA^n. 

Form  of  tha  orbit  determined  by 

tbeeeoratrVity 452 

MafBitada  determined  by  semi- 
axis  muin 453 

ST4.  Pmritkm  of  tlie  plane  of  the  orbit  4^2 

Sn.  Indtnations  of  tha  orUt 452 

are.  Linaof  DodM 452 

977.  Lonieitade  of  aMsnndInf  node i^ 

9T9l  Loasitndaof  perihelion 453 

Rf.  Five  alemants  which  determine 

tha  orbit 458 

dsoMots  WQi^mbt  to  slow  Taristion 

—  Epoch 458 

Tahfteofthaalementsoftheorfalts  458 


n.  Data  to  vgnaagm  tn  Placi  or 
PLAirtr. 

WS,  9f  tha  epoch  and  tha  OMaii  dally 

Botkm 456 

WKL  The  aqnatioa  of  the  esntre 456 

WHL  Table  of  dsta  necwwary  to  deter- 

niaa  placa  of  planet «  45T 

Ml  Tabia  of  extreme  and  mean  di»- 

fndk  sun  and  earth 467 

iaphaUoBdistaiiois  468 


m.  Oo5mTio?r8  Arrscnifo  thi  rersicAt  and 
JfiCHANicAL  State  or  thb  Plawt  ntw^ 

PEKDKNTLT  Or  ITS  QrUT. 

Sect.  Pftiwk 

2087,  Methods  of  computing  quantities 

nnoo   ».'°**  nisKDitudes  in  Table  IV 4G0 

a*88.  Alethodii  of  computing  extreme 

and  mean  apparent  dlametem 

Table  of  distanoea  from  the  sun 
and  earth  In  millions  of  miles...  462 
2989.  SurfiuMs  and  vol  umes— Table  of 
data  affecting  planet  Independent 
of  its  orUt 4^2 

2000.  The  maives "  4(3 

2001.  The  densities "J  403 

2992.  Certain  data  not  exactly  aaecr> 

talned 403 

2003.  Examples  of  the  masMS  and  dens- 

ities of  some  planets  4«3 

2004.  Intenrity  of  solar  light  and  heat  464 

2005.  8up«Tflclal  grarity 4(4 

2096.  OrUUl  TcIodUeii 464 

2007.  Superficial  velocity  of  rotation....  465 

2008.  Solar  graritation 465 

IT.  Tasdlatxd  EuEMxara  or  thi  Satelutb. 

2000.  Elements  of  the  JoTlan.  the  Satur- 

nian,  and  the  Uranian  systems  466 


CHAP.  XVIII. 

OOIOTS. 

I.  Comxtakt  ORBin. 

3000.  Prescience  of  the  astronomer 468 

8001.  Strikingly  illustnit4fd  hj  oometary 

discoTery 409 

8002.  Motion  of  comets  explained  by 

graTitation 460 

8008.  Conditions  Imporad  on  the  orltits 
of  bodies  which  are  sul^ect  to  tho 
attraction  of  graTitation  400 

3004.  Elliptic  orbit 471 

3005.  Parabolic  orbits  472 

8006,  Hyperbolic  orMts  474 

8007.  Planets  olmerre  in  tbHr  motions 

order  not  exacted  by  tho  law  of 

graTitation 476 

3008.  Comets  obx^rre  no  such  order  in 

their  motions  476 

3000.  They  move  in  conic  sncUons  with 

the  sun  for  the  fiinis  477 

3010.  Difflctilty  of  aKocrtaining  in  whnt 

species  of  conic  section  a  comet 
moTes 477 

3011.  Hyperbolic  and  parabolic  comets 

not  periodic  470 

8012.  Elliptic  comets  periodic  like  the 

planets  470 

8018.  Infflrulties  attending  the  analysis 

of  oometary  motions 480 

8014.  Periodicity  alone  proves  the  elllp- 

ticcharacter 480 

8015.  Periodicity    combined    with      he 

Identity  of  the  paths  while  Tlfdhle 

establlfihes  Identity 481 

3016.  Many  comets  recorded — few  ob- 

serred 481 

8017.  Classification  of  the  oometary  or- 

bito 482 


CONTENTS. 


Pan 

2875.  Snrftoa  and  toIuom » WO 

9870.  Diamml  roUtioa  andphyiioiJcbfr- 

racter  of  surftoe  unascartaiiied  800 

2877.  Solar  light  and  haai 391 

2878.  SaapacteU  rings 891 

2879.  SateUites 391 

2880.  Anomalous  inclination  of  thdr 

orblU  892 

288L  Apparent  motion  and  phases  as 

seen  from  Uranus 892 

2882.  Mass  and  density  of  Uranus 882 

IV.  Nkftumc. 

2888.  Disoorerr  of  Neptune 393 

2884.  Unexplslned  disturbances  obserr- 

ed  in  the  motion  of  Uranus 894 

2886.  A  planet  exterior  to  Uranus  would 

produce  a  like  effect 896 

2886.  Retiearches  of  MM.  Le  Verrier  and 
Adams 897 

2887.  Klements  of  the  sought  planet  as* 

signed  by  these  geometers 396 

2888.  Its  actual  disooTery  by  Dr.  Galle 

of  BerUn 899 

2889.  Its  predicted  and  observed  places 

In  near  proximity  399 

2890.  Corrected  elements  of  the  planet's 

orbit 899 

289L  Discrepancies  between  the  actual 

and  predicted  elements  explained  400 
2892.  Comparison  of  the  effects  of  the 

real  and  predicted  planets  401 

2898.  No  part  of  the  merit  of  this  dis- 
covery ascribable  to  chance 403 

2804.  Period  403 

2896.  DisUnoe   403 

2896.  Relative  orbiU  and  distances  of 

Neptune  and  the  earth 408 

2897.  Apparent  and  real  diameter 403 

2898.  SatelUte  of  Neptune 404 

2899.  Mass  and  density  404 

2900.  Apparent  magnitude  of  the  sun 

at  Neptune  405 

2901.  Suspected  ring  of  Neptune 400 

CHAP.  XVI. 

ICUP8E8|  nUKSITS,  AMD    OCCUUTATIONB. 

2902.  Interposition  of  celestial  objects  400 

2903.  General  conditions  which  deter* 

mine  the  phenomena  of  intorpo* 
sition  when  one  of  the  extreme 
ol^jects  ia  the  earth  407 

2904.  Condition  of  no  interposition. — 

External  contact ^ 407 

2905.  Partial  interposition  407 

2906.  Internal  contact  of  interposing 

disk 408 

2907.  Centrical  interposition  of  lesser 

disk 408 

2906.  Complete  interposition 408 

L  SOLAB  EcuFsn. 

2909.  Solar  eclipses  406 

2910.  Partial  solar  eclipse 408 

2911.  Magnitude  of  eclipses  expressed 

by  digits 400 

2912.  Total  solar  edipee 409 

2913.  Annual  eclipses 409 

2914  Solar  eclipsed  can  only  appear  at 

or  near  the  epoch  of  new  moons  410 
2015.  Sfl^oU  of  parallax 410 


S«i. 

2916.  Shadow  produced  by  an  opaque 

globe 412 

2917.  Method  of  determining  the  form 

and  dimensions  of  the  shadow...  418 

2918.  Method  of  determining  the  limltf 

of  the  penumlva 414 

2919.  Total  and  partial  solar  eclipses 

explained  by  the  lunar  shadow  414 

2920.  Annular   eclipses   explained   by 

shadow  414 

292L  PossiUlity    of  annular  ecUpaea 

proved 415 

2922.  Solar  ediptic  limits ^.  417 

2923.  Extreme  and  mean  values  of  aeml- 

diameters  and  horisontal  paral- 
laxes of  sun  and  moon  D8 

2924.  Limits  for    total    and    annual 

eclipses 419 

2925.  Appearances  attending  total  acdar 

eellpses 499 

2926.  Bailv's  beads 430 

2927.  Produced   by  lunar   mountains 

prqjeoted  on  the  sun's  disk 422 

2928.  Flame-like  protuberances 428 

2929.  Solar  eclipse  of  1851 428 

2930.  Observations  of  the  Astronomer 

Royal 428 

2931.  Observations  of  MM.  Dunkin  and 

Humphreys  425 

2982.  Observations  of  W.  Oray,  at  Tune, 

near  SarpsboK 425 

2933.  Observations  of  MM.  Stenhenson 

and  Andrews  at  FrederiKsvaam  420 

2934.  Observations  of    Mr.  Lasseli  at 

TroUhXtUn  Falls 426 

2935.  Observations  of  Mr.  Hind  at  R*- 

velsborg,  near  Engelholm 426 

2986.  Observations  of  Mr.  Dawes  near 

Kngelholm 427 

2937.  Effects  of  total  obMuratinn  on 

surrounding  objects  and  scenery  420 

2938.  Evidence  of  a  solar  atmosphere...  490 

2939.  Probable  causes  of  the  red  emana- 

tions in  total  or  solar  eclipses.....  480 

II.  LURAK  ECUPfflES. 

2940.  Causes  of  lunar  eclipses  431 

2941.  Dimensions  of  the  earth's  shadow  481 

2942.  Conditions  which  determine  lunar 

eclipses 481 

2943.  Lunar  ediptio  limits 438 

2944.  Limits  for  a  total  edipse 484 

2946.  Greatest  duration  of  total  edlpae  484 

2946.  Relative  number  of  solar  and  lu- 

nar eclipses 4S4 

2947.  Eflisctsof  the  earth's  penumbra...  436 

2948.  Effects.of  refiraction  of  the  earth's 

atmosphere  in  total  edipse  486 

2949.  The  lunar  disk  visible  during  total 

obscuration 430 

III.  ECUPSIS,    TBAN8IT8,    AKD   OOOUUEAnONI 
OF  THX  JoVIAIf  STSmC. 

2950.  The  motions  of  Jupiter  and  his 

satellites  exhibit  all  the  effects  of 
Interponition ........'  437 

2951.  Effects  of  intorpoaition w.  438 

295-2.  1<>.  Eclipses  of  tho  satellites 438 

2953.  2°.  Eclipses  of  the  planet  by  the 

»at<?lliti« 436 

2954.  3P.  Occultations  of  the  satellites 

by  the  plauot «  438 


CONTSKTS. 


fat 

^aa.  ¥>.  Traniilte  of  tbe  MtdUtoa  OT«r 

th^plaoet 438 

2U1  Ul  tbew  pfaraomenA  maaiftsted 

atquadratar*  «...» 430 

IMT.  £ifbeCK  Bodifled  at  otbor  eloiig»- 

ikMU  .- ^ 440 

Ml  Pbenomciui  prvdkted  tn  Kantiad 

Aimaaaek  ..» » ~.  441 

SSI.  MoCioB  of  light  difcorered  and  its 

Tidodty  BMaaond  bj  means  of 

mUmm 441 

of  Saturn's  satelUtsa  not 


IT.  IkUHRi  <»  na  iMmiaB  Puunm. 

which   detcmina   a 

.- 44S 

Intctrals  of  the  cecarraioe  of 

tnariU 4U 

fML,  Tba  sna**  tfistanra  determiaad  by 

tha  transit  of  Venos  ....' 445 

tmL  Oeenltatioos  dsAnad 448 

SMIl  OoeallatiOBS  fay  tfaa  moon 448 

9H&,  Determination  of  longitodes  faj 

loaar  oeenltations ». ^450 

9V.  OeBottaCioas  indieata  the  pmanee 
or   abeance  of  an   atmospbare 

aroaad  tlie  ooenlUng  body 450 

SMS.  BIngular  TLrifaUity  of  a  star  after 
tbe  eotnmenoement  of  ooculta- 

tion 450 

SojMssted  ^plication  of  lunar  oo 
cnltations  to  reeolre  doable  start  450 
rOi  Oeenltations  by  fiatom's  rings....  451 


CHAP.  XTIL 

tuKiAM.  luwrni  or  thb  woum.  stbrx. 

an.  Plaaatary  data 451 

L  BsxA  wncK  ncTBumfi  nn  ?OBif,  Mao- 
AXD  Posmos  or  thb  Okbits  op  thx 


of  tbe  orbit  determined  by 

tbe  c<«entfidty 452 

tKl,  Magnitude  determined  by  semi- 
axis  flus^or 452 

974.  FnsitiDn  of  tbe  plane  of  tbe  orbit  4.^2 

an.  IttpHnat1<ms  of  tbe  orbit 452 

m*.  Line  of  nodes 452 

977.  Loagitode  of  aseending  node 4.'>3 

971.  LoBgitnde  of  peribelfcm 463 

97B.  flTC  elements  which  determine 

the  orUt 458 

■■i  HaiiiMifs  siiiyiirit  tr  niiiir  Tsrliifffiii 

.—Kpoeh 45S 

90.  T^ble  of  the  elements  of  the  orbiU  458 

Q.  DaTA.  TO  BCRBimn  thi  Placi  or  tbb 
Plahit. 

9B.  By  the  epoch  and  the  mean  dally 

■aodoa M.  456 

901  Th«  eqoatioB  of  tbe  centre 458 

SH.  Cable  of  data  neoemary  to  deter- 

■ijpa  plsfe  nf  planet «  467 

SB.  Table  of  extreme  and  mean  dis- 

ftoid  san  and  earth 457 

■dapbaUondiatMifliB  458 


m.  OomnTion  APncmro  thi  phtbicai  ard 

MICHAWICAL    STATI    OF    TBJK   PLAITXT     IMD«. 
PUfbJCNTLT  OF  ITS  OrBTT. 

Sect.  Page 

2987.  Methods  of  computing  quantities 

_^^„    ^and  magnitudes  in  Table  IV 4eo 

a»88.  Methods  of  oompoting  extreme 
and  mean  apparent  diameters — 
Table  of  distancee  tr<na  tbe  ran 
and  earth  in  millions  of  miles...  462 
2iK0.  Snr&oes  and  rolnmes — Table  of 
data  affecting  planet  independent 
of  its  orbit 4fl2 

2990.  Tbe  masses 4^ 

2991.  Tbe  densities 468 

2992.  Certain  data  not  exactly  ascer- 

tained  463 

2993b  Examples  of  tlie  masses  and  dens- 
ities of  some  planets  463 

2994.  Intensity  of  solar  light  and  heat  464 

2995.  Superficial  gravity 464 

2996.  Orbital  vcIodUes 464 

2997.  Superficial  Telocity  of  rotation....  466 
2908.  Solar  graTiUtion 466 

IT.  Tabclatxd  EuDfxsTi  of  thi  SATXLuni. 

Elements  of  tbe  Jorian,  the  Satu  r- 
nian,  and  tbe  Uranian  systems  400 


CHAP.  xvni. 

OOXXTS. 
I.  COMXTABT  Oftsm. 

9000.  Prescience  of  the  astmnomer 468 

3001.  Strikingly  illustrated  by  cometary 

dlsoorery 469 

8002.  Motion  of  comets  explained  by 

graTitation 469 

8008.  Conditions  imposed  on  the  nrlnts 

of  l)odip8  whirh  are  sul^ect  to  the 

attniction  of  graritation  409 

8004.  Elliptic  orWt 471 

3005.  Parabolic  orbits  472 

8006.  Hyperbolic  orbits  474 

8007.  Planets  obserre  in  their  motions 

order  not  exact4Ml  by  tlie  law  of 
gravitation 476 

8008.  Comets  obwrre  no  such  order  In 

their  motions  476 

3009.  They  move  in  conic  sections  with 

tbe  sun  for  tbe  focns  477 

8010.  Difficulty  of  ascertaining  in  what 

species  of  conic  section  a  comet 
moves 477 

8011.  Hyperbolic  and  parabolic  comets 

not  periodic  479 

3012.  Elliptic  comets  periodic  like  tbe 

planets  479 

8013.  Difllculties  attending  the  analyvls 

of  cometary  motions 480 

8014.  Periodicity  alone  proves  tbe  elllp- 

ticeharacter 480 

8015.  Periodicity   combined   with      he 

identity  of  the  paths  while  visible 
entablbibes  identity 481 

8016.  Many  comets  recorded  —  few  ob- 

served   481 

8017.  Classification  of  the  cometary  or- 

Uta 4W 


CONTENTS. 


XL  Suipno  Ooian  bitoltiho 
OsBix  07  Satukm. 
Beet.  PttS'B 

8018.  Enck6*»  oomet  ^ 482 

8019.  Table  ot  the  elementa  of  the  orbifc  488 

8020.  Indication  of  the  effeete  of  a  re- 

sisting nediiun  ..••• 484 

8021.  TIm  Inminiferous  ether  would  pro- 

duce snch  an  effect 484 

a02SL  Comets  would  ultimately  fidl  into 

the  snn 485 

8028.  Why  like  effects  are  not  maniftsted 

in  the  motion  of  the  planets ....~  485 

8024.  Corrected  estimate  of  the  mess  of 

Mercury 486 

8025.  Biela's  oomet 486 

8020.  Possibility  of   the   collision    of 

Biela's  comet  with  the  earth  .....  487 

8027.  Besolntion  of  Biela's  oomet  into 

two 488 

8028.  Changes  of  appearance  attending. 

the  separation 488 

80».  Faye's  oomet 489 

8080.  Beappearance  in  186(M1  oalcula- 
•ve      ted  by  M.  Le  Terrier 480 

8081.  De  Yico's  comet 490 

8082.  Brorsen's  oomet 490 

8038.  D*Arrest's  oomet 490 

8034.  Elliptic  comet  of  1743 491 

8085.  Elliptic  oomet  of  1766 491 

8036.  Lexell's  comet 491 

8087.  Analysis  of   Laplace  applied  to 

Lexell's  comet 492 

8088.  Its  orbit  before  1767  and  after 

1770  calcnlated  by  bis  formulaa  492 

8039.  RcTision  of  these  researches  by 

M.  Le  Terrier 493 

8040.  Process  by  which  the  identifica- 

tion of  periodic  comets  may  be 
decided 494 

8041.  Application  of  this  process  hy  M. 

Le  Terrier  to  the  comets  ofFaye, 
De  Tioo  and  Brorsen,  end  that 
of  Lexell — their  dirersity  prored  494 

8042.  Probable   identity  of   De  Tioo's 

comet  with  the  comet  of  1678  ...  495 
8048.  Blainplan's  comet  of  1819  495 

8044.  Pons'fl  oomet  of  1829 495 

8045.  Pigott's  oomet  of  1783 495 

8046.  Peters's  oomet  of  1S46  495 

8047.  Tabular  synopsis  of  the  orbits  of 

the  comets  which  reToWe  within 
Saturn's  orbit  496 

8048.  Diagram  of  the  orbits 496 

8049. )  Planetary  character  of  their  or- 
8060./     bits 496 

m.  EUIPTIO  COMKTS,  WHOSE  MXAK  DlBTAHCU 
AXE  NKAKLT  XQUAL  TO  THAT  OF  UaANUS. 

8051.  Comets  of  long  periods,  first  re- 

cognised as  periodic 499 

8052.  Newton's  conjectures  as  to  the  ex- 

istence of  comets  of  long  periods  499 

8053.  Halley's  researches 500 

8054.  Halley  predicts  its  re-appearance 

in  1768-9 600 

8055.  Great  advance  of  mathematical 

and  physical  sciences  between 
1682  and  1759  501 

8056.  Exact  path  of  the  comet  on  its 

return,  and  time  of  its  perihe- 
lion, calculated  and  predicted  by 
daSraut  and  Lalande  502 


Sect  P»f* 

8057.  BemarkaUe  anticipation  of  tba 

discoTery  of  Uranus 608 

8058.  Prediction  of  Halley  and  Clairaut 

fulfilled  by  re-appearance  of  the 

oomet  in  1758-9  „ 608 

8050.  Disturbing  action  of  a  planet  on 

a  comet  explained  608 

8060.  Effect  of  the  perturbing  action  of 

Jupiter  and  Saturn  on  Halley's 
comet  between  1682  and  1758  ....  506 

8061.  Calculations    of   its  return    in 

1835-6 805 

8062.  Predictions  fulfilled  606 

3063.  Tabular  synopsis  of  the  motion  of 

Halley's  oomet  606 

8064.  Pons's  comet  of  1812 » 606 

3065.  Olbers's  oomet  of  1815 ~.  60T 

8066.  De  Yico's  comet  of  1846 507 

8067.  Brorsen's  comet  of  1847  607 

8068.  Vestphal's  comet  of  1852 607 

8009.  Tabular  synopsis  of  the  motions 

of  these  six  comets 607 

8070.  Diagram  of  their  orbits 608 

8071.  Planetarr  characters  are  nearly 

effaced  m  these  orbits 608 

IT.  BlXiraO  COMBTB,  WBOn  MlAir  DDTABrOB 

xzcuD  TBI  Loots  of  thb  Solak  Ststeil 

807SL  Tabular  synopsis  of  twenty-one 
.  elliptic  comets  of  great  ecoentri- 
dty  and  long  period 600 

8078.  Plan  of  the  form  and  relatiTO  mag- 
nitude of  the  orbits 612 

T.  Htpxsbouo  OointTB. 

8074.  Tabular   synopsis  of  hyi>erbolic 

comets 512 

TI.  Pasabouc  Conns. 

8075.  Tabular  synopsis  of  the  parabolic 

comets 515 

Tn.  DxRBiBXfnoir  of  Comxtart  Osam  or 
Bpaox. 

8076.  Distribution  of  the  cometary  or- 

bits in  space 616 

8077.  Belative  numbers  of  direct  and 

retrograde  comets 615 

8078.  Inclination  of  the  orbits 616 

8079.  Directions  of  the  nodes  and  peri- 

helia  617 

8080.  Distribution  of  the  pointa  of  pe- 

rihelion  «  617 

Tin.  Physical  CoKwiTUTioy  of  OaiuKn, 

8081.  Apparent  form — head  and  taO.....  519 

8082.  Nucleus 619 

3088.  Coma 619 

3084.  Origin  of  the  name 619 

3085.  Magnitude  of  the  head 519 

8086.  Magnitude  of  the  nucleus ^  620 

3087.  Thetafl 520 

8068.  Mass,   density,   and  Tolume   of 

comets 522 

8089.  Light  of  comets 523 

8090.  Enlargement   of   magnitude  on 

departing  fh>m  the  sun 524 

8091.  Professor  StruTe's    drawings  of 

Knck6's  comet «...  526 

8092.  Bemarkable  physical  phenomma 

maniftsted  by  Halley's  eo]net.M. 


CONTENTS. 


••• 
xxm 


IrL  Pag* 

Int.  atraroFii  drmwingi  of  the  comet 

u>proachixi«  th«  «an  In  18S5 62? 

lOM.  Iumppe«rmBceo|ithe29thofSept  5^^ 

lOM.  Appearance  rm  Oct.  3^ J^ 

tm.  AppeM*nc*xmOcL8 -  Jg 

MT.  App«r»iK»  on  Oct.  9 -  $;» 

KM».  Appearance  on  Oct  IX...— »** 

IMW.  Appearance  on  Oct  U J^ 

noi-  Appearance  <m  Oct  29...... J^ 

jl(l2.  ApfMarance  on  Not.  6>.... «  OJW 

nox  aSr  J.  Hewchers  dednetkma  from 

tfaeee  phenomena. W** 

1104.  Anpeannoe  of  the  comet  after  pe- 

ilhellon ........~«. .;  MO 

SMML  OtMrratlons   and   drawlngi   of 

MM.  Madear  and  Smith Ml 

SUM.  Appearance  on  Jan.  24 ~ Ml 

JW7.  Appearanca  on  Jan. » - Ml 

no*.  Appearance  on  Jan.  26. mi 

lltfft.  Appearance  on  Jan.  27...— ^| 

MIO.  Appearance  on  Jan.  28 -.  Ml 

Jilt  Appearance  on  Jan.  30 "••••  ^^ 

3112.  Appearance  on  Feh.  1 M^ 

aii  Appearance  on  J«h.  7  ~ « ojj 

8114.  Appearance  on  Feh.  10.......^. ^ 

Slli.  Appearance  on  Feb.  Wand  23  ...»  M2 

8tl«.  Number  of  oometa  ». •••  »* 

ai7.  Duration  of  the  appearance  of  ^^ 

IU8.  Sear  app^iJS'of  «»ii^  ***  *^  632 


CHAP.  XIX. 


;T  Of  TABIABU  OBBXfS. 


ai9.  Oooditiona  under  which  elliptic 
orUt«  are devrlbed i:";-!' 

SUO.  Foceee  other  than  the  central  at- 
tnetkm  would  destroy  the  ellip- 
tle  fcrm 

«q  But  when  thew  ftwoee  are  feeble 
eompared  with  the  central  atr 
tiwikm.  the  elllpcic  fbrm  is  only 

■lightly  affected  « •• 

Tbto  is  the  case  in  the  system  of 


533 


533 


Bance  proceea  great  fedlities  of 
Invasl^E^lon  and  calculation  .... 
Purturbations    and    disturbing 


533 

684 

634 

634 

Method  of  Tariabie  elemwite.— 

The  instantaneous  edipee 586 

ti^t  fMiiianess  of  the  disturbing  Ibroes 
ta  tlM  caMS  presented  in  the  so- 
lar system  explained 

Xm.  Ocdtrofemposltlon — .........".... 

of    the    disturbing 
into  rectangular  compo- 


Seet                                                      P»«» 
8134.  Badial  and   transrersal   oompo- 
nonts  affect  the  central  attrac- 
tion and  angular  motion 530 

8136.  Tangential  and    normal   compo- 

nents affect  the  linear  relodty 

and  curvature  ~ 540 

8186.  PoeltiTe  and  negatlre  components  541 

8137.  In  slightly  ellipUc  orbits  the  noi^ 

m^  and  radial  components  and 
the  tangential  and  transrersal 
coincide  Ml 


686 

537 


Beeolution  of  the  disturbing  force 
with  relation  to  the  radius  Tee- 
tor  and  the  |d«Be  of  the  orbit  ... 

Orthofonal  component  - 

HSL  Badksf  and  transrersal   compo- 
nents  -.- ; 

fnA  normal  compo- 


8U9. 


SUO. 


or  Tin  Radial  Ooicpoinarr  of 

TBS  DlBTUKBIXa  FOEOB. 


542 


542 

543 


I«  BvFicn 


8188.  Equable  description  of  arwa  not 

d^urbedby  ft M2 

8139.  Its  effect  on  the  mean  distance 

and  period 

8140.  If  the  rsdial  component  ▼"7  «^ 

cording  to  any  conditions  which 
depend  solely  on  tbe  distance,  It 
will  not  change  the  form  or 
magnitude  of  the  instantaneous 

ellipse •• 

8141.  Effectof  a  gradually  increasing  or 

decreasing  radial  component  .... 

8142.  Effects  on  the  period  and  mean 

motion  more  sensible  Uian  those 

on  the  mean  distance -  54.3 

3143.  Its  effect  on  the  posiUon  of  the 

appides ••••  ^« 

It  dimlnwhes  or  increases  the 
angle  under  tbe  radius  rector 
and  tangent  according  as  it  is 
positive  or  negatlre 543 

It  rainca  or  dcprew»e  the  empty 
focus  of  the  elliptic  orbit  above 
or  below  the  axis  according  to 
the  position  of  the  disturbed  body 
in  its  elliptic  orbit 544 

8146.  EffecU  of  a  posiUve  radial  oompo- 
nent  on  the  apoides  -  545 

8147.  Effects  of  a  radial  negatire  oompo- 
nent  on  the  position  of  the  axis  646 

8148.  Diagram  indicating  these  effects  647 
3148.  This  motion  of  the  apsides  bears  a 

▼ery  minute  proportion  to  that 
of  the  disturbed  body 

8150.  Diagram  illustrating  the  motion 
of  the  apsides  •■• •••• 

8151.  This  motion  of  the  apsides  in- 
creases  as  the  eccentricity  of  the 
orbit  diminishes,  other  things 
being  the  same  •••  — 

8152.  Effect  of  the  radial  component  on 
the  eccentricity 


3144. 


8145. 


54" 
547 


548 
549 


637 


538 
639 

599 

589 


II.  Errwrre  or  the  trasrvkhsal  Component 
OF  rax.  DiSTCKBixG  Force. 


81M. 


retards  the  or- 


iD^teatloB 


eni  affects  the 
tbe  nodes 


550 


660 


639    I 


It  accelerates  or 

bital  motion ••• •.'•• 

8154.  It  increases  or  decreases  the  major 

axUi  according  as  it  is  positive  or 

negative 'Vlv. 

8156.  It  produces  progression  of  tj>c  *P- 

rides  ftoaiAerlbeliontottphelion 

-nd  regresrion  from  aphelion  to 
perihelion  when  ponUre,  and 
be  contrary  when  negalWe &&w 


CONTENTS. 


Beet  P>f« 

8160.  Its  effect  on  the  eecentridty ^  W2 

3167.  Its  effects  on  the  major  axis  at  the 

apeidea 668 


OF    TBI    OSTBOOOIVAI.    OOMFO* 
WWKt  or  TBS  DXffUEBOlO  FOBd. 


Ill-   Xffbcts 


8168w  It  ebaogea  the  plane  of  the  orhit 

— plane  of  reliwenoe 666 

8U0.  Nodea  of  dintorbed  orUt  on  plane 

of  reference -  6W 

8100.  Effect  of  orthogonal  component 

Tarlee  with  diatanee  flrom  node  666 

8101.  Nodea  progreaa  or  regreaa  accord- 

ing as  the  component  la  poaitiTe 
ornegatiTe W* 

8102.  Sffeet  upon  the  indination 660 


lY.  OmouL  SumcART  or  trb  Emcn  of  a 

DiBTUBBIRa  FORd. 

8108.  TBhular  BTnopala  of  the  effecta  of 
the  aereral  components  of  the 
disturbing  force 667 


CHAP.  XX. 

nOBLSM  OF  THBBB  WODIME. 

8101.  Attraction   independent   of   the 

mass  of  the  attracted  bodj  668 

8106.  Hence  the  denomination,  "  accele- 

rating force" 668 

8100.  Accelerating  force  of  grarlUtion  660 

8107.  Problem  of  two  bodiea 659 

8108.  Problem  of  three  bodiea 660 

8100.  Shnplified    bj  the   comparatiTe 

feebleneaa  of  the  foroea  exerted 
l^  the  third  body 601 

8170.  Attracting  force  of  the  third  bodj 

notwboUj  disturbing ~  601 

8171.  Attracting  force  which  would  pro- 

duce no  disturbing  effect  601 

8172.  This  would  be  the  cbm  if  the  third 

bodj  were  enormously  distant 
compared  with  the  second 661 

8173.  Example  of  a  force  aupposcd  to 

act  on  the  solar  system 662 

8174.  Caae  in  which  the  distance  of  the 

third  body  is  not  oomparatiTcly 
great 602 

8176.  To  determine  the  ratio  of  the  dis- 
turbing to  the  central  foree 603 

S170.  How  the  direction  of  the  disturb- 
ing force  raries  with  the  relatlre 
distances  of  the  disturbed  and 
disturUng  from  the  central 
body 664 

8177  PibstCabb. — The  component  of 
ttie  disturbing  force  In  the  plane 
of  tb«  orUt  when  the  disturbing 
bedy  is  outside  the  orbit  of  the 
disturbed  body  606 

8178.  To  determine  the  sign  of  each  of 
the  components  of  the  disturbing 
force  in  each  suooesslTe  point  of 
the  orbit 660 


Sect. 

8170.  Diagram  illustrating  thaia  ehan- 
gas  of  directions 

8180.  BBOoivn  Casb^  in  which  the  die. 

turbing  body  Is  within  the  dfa- 
turbed  orUt 

8181.  Changes  of  sign  of  the  oompoiMntB 

in  this  case 

8182.  General  summary  of  the  ehangw 

of  direction  of  the  radial  and 
transrersal  oomponents  of  tha 
disturbing  force  during  aaynodte 
_period  of  the  disturbed  body  ....  fill 

8188.  varytog  effects  of  the  orthomal 
component  during  a  ayno^  f 
Tolution ~.  Vfl 

8184.  Periodic  and  aecolar  pertorbatlana  ITS 


CHAP.  XXL 

LUIf  AK  TBBOBT. 

8186.  Lunar  theorr  ap  Important 

of  the  proUem  of  three  bodiea...  6T4 
8180.  It  auppUea  atriking  proof  of  the 

trutn  of  the  theory  of  graTltatioa  6T4 

8187.  The  aun  alone  aenaibry  diaturba 

the  moon 67f 

8188.  Linea  of  sysygy  and  quadrature  676 
3189.  Direction  of  the  disturbing  force 

of  the  sun 670 

8190.  Points  where  the  disturbing  force 
is  wholly  radial  and  wholly  tan- 
gential   677 

3101.  Intensities  of  the  disturbing  forces 

at  sysygies  and  quadratures 678 

3192.  The  sun's  disturbing  force  at 
equal  angles  with  syiygy  Tsriea 
in  the  direct  ratio  of  the  moon*s 
distance  from  the  earth 670 

8193.  AnalTsisoftheTariationsofsign 
of  the  oomponents  of  the  dis- 
turbing force  during  a  Bjnodle 
period 680 

3194.  Effects  of  the  disturbing  force  on 
the  moon's  motion — the  annual 
equation 683 

8196.  Acceleration  of  the  moon's  mean 

motion 686 

8190.  Effect    upon    the   form   of  the 

moon's  orbit -. 680 

3107.  Moon's  TariaUon  687 

3198.  Parallactio  inequality 688 

3199.  Inequalities  dependbig  on  the  el- 

liptic form  of  the  lunar  orbit .....  688 

8200.  Equation  of  the  centre 6S8 

3201.  Method  of  Inrestigating  the  Taria- 

tiobs  of  the  elliptic  elements  of 

the  lunar  orbit 680 

8202.  Moon's  mean  distance  not  subject 

to  secular  variation 680 


FiBBT  CaSB. 
WHXX  PBRIOKB  IS  I.f  CO!f  JUKCnON. 

9903.  Motion  of  the  apHdes  602 

8204.  Effects  on  eccentricity 608 


f 


C0NTBNT6. 


zzv 


WBn  pKBioxB  0  or  opFOcmoir. 


SteL 

aSD6.  Motloa  of  tfaa  aptldta ... 


ixa  n  QdiMusuBa. 


SS07. 


of  «1m  afMidM 


•«•••••••••«••••• 


UIQ. 


sn4. 


SZ16w 
SZ17. 

azu. 

ttlA. 


tiM  «een>trldty 606 

WMMoa  of  tlM  •paidM  mater 
Ib  wjwjpm  than  m  qaauatnn  £06 


Voamta  Gabi. 

ABS  OBUQUB  fO  TBI  UHB 

or  Binyuf. 

MoUoBofthoapddM.. (WT 

WlMn  moon's  Mrig«e  iaMPUfT' 
btlwB  the  pomt  of  eo^Jnnetioii  806 
Wken  the  moon's  perIgM  is  M^ 
4r  7"  bablnd  fho  point  of  oppo- 

ritkm MO 

Wbon  p«lcM  Ss  640  44' 7"  bdbra 

tho  point  of  opposition 600 

~  i&64044'7"beliind 

n  .- 601 

of  tho  motions  of  the 
>••••.*.••.  ..................  60(1 

of  the   dtetnrfaing  Ibroe 

the  eeeentrldtj 602 

pwigee  U  64°  4i'  7''  befiire 

the  point  of  eonjuneticm. 603 

When  perigee  is  64°  44^  7*  behind 

opposition 608 

When  perigee  Is  64°  44^  7^^  before 

opposition 604 

When  perigee  U  64044^  7'' behind 

eof^anfltkm 604 

Bztrcme  end  mean  Telne  of  eo* 
tclettj 004 


Of  TBI  BorcBunfo  fOBci  uroif  the 

UTBAB  BOMS  AMD  DlCUIf ATlOir. 

Taat  Came. 


When  the  line  ct  syxygles  Is  In 
the  line  of  nodes 606 


8100HD  Case, 

tt23b  When  the  line  of  nodes  Is  in 

qnedxatnze..... 606 

Tbzbd  Gasb. 

1234.  When  the  line  of  sjirgles  Is  less 

then  00^  before  the  Une  of  nodes  607 


fiooBTB  Casb. 

When  theltne  of  mjgles  Is  more 
than  OOObeiyre  the  iTnt  of  nodes  606 


SecL  Page 

3226.  General  summary  of  the  lanar 

ineqoalities ^  60O 

8227.  Other  lesser  inequalities 610 


OHAP.  XXIL 

IKBOBT  or  tBl  JOVXAB  ilBIXIC. 

Analogy  of  the  Jortan  to  the  ter> 

restrU  system 610 

8229.  Why  the  same  inequalities  are  not 

manifosted 611 

8280.  Mutual  perturbations  of  the  satel- 

lites    di 

8281.  Ketrogresslon  of  the  lines  of  con- 

JunoUon  of  the  first  tliree  satel- 
lites  „  611 

8282.  Ghange  of  direction  of  line  of 

eoB^unetion  in  eaeh  qmodie  r»> 
Tolution 618 

8288.  AppUeation  to  the  three  Inner  s»> 

tellites ., 618 

8284.  Regression  ofthe  lines  of  eopjono- 

tion  of  the  three  satellites  equal  613 

8286.  Line  of  coi^unction  of  the  first 
and  second  In  oppoeitlon  to  that 
of  the  second  and  third 614 

8286.  XfEeets  of.  their  mutual  pertorba- 

tions  upon  the  fbrms  of  their 
orbits 614 

8287.  Motion  of  the  apsides  equal  to 

that  ci  the  lines  of  conjunction.  614 

8288.  The  lines  of  apsides  oohkcide  with 

the  lines  of  conjunction 614 

8280.  Positions  of  the  per^Tes  and  apo- 

JoTes  of  the  three  orbits »  615 

8240.  Yalue  of  the  eccentricity 615 

8241.  Remarkable  prediiion  in  the  ful- 

filment of  these  laws 616 

8242.  Effects  of  the  eccentricity  of  the 

undisturbed  orbit  of  the  third 
satellite 616 

8243.  Perturbations  of  the  fourth  satel- 

lite  617 

3244.  Gomplicated  perturbations  of  this 

system 619 


GUAP.  xxin. 

TBIOBT  or  PLAmTABT  PKBTURBATIOXS. 

3245.  The  theory  simplified  by  those  of 

the  moon  and  Jovian  system....  610 

8246.  Perturbations  of  the  terrestrial 

by  the  miyjor  planets 620 

8247.  Gases  in  which  the  disturbing  is 

in  closer  proximity  with  the  dis- 
turbed planet ».  G21 

8248.  Gase  in  which  the  disturbing  is 

within  the  orbit  of  the  disturbed 
planet 622 

8240.  Perturbation  affected  by  the  poiii- 
tion  of  the  apsides  and  nodes  in 
relation  to  the  line  of  conjuuo- 
tion 922 

3250.  Method  ofdetermining  the  change 
of  direction  of  the  line  of  con- 
junction  QM 


zxti 


CONTENTS. 


Pag« 

326L  Oondltlon  nndor  whkh  the  dlreo* 
tlon  of  the  line  of  ooi\JancUon 

U  hiTftriable 027 

8252.  To  determine  the  oondltlon  under 
which  the  line  of  oonjanctlona 
shall  hare  a  limited  number  of 

inrariable  poeitions. ^  827 

8258.  XlTecta  of  the  diaturbing  Ibroe  in 

oaeea  of  oommen«arabw  perloda  62B 

8254.  Planets  present  no  case  of  com- 

mensmmbto  periodSy  hat  some 
nearly  so 680 

8255.  Long  inequaUtSes 881 

8268.  Long  inequality  of  Jupiter  and 

Saturn ~  682 

8267.  Period  of  this  InequaUtj  about  880 

years 882 

8268.  Its  elfeet  upon  the  ttkaynr  aads  and 

periods ~.  838 

8250.  Its  eflSsct  upon  the  eoeentrMtles...  688 
8200.  SUM*  on  the  direetlon  of  the 

apsides 638 

8261.  Long  inequality  of  Vmus 681 

8282.  Other  long  inequalities 636 

8288.  Long  inequalities  of  the  nodes  and 

inclinations 885 

8264.  Secular  inequalities 886 

8286.  Secular  constancy  of  mi^O'  a*^  836 

8268.  Secular  Tariatlon  of  apsides 630 

8267.  Secular  Tarlatkm  of  ecoentrloity»  840 

8288.  Secular  Tariatlon  of  nodes 640 

8260.  SecularTariation  of  inclination...  841 

8270.  Laplace's  theorems  of  the  rel»> 

ttons  between  the  eccentricity 
Mid  inclinations  of  the  planetary 
orbits 841 

8271.  ConserratiTe    Influence    errone> 

ously  ascribed  to  these  theorems  842 


CHAP.  XXIY. 

mOKT  07  SFHBOIDAL  PIETUaiATIOVS. 

8272.  Attraction  of  planets  would  be 
central  If  their  forms  were  ex* 
acUy  spherical 648 

8278.  Disturbing  forces  consequent  on 

nheroidsl  forms 843 

8274.  BDacts  which  would  be  produced 
if  a  satellite  were  attached  to  the 
surftoe  of  the  earth  at  the 
equator 843 

8276.  like  eflTects  would  be  produced  by 

any  number  of  sucn  satellite^ 
or  what  would  be  equlTalent,  by 

the  spheroidal  form 844 

8278.  Precession  of  Hm  equlnozes 846 

8277.  The  sun  returns  to  the  equinoctial 

point  before  completing  its  rero* 
lutlon 846 

8278.  Bqulnoctlal  and  sidereal  year 648 

88*0.  Pniod  of  the  precession 846 

8280.  Its  effect  upon  the  longitude  of 

celestial  ohiects 848 

8281.  Precession  &[  equinoxes  produces 

a  rotation  of  the  pole  of  the 
equator  round  that  of  the  ecliptic  848 
DIstaace  of  pole  of  equator  from 
pole  of  ecliptic  Tarles  with  the 
•faUqulty .,  847 


Sect 
8283. 
82K4. 
8286. 


8287. 
8288. 


3289. 


82B1. 

8202. 
8203. 


Pole  star  Tarles  IhMB  age  to  ift^.  847 

Former  and  Aiture  pole  Stan 848 

Remarkable    dreumstance 

nected  with  the  pytamtils  ,. 

Nutation 

Ekjuation  of  the  equinoxes......... 

Proportion  of  the  mean  precession 

due  to  the  distarfaiag  forces  of 

the  moon  and  sun » 

Like  effects  prodnead  in  tlit  eaaa 

of  other  planets 861 

ElliBcts  of  spheroidal  pertortaatkm 

on  the  motions  or  tha  moon 

generally  minute ^  811 

Spheroidal  Inequality  of  the  ineU- 

nation  of  the  moon's  orbit  ob> 

sexrable 851 

Spheroidal  Inequalities  of  the  Jo* 

Tian  system 

Spheroidal  ineqnaUtles  of  the  S^ 

tumian  qr^em 864 


CHAP.  ZZT. 

■flU.— RSLUS  FAIAUAX  IKB 
MtTAWCa. 


CHS 


8204.  Creation  not  drenmaaribed  bj 
solar  system «. 

8206.  The  solar  system  surrounded  bj 

a  Test  but  limited  Told 856 

8208.  The  stars  must  be  placed  beyond  . 
the  surrounding  Toid — absenea 
of  sensible  parallax 858 

8287.  Annual  parallax — parallaetle  el- 
lipse   868 

8208.  Bocientrlclty  of  parallactic  elllpee 

depends  on  star's  latitude 860 

8200.  IMfllcuUy  of  determining  the  pa- 
rallax arises  firom  its  minute 
amount »  080 

8800.  How  the  distance  is  inforred  fh>m 

the  parallax 061 

8801.  Motion  of  light  supplies  a  oouto- 

nient  unit  for  the  stellar  dia> 
tanoe 881 

8802.  Methods  of  ascertaining  the  paral- 

lax and  consequently  the  dis- 
tance  .,  882 

8308.  Professor  Henderson's  discoTcry 

of  the  parallax  of  a  Oentauri....  88S 

8304.  IMfferentia]  method 888 

8806.  Position  micrometer,  its  ^ipllea- 

tion  to  this  problem 888 

8808.  Case  of  two  stars  hsTing  equal 

parallax 007 

8307.  Oue  in  which  they  haTe  unequal 

parallax 007 

8308.  Parallax  of  nine  stars  ascnrtained  008 


CHAP.  XXVL 

MAOinTUDK  AND  LU8TRX  OF  THl  STAJtS. 

8300.  Orders  of  magnitude  of  the  stars 

8810.  Theee    TarieUes    of    magnitude 

caused  ehiefly  bj  dUUnrenoe  of 

distance r 


CONTENTS. 


XXVU 


SSll. 


S814. 


asiT. 


Pag« 
Btan  aa  diitaat  from  Meh  other 

generally  m  they  are  £roin  the 

eon».». M.....^......*.....****  071 

Why  ttan  increaae  in  number  aa 

tb^  decreaae  in  Bafnitude 871 

What  are  the  fixed  rtaraf 872 

TUeeeopee  do  not  magnify  them 

Uke  the  plaoeta  « ~  072 

The  ahaenre  of  a  disk  prored  by 

ttdr  oecnltatkm  bj  the  momi...  872 
Meaning  of  the  torn  magnitude 

aa  applied  to  etan »  678 

Why  stars  may  be  rendered  im- 


pereeptible  by  their  dletanoe 

ClaisMwation  of  stars  by  magnl> 


ms. 


67S 

tade  arUtranr  and  insQflcJent»  874 

Lnportaaoe  c»r  more  exact  astro- 
metric  expedients ~  874 

Aatrometer  oontrired  and  applied 
bv  Sir  J.  Hersebel 875 

Principle  on  which  the  soooessiTe 
ofders  of  stellar  magnitude 
ahoald  be  based ~».  877 

Gbmparatire  lustre  of  a  Oentauri 
with  that  of  the  ftill  moon 877 

Oomparlson  of  the  lustre  of  the 
fUl  moon  with  that  of   the    ' 

.-.  877 


Oomparieon  of  the  sun's  light  with 
that  of  a  Centanri 

Comparlaon    of    the    intrlnsie 
splendour  of  the  sun  and  a  fixed 


878 


SS98L  Jkatraneter    suggested    by   I>r. 


8334. 
S38&. 


878 

678 
Oomparieon  of  the  sun  andaCen- 

tanri -  680 

Oomparieon  of  the  sun  and  Sirius  680 
Astrometrie  table  of  190  principal 

stare 681 

Use  of  the  telescope  in  stellar  ob> 

eerratlQns 681 

teace  penetrating  power..... 687 

lUceoople  stars 688 

Mellar  nomenclature ~  688 

Use  of  pointers 600 

Useof  starmape. OM) 

Use  of  the  celeetial  globe 601 

To  find  the  place  of  an  ol^ect  on 
the  globe  when  Its  right  ascen- 
sion and  declination  are  known  601 


CHAP.  XXTIL 

■uLTms,  Ajn>  TDironAXT  stabc — 
■oTum  or  RAia.— MonoH  of  thb 


obserrationa  on  indS- 
808 


Tsleeeopic 
Ttdiuklst 


L  PaooBio  BiAis. 

Stars  of  TarlaMe  lustre _  803 

Bewarkahle  stars  of  this  elaas  in 
tim  eonatrilationa  of  Cetua  and 

riMBMMM  MM 

Tlible  of  the  periodic  atars  ~ « 


Sect  Pag, 

S342.  Hypotbeeee  propoaed  to  explain 

thcee  phenomena... 007 


n.  TmroKAiT  Stau. 

8343.  Temporary  atara  aeoi  in  andent 

timee 008 

8344.  Temporary  atar  obaerred  by  Mr. 

lllnd „  000 

8346.  Ifiasing  atara 600 


in.  DOUBUt  Staii. 

8346.  Reeearehea  of  Sir  W.  and  J.  Her- 

achel  aa  to  double  stars .'700 

8347.  Stars  opUoally  double. 700 

8848.  This  sappositlon  not  generally  ad- 

mimrible 700 

8840.  Argument  against  mere  opUcal 

double  stars  deriTed  ttom  their 

proper  motion 701 

8360.  StruTe's  dassifloation  of  double 

stars 702 

8351.  Selection  of  double  stars. 702 

8362.  Coloured  double  stars 702 

8853.  Triple  and  other  multiple  stars...  702 
8354.  Attempts  to  dlsooTcr  the  stellar 

parallax  by  double  stars »  704 

3355.  OhserTationsof  Sir  W.IIersohel...  704 

3356.  HlsdiaooTery  of  binary  stars 705 

8857.  Extension  of  the  law  of  gravita- 

tion of  the  stars 706 

8858.  Orbit  of  star  round  star  elHptio...  700 

8850.  Remarkable  ease  of  yVirginis 707 

8860.  Singular  pbenomeoa  produced  by- 
one  system  rcTolTing  round 
another 708 

3361.  MainiitudeM  of  stellar  orbits 709 

8362.  Maiweii  of  binarT  stars  determined 

by  their  parallax  and  period 710 


IT.    P&OPER  MonON  OP  THX  Staxs. 

33M.  The  sun  not  a  fixed  centre 711 

3365.  Effect  of  the  nun's  suppoM^l  mo- 

tion on  the  apparent  planes  of 
the  stars 711 

3366.  Motion  of  the  sun  inferred  fh<m 

the  motion  of  the  stars 712 

8367.  Velodty  of  the  sun 713 

8368.  Probable  centre  of  its  motion 714 


CHAP.  XXVIIL 

TRX  FOKM  AKD  VnaontlOTn  OF  TBI  MASS   OF 
STABS  WHICH  COMPOaX  THX  PXBMAICKMT. 

8360.  Distribution  of  stars  on  the  firma- 
ment    714 

8370.  Galactic  drde  and  poles„ 715 

3371.  Variations  of  the  stellar  density 

in  relation  to  this  drde 715 

8872.  Struve's  analysis  of  Hersdiel's  o»>- 

serrations J'J 

8373.  Milky  way 716 


xxTiii 


COKTBKTS. 


8374. 
8375. 


3S76i 


8377. 
8378. 

8279. 

8880. 
888L 

8882. 

8888. 
8884. 

SS85. 
8888. 
8887. 
8888. 


8889. 
8800. 


Page 
It  oonidftfi  of  Innomerftble  itan 

crowded  together 717 

The  probeble  form  of  the  stratum 

of  Stan  in  which  the  aun  ia  placed  718 


CHAP.  XXIX. 

tmUkE  OLUVtBtS  AAD  KEBULM, 

The  stars  whidi  Ibnn  the  llrm»> 
ment  a  stellar  elaster.1 — ^Analogy 
suggests  the  probable  existence 

of  others. 720 

Such  clusters  innumerable 721 

Distribution  of  dusters  and  ne- 

buIsB ; »  721 

Oonstellation  of  the  dusters  and 

nebttUe 722 

Nebular  hypothMis 723 

Forms  apparent  and  real  of  the 

dusters 728 

Forms  apparent  and  real  of  ne- 

bnlsB. 724 

Double  nebulas 724 

Planetary  nebulae 726 

Annular  nebulas 725 

Spiral  nebulas 726 

Number  of  nebulas 726 

Remarkable  nebulas,  with  nume- 
rous drawings  of  them  bj  the 
EarlofRoaseandSir  J.Herschel  T28 

Large  and  irregular  nebulas. 781 

Rldi  cluster  in  the  Oentanr,  with 
drawing. »•••..•.......»»..  782 


sect. 

3391.  Great  nebula  in  Orion,  with  draw> 

ing »  788 

8302.  Great  nebula  in  Argo,  with  draw- 
ing   788 

889S,  Magellanic  douds 738 


CHAP.  XXX. 

HoncES  or  kkmarkabli  lanoiroiaGAL 
nrenuifEBnn. 

8894.  Classiflcatlon  of  the  instruments 

of  obeerration 784 

8395.  Sir  William    Herschers   400  ft 

telescope  with  drawing. 738 

8896.  The  lesser  Roese  tdeeoope,  with 

drawing. 737 

8897.  The  greater  Rosse  telescope,  with 

drawing 788 

8398.  The  Oxford  heliometer, with  draw- 
ing   «,  T80 

8899.  The  transit  drde  by  iSrougbton, 
•     withdrawing. 711 

8400.  The  Greenwich  transit  drde,  with 

drawing 742 

8401.  The  Pultowa  prime  rertical  in* 

strument,  with  drawing 748 

8402.  Troughton*s  altitude  and  aslmuth 

drde,  with  drawing 748 

8408.  The  Greenwich  altazimuth  instm- 

ment,  with  drawing 749 

8404.  The  Northumberland  telescope — 

Cambridge    obeerratory,    with 

drawing ^,^  7M 


LIST 

OF 

THE  PBINGIPAL  ILLUSTRATIONS  IN  THIS  VOLUllB. 


METSOROLOGT. 

tanaee  of  water-spoota , 63 

IT  crytUlf 72 

itaiag  oondactor 88 

)ra  Borealis,  leen  bj  M.  LoUin 89 

Ditto  Ditto     90 

Ditto  Ditto     90 

Ditto  Ditto     90 

ASTRONOMY. 

siorial  inttnunent 119 

int  instrument 152 

a1  circle 169 

itnUion  of  the  ■eaflons 181 

itntion  of  the  lunar  phases 197 

•copie  view  of  the  crescent  moon 207 

TK  L — Telescopic  chart  of  the  soath-eastem  qaadrant  of  the  moon's  disk, 

f  MM.  Beer  and  Madler To/aee  TUU 

TB  II. — Telescopic  chart  of  Tycho  and  the  sarrounding  regions,  as  they 

>pear  on  the  disk  of  the  moon  in  the  third  quarter 211 

TB  IIL — The  appearance  of  the  same  when  the  moon  is  fail 211 

TB  IV. — Plan  of  the  lunar  mountain  Qassendi,  by  Miidler,  from  observa- 

ons  with  the  Dorpat  telescope 212 

TB  v. — Solar  spots  obsenred  by  Capocci,  in  1826 212 

1  of  the  solar  spots  as  they  appeared  in  1836-7 238 

TB  VL^Solar  spots  observed  by  Pastorff,  in  1826 239 

TB  VIL— Solar  spots  obsenred  by  Pastorff,  in  1828 239 

ttire  orbits  of  Mercury  and  the  Earth 289 

ttire  volumes  of  Mercury  and  the  Earth 291 

fttive  apparent  magnitudes  of  the  Sun  at  Mercury  and  the  Earth 293 

ttive  orbits  of  Venus  and  the  Earth 296 

stive  apparent  magniUides  of  the  Sun  at  Venus  and  the  Earth 298 

«M  of  Venus 300 

stive  orbits  of  Mars  and  the  Earth 304 

stive  apparent  magnitudes  of  the  Sun  at  the  Earth  and  Mars 306 

iTB  VIIL — Telescopic  views  of  Mars,  by  Beer  and  Miidler 308 

.TB  IX. — Telescopic  projection  of  the  two  hemispheres  of  Mars,  by  Madler  308 

ative  orbits  of  Jupiter  and  the  Earth 318 

ative  volumes  of  Jupiter  and  the  Earth 322 

ative  apparent  magnitudes  of  the  Sun  at  Jupiter  and  the  Earth 322 

iTB  X. — Telescopic  views  of  Jupiter,  by  Madler  and  Uerschel 320 

kTB  XL — Telescopic  views  of  Saturn,  by  Schmidt 320 

iter  and  hii  satellitei 3o0 

BtiTO  orbiU  of  the  Earth  MndSutam UJL 


LIST  OF  ILLUSTBATIONS. 

Belatire  Tolameis  of  the  Earth  and  Satarn 346 

Relative  apparent  magnitudes  of  the  Son  at  the  Earth  and  Saturn S46 

Phases  of  Saturn  and  his  ring 351-2 

Plan  of  Saturn  and  his  ring 353 

Shadows  of  the  ring  on  Saturn 355 

Shadows  of  Saturn  on  the  ring 356 

Platb  XII. — Telescopic  yiew  of  Saturn  and  his  ring,  by  Mr.  Bawes 354 

Platb  XIII. — Total  solar  eclipse  in  1851,  by  MM.  Airy,  Grey,  Stephenson, 

Lassell,  Hind,  and  Dawes 364 

Section  of  Saturn  and  his  ring 389 

Appearances  of  the  ring  as  seen  from  Saturn 382-3-4 

Relative  orbits  of  the  Earth  and  Uranus ^,  390 

Relative  apparent  magnitudes  of  the  Sun  at  the  Earth  and  Uranus 391 

Illustration  of  the  discovery  of  Neptune 396 

Relative  positions  of  the  planets  predicted  by  Le  Verrier  and  Adams,  and 

of  Neptune 399 

Relative  orbits  of  the  predicted  and  real  planets 401 

Relative  orbits  of  Neptune  and  the  Earth 40S 

Relative  apparent  magnitudes  of  the  Sun  at  Neptune  and  the  EarUi 405 

BaU/s  beads 421-1 

Belipse  of  Jupiter's  satellites 437 

The  relative  distances  of  the  planets 467 

Elliptic,  parabolic,  and  hyperbolic  orbits 470 

Place  of  the  orbits  of  thirteen  comets  included  within  the  orbit  of  Saturn...  497 

Disturbing  force  of  a  planet  on  a  comet 504 

Plan  of  the  orbits  of  six  elliptic  comets,  having  a  mean  distance  nearly 

equal  to  that  of  Uranus *5(M 

Plan  of  the  most  eccentric  of  the  elliptic  orbits  of  comets 512 

Platb  XIY. — Struvo's  drawing  of  £nck6's  comet 526 

Plate  XV. — Struve's  drawings  of  Bailey's  comet  i4)proaching  the  Sun,  in 

September  and  October,  1835 526 

Plate  XVI. —  Ditto  Ditto 528 

Plate  XVII.— Ditto  Ditto,  in  Oct  and  Nov.,  1836 528 

Plates  XVIII.  and  XIX. — Drawings  of  Halley's  comet,  receding  from  the 

Sun,  in  1836,  by  MM.  Maclear  and  Smith 532 

Disturbing  action  of  an  exterior  upon  an  interior  planet 565 

Disturbing  action  of  an  interior  upon  an  exterior  planet 568 

Lunar  perturbations 580 

Plate  XX. — Telescopic  drawings  of  nebulce  and  clusters,  by  the  Earl  of 

Rosse  and  Sir  John  Hersohel. 727 

Plate  XXI.  Ditto  Ditto 727 

Plate  XXII.         Ditto  Ditto 72» 

Plate  XXIII.       Ditto  Ditto 721 

Plate  XXIV.        Ditto  Ditto 7SS 

Plate  XXV.         Ditto  Ditto 7tt 

Plate  XXVI. — Drawing  of  the  cluster  which  contains  the  Sun 734 

Plate  XXVII. — Sir  William  Herschel's  great  telescope,  focal  length  40  feet» 

aperture  4  feet 787 

Plate  XXVIIL — The  lesser  Rosse  telescope,  focal  length  27  feet,  aperture 

3  feet 787 

Plate  XXIX. — The  great  Rosse  telescope,  focal  length  53  feet,  aperture  6 

feet,  north  side 789 

Plate  XXX.  Ditto  Ditto,  south  side 788 

Plate  XXXI.— The  Oxford  heliometer 748 

Plate  XXXII. — Troughton's  transit  circle 748 

Plate  XXXIII. — The  great  Greenwich  transit  circle 748 

Plate  XXXIV. — The  Pultowa  prime  vertical  instrument 748 

Plate  XXXV. — Troughton's  altitude  and  azimuth  circle 748 

Plate  XXXVI. — The  great  Greenwich  altazimuth  instrument 748 

Plate  XXXVIL— The  Northumberland  equatorial,  Cambridge ,  768 


HAND-BOOK 


OV 


NATUEAL  PHILOSOPHY 


▲HD 


ASTRONOMY. 


<»WWWV</WNi>WV%/WWW%/V^V\/WVWVWWWWVWVW» 


THIRD    COURSE. 


BOOK   THE   FIRST 


MXTEOROLOa Y. 


CHAPTER  I. 


TERRESTRIAL  HEAT. 


2160.  Insufficiency  of  thermal  €hiervation$,  —  To  aacertain  tho 

itVB  which  regulate  the  distribation  of  heat  and  the  periodical  vicis- 

■todes  of  temperature  on  and  below  the  surface  of  the  earth  and  in 

tlie  superior  strata  of  the  atmosphere,  is  a  problem  of  which  the 

oomplete  solution  would  require  a  collection  of  exact  thermal  obser- 

ntioDSy  made  not  only  in  every  jMirt  of  the  earth,  but  for  a  long 

series  of  years,  not  to  say  ages.     Experimental  research  has  not  yet 

npplied  such  data.     Obiservations  on  temperature  made  at  periods 

eren  so  recent  as  those  within  which  physical  science  has  been  culti- 

Tited  with  more  or  less  ardour  and  success,  were  in  general  scattered 

and  unconnected,  and  marked  neither  by  system  nor  precision.     It 

was  only  since  the  commencement  of  the  present  century  that  obser- 

Tafcions  on  terrestrial  heat  were  accumulated  in  sufficient  quantity, 

and  directed  with  the  skill  and  precision  indispensable  to  render  them 

the  source  from  which  the  laws  of  temperatuie  could  be  e^oVxed. 

nr.  3  25 


26  METBOaoLOaT. 

The  ezperimente  and  observatioDS  of  Humboldt,  and  the  profouDd 
theoretical  researolieg  of  Fourier  and  Laplace,  supplied  at  once  the 
nucleus  of  our  preseut  knowledge  in  this  department  of  pbjaica, 
and  gave  an  impulse  to  en()uiry,  b;  which  others  have  been  carried 
forward  and  guided;  80  that  if  ne  do  not  yet  possess  all  tbe  data 
which  snfGcientlj  extended  and  long-continued  obserration  and  ex- 
periment might  afford,  enough  bas  at  least  been  done  to  establish 
witb  certainty  some  general  laws  which  prevail  in  the  physics  of 
heat,  and  to  uiadow  forth  others  which  future  enquirers  will  confirm 
or  modify. 

2161.  Load  nariation*  of  temperature.  —  Tbe  superfioial  ttmp^ 
rature  of  tbe  earth  varies  with  the  latitude,  gradually  decreasing  in 
proceeding  from  the  equator  towards  the  poles. 

It  also  varies  with  the  elevation  of  tbe  point  of  observation,  do- 
creasing  in  proceeding  to  heights  above  the  level  of  tbe  sea,  and 
varying  according  to  certain  conditions  below  that  level,  but  in  all 
cases  increasing  gradually  for  all  depths  below  a  certain  stratum,  at 
which  the  temperature  is  invariable. 

At  a  g^ven  latitude  and  a  given  elevation  the  temperature  varies 
with  the  character  of  the  surface,  according  as  tbe  place  of  obeer- 
vation  is  on  sea  or  land;  and  if  on  land,  according  to  the  nature, 
prodnctioDs,  or  condition  of  the  soil,  and  tbe  accidents  of  the  snr&oe, 
Buoh  as  its  inclination  or  aspect. 

2162.  Diurnal  thermometric  period. — At  a  ffjaa  place  tbe  tem- 
perature undei^s  two  prindpal  periodic  variations,  diurnal  and 
annuof. 

The  temperatcre  falling  to  a  minimum  at  a  certain  moment  near 
Bunrise,  augments  until  it  attuns  a  maximum,  at  a  certun  moment 
after  the  sun  has  passed  the  meridian.  The  temperature  then  gra- 
dually falls  until  it  returns  to  the  minimum  in  the  morning. 

Tlus  dinmal  thermometric  period  varies  with  the  latitude,  the  ele- 
vation of  the  place,  the  character  of  the  surface,  and  witb  a  mat 
variety  of  local  ctmditions,  which  not  only  afiect  tbe  hours  of  tka 
maximum,  minimum,  and  mean  temperatures,  but  also  the  differenea 
between  the  maximum  and  minimum,  or  tbe  extent  of  the  variation. 

2163.  Aftnuai  therTKometrie  period.  —  The  annual  thermometrie 
period  also  varies  with  tbe  latitude,  and  with  all  tbe  other  ocmditiou 
tnat  a&ot  the  thermal  phenomena. 

In  order  to  be  enabled  to  evolve  the  general  thermal  laws  from 
phenomena  so  eomplicated  and  shifting,  it' is  above  all  things  neces- 
sary to  define  aud  ascertain  those  mean  conditions  or  states,  round 
which  the  thermomclrio  oscillations  take  place. 

2164.  The  mean  divmal  (emperatiire. — This  is  a  temperature  M 
taken  between  the  extremes,  that  all  those  temperatures  which  are 
snperior  to  it  shall  exceed  it  by  exactly  as  much  as  those  which  an 
'  '    '  rtoit  shall  Ml  short  of  it. 


TEBRB8TRIAL  H£AT.  27 

To  render  this  more  clear,  let  ns  suppose  that  the  temperature  is 
obeerved  every  second  in  twenty-four  hours.  This  would  give 
86,400  observed  temperatures.  Suppose,  that  of  these  43,000  are 
above,  and  43,400  below  the  mean  temperature.  If,  then,  the  mean 
temperature  be  subtracted  from  each  of  those  above  it,  and  if  each 
of  those  below  it  be  subtracted  from  it,  the  sum  of  the  remainders 
in  the  one  case  most  be  equal  to  the  sum  of  the  remainders  in  the 
other. 

This  18  equivalent  to  stating  that  the  mean  temperature,  multiplied 
by  86,400,  will  give  the  same  result  as  would  be  obtained  by  adding 
together  all  the  86,400  observed  temperatures. 

Bat  the  thermometric  column  is  not  subject  to  such  rapid  changes 
as  to  show  any  observable  difference  of  elevation  'from  second  to 
■econd,  nor  even  from  minute  to  minute.  If  its  height  be  observed 
every  hour,  the  mean  diurnal  temperature  will  be  obtained  by  adding 
together  the  twelve  horary  temperatures,  and  dividing  their  sum  by 
12.  But  even  this  is  not  necessary,  and  the  same  result  is  more 
easily  obtained,  either  by  taking  the  snm  of  the  temperatures  at 
sunrise,  at  2  p.  M.,  and  at  sunset,  and  dividing  the  result  by  3,  or 
more  simply  still  by  adding  together  the  maximum  and  mininum 
temperatures,  and  taking  half  their  sum.  Whichever  of  these 
methods  be  adopted,  the  same  result  very  nearly  will  be  obtained. 
[The  second  is  the  method  adopted  at  the  Observatory  of  Paris.] 

2165.  ITie  mean  tempemiure  of  ^  month.  —  This  is  found  by 
dividing  the  sum  of  the  mean  diurnal  temperature  by  the  number 
of  days. 

2166.  The  mean  temperature  of  the  year,  — This  may  be  found 
by  dividing  the  sum  of  the  mean  monthly  temperatures  by  12. 

2167.  Month  of  mean  temperature. — It  is  found  that  in  each  cli- 
mate there  is  a  certain  month  of  which  the  mean  temperature  is 
identical  with  the  mean  temperature  of  the  year,  or  very  nearly  so. 
This  circumstance,  when  the  month  is  known,  supplies  an  easy 
method  of  observing  the  mean  temperature  of  the  year. 

In  the  climate  of  Paris,  this  month  is  October. 

[The  mean  temperature  of  the  year  may  also  be  found  by  taking 
the  mean  of  the  temperatures  corresponding  to  a  single  hour  of  the 
day,  which,  for  the  latitude  of  Paris,  is  9  o'clock,  a.  m.] 

2168.  The  mean  temperature  of  the  place.  —  The  mean  annual 
temperature  being  observed  in  a  given  place  for  a  series  of  years, 
the  comparison  of  these  means,  one  with  another,  will  show  whether 
the  mean  annual  temperature  is  subject  to  variation,  and,  if  so, 
whether  the  variation  is  periodic  or  progressive.  All  observations 
hitherto  made  and  recorded  tend  to  support  the  conclusion,  that  the 
variations  of  the  mean  annual  temperature  are,  like  all  other  cosmi- 
eal  phenomena,  periodic,  and  that  the  oscillations  are  made  within 
dtfnite  limits  sod  deJBnJte  jotervah.    There  exists^  therefore,  iot 


28  MBTEOROLOGT. 

eyerj  place,  another  mean  temperature  superior  to  tbe  annnal,  and 
which  is  called  the  mean  temperature  of  the  place.  This  is  obtained 
bj  adding  together  the  mean  annual  temperatures  of  all  the  years 
which  constitute  the  thermometric  period,  and  dividing  the  sum  thus 
obtained  by  the  number  of  years. 

But  even  though  the  period  of  the  variation  of  the  mean  annual 
temperature  be  not  known,  a  near  approximation  to  the  mean  tem- 
perature of  the  place  may  be  obtained  by  adding  together  any  attain- 
able number  of  mean  annual  temperatures  and  dividing  their  sum 
by  their  number.  The  probable  accuracy  of  the  result  will  be 
greater,  the  less  the  difference  between  the  temperatures  computed. 

Thus  it  was  found  by  a  comparison  of  thirty  mean  annual  tempe* 
ratures  at  Paris,  that  the  mean  was  51^*44,  and  that  the  difference 
between  the  greatest  and  least  of  the  mean  annual  temperatures  was 
only  5^*4.  It  may  therefore  be  assumed  that  51^*44  does  not  differ 
by  so  much  as  two-tenths  of  a  degree  from  the  true  mean  tempera- 
ture of  that  place. 

Observation,  however,  has  been  hitherto  so  limited,  both  as  to 
extent  and  duration,  that  this  thermal  character  has  been  determined 
for  a  very  limited  number  of  places.  Indications,  nevertheless, 
have  been  obtained  sufficiently  clear  and  satisfactory  to  enable  Hum- 
boldt to  arrive  at  some  general  conclusions,  which  we  shall  now  briefly 
state. 

2169.  Isothermal  lines.  —  In  proceeding  successively  along  the 
same  meridian  from  the  equator  towards  the  pole,  the  mean  tempe- 
rature decreases  generally,  but  not  regularly  nor  uniformly.  At 
some  points  it  even  happens  that  the  mean  temperature  augments, 
instead  of  decreasing.  These  irregularities  are  caused  partly  by  the 
yaryinff  character  of  the  surface,  over  which  the  meridian  passes,  and 
partly  by  the  atmospheric  effects  produced  by  adjacent  regions,  and 
a  multitude  of  other  causes,  local  and  accidental.  As  these  causes 
of  irregularity  in  the  rate  of  decrease  of  the  mean  temperature,  pro- 
ceeding from  the  equator  to  the  poles,  are  different  upon  difierent 
meridians,  it  is  evident  that  the  points  of  the  meridians  which  sur- 
round the  globe,  at  which  the  mean  temperatures  are  equal,  do  not 
lie  upon  a  parallel  of  latitude,  as  they  would  if  the  causes  which 
affect  the  distribution  of  heat  were  free  from  all  such  irregularities 
and  accidental  influences. 

If,  then,  a  series  of  points  be  taken  upon  all  the  meridians  sur- 
rounding  the  globe,  having  the  same  mean  temperature,  the  line 
upon  which  such  points  are  placed  is  called  an  isothermal  line. 

Each  isothermal  line  is  therefore  characterized  by  the  uniform 
mean  temperature,  which  prevails  upon  every  part  of  it. 

2170.  Jsothennal  zones.  —  The  space  included  between  two  iso- 
thermal lines  of  given  temperatures  is  called  an  isothermal  zone. 

The  noribera  hemisphere  has  been  distributed  in  relation  to  its 


TERRESTRIAL  HEAT.  29 

thermftl  condition  into  six  sones,  limited  bj  the  seven  isothermal 
linesy  cbaracteriied  by  the  mean  temperatures,  86^,  74**.  68°,  59°, 
50°,  41°  and  82°. 

2171.  The  JirU  thermal  or  Unrid  zone.  —  This  zone  is  a  space 
sarronnding  the  globe,  included  between  the  equator  and  the  isother- 
mal line,  whose  temperature  is  74°. 

The  mean  temperature  of  the  terrestxial  equator  is  subject  to  very 
little  variation,  and  it  may  therefore  be  considered  as  very  nearly  an 
isothermal  line.  Its  mean  temperature  varies  between  the  narrow 
limits  c^  81j^°  and  82^°.  [This  mean,  however,  is  modified  by  the 
great  extent  of  the  equatorial  seas;  under  the  line,  the  continents 
oocapy  only  a  sixth  of  the  earth's  circumference.  Hence,  in  approach- 
ing the  tropics,  and  particularly  the  tropic  of  Cancer,  we  must  not 
be  surprised  at  finding  mean  temperatures  which  sensibly  exceed  that 
of  the  terrettrial  equator;  at  Pondicherry,  for  example,  in  lat.  11° 
55'  N.,  the  mean  is  85°'28,  and  at  Eoulka,  in  Africa,  kt  13°  10', 
the  mean  is  87°-26.] 

2172.  Thermal  equator.  —  If,  upon  each  meridian,  the  point  of 
greatest  mean  temperature  be  taken,  the  series  of  such  points  will 
follow  a  certain  course  round  the  globe,  which  has  been  designated 
as  the  thermal  equator.  This  line  departs  from  the  terrestrial  equa- 
tor, to  the  extent  of  ten  or  twelve  degrees  on  the  north  and  about 
eight  degrees  on  the  south  side,  following  a  sinuous  and  irregular 
course,  intersecting  the  terrestrial  equator  at  about  100°,  and  160°, 
east  longitude.  — It  attains  its  greatest  distances  north  at  Jamaica, 
and  at  a  point  in  Central  Africa,  having  a  latitude  of  15°,  and  east 
longitude  10°  or  12°.  The  greatest  mean  temperature  of  the  ther- 
mal equator  is  86°. 

The  isothermal  line  having  the  temperature  of  74°  is  not  very 
nnaous  in  its  course,  and  does  not  much  depart  from  the  tropics. 

2173.  The  second  thermal  zone.  —  This  zone,  which  is  included 
between  the  isothermal  parallels  characterized  by  the  mean  tempe- 
ntnres  of  74°  and  68°  is  much  more  sinuous,  and  includes  very 
Tarions  latitudes.  At  the  points  where  it  intersccte  the  meridians 
of  Europe,  it  is  convex  towards  the  north,  and  attains  ite  greatest 
latitude  in  Algeria. 

2174.  The  third  thermal  zone, — ^This  zone,  included  between  the 
isothermal  parallels  which  have  the  mean  temperatures  of  68°  and 
59°,  passes  over  the  coaste  of  France  upon  the  Mediterranean,  about 
the  latitude  43°,  and  from  thence  bends  southwards,  both  east  and 
west,  on  the  east  towards  Nangasaki  and  the  coasts  of  Japan,  and  on 
the  west  to  Natehez  on  the  Mississippi. 

2175.  The  fourth  thermal  zone,  —  This  zone  is  included  between 
the  parallels  of  mean  temperatures  59°  and  50°,  It  is  convex  to  the 
nortL  in  Europe,  including  the  chief  part  of  France,  and  thence  falls 
lo  the  sooth  on  both  sides,  jDoludiog  PeJrin  on  the  east,  and  ¥\i\W 

3* 


80  HBTBOROLOST. 

delphia,  New  York,  and  Cindnnati  on  tbe  west.  It  ii  evident  from 
this  Bmngemeiit  of  the  fourth  thermal  lone,  that  the  climate  of 
Europe  ie  warmer  than  that  of  those  parte  of  the  eastern  and  weatem 
continentB  which  have  the  aame  latitude. 

2176.  The  fifth  thermal  zone.— The  Sfth  tone,  included  between 
the  mean  temperatures  of  50°  and  41°,  is  more  ainuone,  and  iaclndea 
latitudes  more  TarioDS  oven  than  the  preceding.  [By  comparing  the 
mean  temperatures  of  FayetteTille  and  of  Copenhogea,  of  Quehee 
and  of  Stockholm,  of  Kendal  and  of  Berlin,  we  may  see  more  and 
more  the  difference  which  exists  between  the  climate  of  the  I^iii 
meridian,  and  the  climates  to  the  east  and  west  of  this  meridian.] 

[2176.*  The  tixth  thermal  zone.  —  The  sixth  zone  is  included 
between  the  mean  temperatures  of  41°  and  32° ;  and  it  is  to  be  n- 
gretted  that  we  do  not  possess  in  this  eodc  several  series  of  obser^ 
vatione  in  Siberia  aod  the  north  of  America.  These  obserratiou 
would  be  so  much  the  more  interesting  as  they  would  enable  us  to 
trace,  with  some  preciiiioo,  the  limits  to  which  vegetation  extends. 
However,  this  lone  appears  to  be  comprised  between  the  latitudes  of 
60°  and  70°.] 

2177.  The  polar  regions. —  The  circle  whose  area  is  comprised 
within  the  isothermal  parallel  whose  mean  temperature  is  32°,  ia 
still  less  known.  Nevertheless,  the  results  of  the  observations  made 
by  arctic  voyagers  within  the  last  twenty  years,  afford  ground  for  in- 
ferring that  the  mean  temperature  of  the  pole  it^lf  must  be  some- 
where from  13^  to  36°  below  the  zero  of  Fahrenheit,  or  45"  to  68" 
below  the  temperature  of  melting  ice. 

2178.  Climate  variei  on  the  same  iiolhermai  itnc  —  When  it  is 
considered  how  different  arc  the  vegetable  productions  of  places 
ntoate  upon  the  same  isothermal  line,  it  will  be  evident  that  other 
thermal  conditions  besides  the  mean  temperature  must  be  ascertained 
before  the  climate  of  a  place  can  be  known.  Thus  London,  New 
York,  and  Fekin  are  nearly  on  the  same  isothermal  line,  yet  their 
climat«s  and  vegetable  produotions  are  ectremely  different. 

21 7S.  Conitant,  variable,  and  extreme  climates. — One  of  the 
oircnmstances  wbioh  produce  the  most  marked  difference  in  the  cli- 
mates of  places  having  the  same  mean  temperature  is  the  difference 
between  the  extreme  temperatures.  In  this  respect  climat«s  are 
classed  as  constant,  variable,  and  extreme. 

Constant  climates  are  those  in  which  the  maximnm  and  minimum 
monthly  temperatures  differ  hut  little;  variable  climates  are  those  in 
which  the  difference  between  these  Atremes  is  more  considerable, 
and  extreme  climates  are  those  in  which  this  difference  is  very  great 

Constant  climates  are  sometimes  called  insalar,  because  the  effe«t 
of  the  ocean  in  equalising  the  temperature  of  the  air  is  such  as  to 
pve  this  character  to  the  climates  of  islands. 
SIStJ.  .iicamplef  of  the  dattijicalion  of  dimalei. — The  feUowiDg 
exvnpJeg  frill  UloBtmto  tiua  oluaificatioa  of  QUm&tea*. — 


TERRESTRIAL  HEAT. 


31 


I  "- 

MMaTonpen. 
tiai«oftlMy«Lr. 

Higheftmean 

MonthlT  Tempe- 

ninrs. 

Lovcstmean 

Monthly  Tempe- 

rmtore. 

DifTerenoe. 

Funehal 

o 

68-54 

o 
75-66 

o 
62-96 

o 
12-60 

London 

Paris 

50-36 
51-08 
54-14 

66-92 
65-80 
64-40 

41-72 
36-14 
87-76 

26-20 
29-16 
26-64 

dLlUlo. 

1  NevTork*.... 
1  IN*iD 

53-78 
54-86 

80-78 
84-88 

25-34 
24-62 

66-44 
6976 

FoDchal  offers  the  example  of  a  constant  or  insular  climate; 
LondoDy  Paris,  and  St  Malo,  of  a  variable;  and  New  York  and 
Pekin  c^  an  extreme  climate. 

2181.  Climatological  conditions.  —  A  complete  analysis  of  those 
eonditions  on  which  climate  depends,  requires  also  that  the  epochs 
of  the  extreme  temperature,  and,  in  a  word,  the  general  distribution 
of  heat  through  the  seasons,  should  be  stated.  For  this  purpose  we 
ehoald  have  an  exact  record,  not  only  of  the  extreme  temperatures 
and  the  mean  annual  and  monthly  temperatures,  but  also  the  mean 
diuniaL  The  importance  of  such  data  in  any  climatological  inquiries 
vill  be  perceived,  when  it  is  considered  that  a  few  degrees  difference 
m  the  lowest  temperature  will  decide  the  question  of  the  possibility 
of  certain  vegetable  productions  continuing  to  live,  and  the  difference 
cf  a  few  degrees  in  the  highest  temperature  will  render  it  poKsible 
or  not  for  certain  fruits  to  ripen. 

2182.  Tabh  of  Paris  temperatures.  —  The  following  table,  pub- 
fiihed  by  M.  Arago,  shows  the  extremes  of  the  temperature  of  the 
air  io  Paris  for  more  than  a  century : — 


Orttatest  Heat 

GreatMt  Cold. 

T«w. 

Month. 

Tempenture 
Fahrenheit. 

Year. 

Month. 

Temperature 
Fahrcuheit. 

1 

1706 
17o3 
1754 
1755 
.1793 
1793 
UOO 
1802 

im 

1818 

August  8. 
July  7. 

"  14. 

"14. 

"    8. 

"  16. 
August  18. 
8. 
8. 
July  15. 

*•  24. 

o 

96-5 
96-1 
96-0 
94-5 
101-1 
99-1 
95-9 
97-5 
981 
97-2 
94-1 

1709 
1716 
1764 
1765 
1768 
1776 
1783 
1788 
1795 
1798 
1823 

January  13. 
13. 

8. 

8. 

8. 
29. 
December  30. 

31. 
January  26. 
December  26. 
January  14. 

o 

—  9  0 

—  1-7 
-f   C-G 
-1-  3-9 
-f   1-2 

—  2-4 

—  2-4 

—  8-1 
10-3 

-f  0-3 
-f  6-9 

MXTEOBOLOQY. 


2188.  Extreme  temperature  in  torrid  zone. — ^The  highest 
rature  of  the  air  which  has  heen  observed  withio  the  torrid 
180^,  which  was  observed  by  MM.  Lyon  and  tlitohie,  in  th 
of  Mourzouk.    This,  however,  is  an  extreme  and  exception 
the  temperature,  even  in  this  zone,  rarely  exceeding  120^. 

2184.  Extreme  temperature  in  polar  regions,  —  The  lowc 
peratores  observed  by  arctic  voyagers  in  the  polar  regions  ranj 
10^  to  60^  below  zero  of  Fahrenheit,  which  is  from  70°  to  90 
the  temperature  of  melting  ice.  Thus  it  appears  that  the  ai 
sur&ce  of  the  earth  ranges  between — 60°  and  -f- 120°,  the  e: 
differing  by  180°. 

2185.  The  variation  of  temperature  depending  on  the  c- 
o/  the  observer  above  the  level  of  the  sea. — ^Innumerable  phe; 
i^ow  that  the  temperature  of  the  air  falls  as  the  elevation  in 
The  presence  of  eternal  snow  on  the  elevated  parts  of  m 
ranges,  in  every  part  of  the  globe,  not  excepting  even  the  torr 
is  a  striking  evidence  of  this. 

Numerous  observations  have  been  made  on  the  slopes  of 
tains,  and  by  means  of  balloons  and  kites,  to  ascertain  the 
cording  to  which  the  temperature  falls  as  the  height  in 
Captain  Parry  raised  a  self-registering  thermometer  to  the  he 
about  400  feet,  by  means  of  a  kite,  at  Indoolick,  latitude  ( 
At  this  elevation  the  temperature  was  24°  below  zero,  be 
same  temperature  as  at  the  surface.  At  the  equator  Humbol< 
an  extensive  series  of  observations,  the  general  results  of  wl 
as  follows : — 


Eleration  in  Feet 

Heui  Temperature. 

'        Difference. 

0 

o 

81 

o 
0 

8,250 

71 

10 

6,600 

66 

6 

9,760 

68 

7 

18,000 

'4 

"4 

16,260 

It  appears  from  these  observations,  which  were  made  u] 
declivities  of  the  vast  mountain  ranges  which  traverse  the  eq 
regions,  that  the  decrease  of  temperature  is  neither  unifc 
regular.  The  rate  of  decrease  is  least  between  the  elevation 
wm,  6000  feet.  This  is  explained  by  the  fact^  that  this  stn 
the  atmosphere  at  the  Line  is  the  habitual  region  of  olouds. 


TSRRB8TRIAL  HBAT.  83 

there  ihai  ihe  rapooTS  ascending  from  the  surface,  being  more  or  less 
eoDdensedy  absorb  a  large  portion  of  the  solar  heat,  and  it  is  not 
iherefore  surprising  that  this  stratum  should  be  cooled  in  a  less  degree 
than  the  strata  consisting  of  air  less  charged  with  vapour. 

The  observations  made  in  temperate  climates  give  results  equally 
irregular.  Gaj-Lussac  found,  ascending  in  a  balloon,  that  the  tber- 
mometric  column  fell  one  degree  for  an  elevation  of  about  320  feet. 
On  the  Alps  the  height  which  produces  a  fall  of  one  degree  is  from 
260  to  280  feet,  and  on  the  Pyrenees  from  220  to  430  feet.  It  may 
iherefore  be  assumed,  that  in  the  equatorial  regions  an  elevation  of 
about  360  feet,  and  in  our  latitudes  from  300  to  330  feet,  corresponds 
to  a  fiill  of  one  degree  of  temperature  on  an  average,  subject^  how- 
ever, to  considerable  local  variation. 

2185*.  Elevation  of  the  limit  of  perpetual  snow. — It  might  appear 
that  in  those  elevations  at  which  the  mean  temperature  fuls  to  32°, 
watar  cannot  exist  in  the  liquid  state,  and  we  might  expect  that 
above  Uiia  limit  we  should  find  the  surface  invested  with  perpetual 
mow.     Observation  nevertheless  shows  such  an  inference  to  be  erro- 
neous.    Humboldt  in   the  equatorial  regions,  and  M.  Leopold  de 
Buch  in  Norway  and  Lapland,  have  shown  that  the  snow-line  does 
not  correspond  with  a  mean  temperature  of  32°  for  the  superficial 
Atmosphere,  but  that  on  the  contrary,  within  the  tropics,  it  is  marked 
ly  a  mean  temperature  of  about  35°,  while  in  the  northern  regions, 
in  latitudes  of  from  60°  to  70°,  the  mean  temperature  is  21°. 

2186.  Conditions  ichich  affect  it.  — It  appears  that  the  snow-line 
is  determined  not  so  much  by  the  mean  annual  temperature  of  the 
iir  as  by  the  temperature  of  the  hottest  month.  The  higher  this 
temperature  is,  the  more  elevated  will  be  the  limit  of  perpetual  snow. 
But  the  temperature  of  the  hottest  month  depends  on  a  great  variety 
of  local  conditions,  such  as  the  cloudy  state  of  the  atmosphere,  the 
nature  of  the  soil,  the  inclination  and  aspect  of  the  surface,  the  pre- 
Tailiog  winds,  &c. 

[Other  things  being  equal,  the  snow-line  will  be  so  much  the 
more  elevated  as  the  mass  of  snow  itself  is  of  less  extent.  A  peak 
of  small  dimensions,  for  example,  rising  in  a  plain  to  the  region  of 
mows,  will  always  have  at  its  summit  much  warmer  summer  months 
than  an  enormous  mass,  which,  after  being  cooled  down  during  the 
winter,  may  react  for  a  longer  time  on  the  temperate  air  which 
envelops  it  in  summer,  and  may  consequently  determine  a  more  or 
kn  considerable  depression  of  temperature.] 

2187.  Table  of  heights  of  mow-line  observed. — In  the  following 
table  are  collected  and  arranged,  the  results  of  the  most  important 
and  accurate  observations  on  the  snow-line. 


84 


METBOROLO0T. 


Obnorrer. 


Humboldt 

« 

tt 

P«ntluid  

u 
Humboldt 

u 

f( 

»  a 

Webb  ......""""!!"!!!"! 

u 

Engelhardt  and  Parrot 
Bamond 

Wahlenberg. 

Leopold  de  Buch 


Lat. 


o 
0  to  10 

M 
U 
« 
U 
M 

14  to  19 
u 

19  to  20 
«( 

« 

u 

27  to  36 

M 

42  to  43 
if 

45  to  46 
49 
61 
70 


Plaoe. 


Rucupichincha 

Huauplnehineha 

Antiaana #. 

Cioraion ^ 

Cotopaxi 

Chimboraso 

Eantem  Ck>rdillera8  of  Upper  Peru 
Western  ditto  ditto 

Oribaxa 

Popocatepetl 

Femmeblanche 

Nevado  de  Toluca 

Himalaya  (south  nide) 

"         (north  aide) 

Caueaaua 

Pvrenees 

Alps 

Carpathians 

Peak  of  Saletind » . 

The  Stonrana-Field 


Height 
in  Feet 


16,730 

M 


U 
U 
U 


17,060 
16,830 
16,026 


u 

12,630 
16,400 
10,660 
80M 
8760 
8600 
6640 
3480 


Ten*' 
nit*ial 


0 

u 
a 

« 

m 


8H 


414 


2188.  Further  results  of  JHumboldt^s  and  Pentland*s  research^ 
— ^To  these  general  results  may  be  added  the  foUowiDg  observadfNM 
of  M.  Humboldt*  :— 
<'  1.  The  sDow-liue  on  the  Andes  does  not  vary  more  than  70  to  IOC 

feet  in  its  elevation. 
''The  plains  of  Antisana,  at  an  elevation  of  13,800  feet,  dotlMJ 

with  a  rich  vegetation  of  aromatic  herb,  are  covered  with  a  depd 

of  three  or  four  feet  of  snow  for  five  or  six  weeks. 
''In  Quito,  mean  teiqperature  48^,  snow  is  never  seen  below  th 

elevation  of  12,000  feet. 
"  Hail  falls  in  the  tropical  regions  at  elevations  of  from  2000  ll 

8000  feet,  but  is  never  witnessed  on  the  lower  plateaux.     It  fall 

once  in  five  or  six  years. 
"  No  mountains  have  been  observed  in  tropical  Africa  which  rise  ^ 

the  snow-line. 
''  2.  Pentland  found  that  from  14*^  to  19^  lat.  S.  the  snow-fine  1 

higher  than  upon  the  Line.     This  might  probably  be  expUdna) 

by  the  nature  and  configuration  of  the  surface. 
"8.  Between  the  Line  and  20^  lat.  N.  the  snow-line  falls  only  7(N 

feet.     The  variation  of  the  height  of  the  snow-line  increases  win 

the  latitude. 

MBA  -  '1^ 

"  The  summit  of  Mowna  Roa  (0  why  bee),  Sandwich  Islands,  whoip 
height  exceeds  16,000  feet,  is  sometimes  divested  of  snow. 

"  4.  The  elevation  of  the  snow-line  on  the  southern  declivity  of 
Himalaya  agrees  with  observations  made  in  Mexico;  but 
northern  declivity  presents  a  singular  anomaly,  the  snow-line  nai 

•  "  Notice  on  the  Snow-line,"  Ann,  de  Ch,  et  Phyt.  torn.  xiv.  p.  L 


TERRESTRIAL  HEAT.  85 

OO  feet,  a  greater  eleTation  than  upon  the  Line.  [The  ez- 
m  of  diis  phenomenon  must  be  songht  in  the  immense 
of  the  plateaoxy  and  in  the  configuration  of  the  surface.] 

snow-line  on  the  Caucasus  is  higher  by  1300  feet  than  on 
renees^  which  are,  nevertheless,  in  the  same  latitude. 

snow-line  on  the  chain  of  mountains  which  extends  along 
f,  ^m  bS""  to  70''  lat.,  is  at  an  elevation  of  5000  feet 
■eat  elevation  in  latitudes  so  high  b  probably  explicable  by 
mospheric  phenomena,  and  the  proximity  of  the  sea.'' 

Thermal  phenomena  below  the  surface. — At  a  given  place 
36  of  the  ground  undergoes  a  periodical  variation  of  tem- 
attaining  a  certain  maximum  in  summer,  and  a  minimum 
and  gradually,  but  not  regularly  or  uniformly,  augmenting 
minimum  to  the  maximum,  and  decreasing  from  the  mazi- 
he  minimum. 

leation  then  arises  as  to  whether  this  periodic  variation  of 
ire  ifi  propagated  downwards  through  the  crust  of  the  earth, 
,  whether  in  its  descent  it  undergoes  any  and  what  modifi- 

tlun  the  phenomena  which  have  been  ascertained  by  obeer- 
t  us  express  the  mean  temperature  by  M,  and  let  the  maxi- 
.  minimum  temperatures  be  T  and  i, 
penetrate  to  depths  more  or  less  considerable,  we  shall  find 
mean  temperature  M  of  the  strata  will  be  very  nearly  the 
at  the  surface.  The  extreme  temperatures  T  and  /,  will, 
undergo  a  considerable  change,  T  decreasing,  and  t  increas- 
us  the  extremes  gradually  approach  each  other  as  the  depth 
the  mean  M  remaining  nearly  unaltered. 

Stratum  of  invariable  temperature,  —  A  certain  depth 
^ore  be  attained  at  length,  when  the  maximum  temperature 
continual  decrease,  and  the  minimum  temperature  t,  by  its 

increase,  will  become  respectively  equal  to  the  mean  tem- 
M.  At  this  depth,  therefore,  the  periodical  variations  at 
ce  disappear ;  and  the  mean  temperature  M  is  maintained 
itly  without  the  least  change. 

nean  temperature,  however,  though  nearly  is  not  precisely 
the  mean  temperature  at  the  surface.  In  descending  M 
8  a  slight  increase,  and  at  the  depth  where  T  and  t  become 
M,  and  the  variation  disappears,  the  mean  temperature  is  a 
her  than  the  mean  temperature  of  the  surface. 

ItM  depth  varies  with  the  latitudc-^Tha  depth  at  which  the 
d  vicissitudes  of  temperature  disappear  varies  with  the  lati- 
;h  the  nature  of  the  surface,  and  other  circumstances.  In 
ates  it  varies  from  80  to  100  feet  It  diminbhes  in  pro- 
towarda  the  equator^  and  increases  towards  the  pole.    TViQ 


86  METKOKOLOGY. 

excess  of  the  permaoent  temperature  at  this  depth  above  the 
temperature  at  the  surface,  increases  with  the  ktitade. 

2192.  Its  depth  and  temperature  at  Paris, — ^The  same  thenwh 
meter  which  has  been  kept  for  siztj  years  in  the  yaolts  of  the  Ob- 
servatory at  Paris,  at  the  depth  of  eighty-eight  feet  below  the  sm^ 
face,  has  shown,  during  that  intervsu,  Uie  temperature  of  lP-82 
Cent,  which  is  equal  to  53 {^  Fahr.,  without  varying  more  than  hilf 
a  degree  of  Fahr. ;  and  even  this  variation,  smidl  as  it  is,  has  baoa 
explained  by  the  effects  of  currents  of  air  produced  by  the  qoanying 
operations  in  the  neighbourhood  of  the  Observatory. 

[This  phenomenon  was  first  observed  by  Cassini,  in  1671.] 

2193.  Its  form, — ^We  must  therefore  infer,  that  within  the  nn<- 
face  of  the  earth  there  exists  a  stratum  of  which  the  tempermtnre  a 
invariable,  and  so  placed  that  all  strata  superior  to  it  are  more  or  lea 
affected  by  the  thermal  vicissitudes  of  the  sur&oe,  and  the  moire  n 
the  nearer  they  are  to  the  sur&ce,  and  that  this  stratum  of  invariaUe 
temperature  has  an  irregular  form,  approaching  nearer  to  the  au^ 
face  at  some  places,  and  receding  further  from  it  at  others;  the  na- 
ture and  character  of  the  surface,  mountains,  valleys,  and  plaini, 
seas,  lakes,  and  rivers,  the  greater  or  less  distance  frx>m  the  equator 
or  poles,  and  a  thousand  other  circumstances,  imparting  to  it  varia- 
tions of  form,  which  it  will  require  observations  and  experiments 
much  more  long  continued  and  extensive  than  have  hitherto  bce& 
made,  to  render  manifest. 

2194.  Thermal  phenomen<i  between  the  surface  and  the  stratum 
of  invariable  temperature. — The  thormometric  observations  on  the 
periodical  changes  which  take  place  above  the  stratum  of  invariable 
temperature  are  not  so  numerous  as  could  be  desired;  [and  even 
these  observatioDs  generally  extend  only  to  a  depth  of  about  25 
feet :]  nevertheless,  the  following  general  conditions  have  been  as- 
certained, especially  in  the  middle  latitudes  of  the  northern  hemi- 
sphere:— 

1.  The  diurnal  variations  of  temperature  are  not  sensible  to  a 
greater  depth  than  3}  feet. 

S2.  The  mean  annual  temperatures  of  the  different  strata  di&r 
e  from  the  mean  annual  temperature  of  the  air.] 

3.  The  difference  t  —  t  between  the  extreme  temperatures  of  the 
strata  decreases  in  geometrical  progression  for  depths  measured  in 
arithmetical  progression,  or  nearly  so. 

4.  At  the  depth  of  26  feet,  t  —  <  =  2°.  At  60  feet  t  —  <  =  0® -2  ; 
and  at  60  to  80  feet,  T  —  t=  0*^-02. 

5.  Since  the  effects  of  the  superficial  variation  must  require  a 
certain  time  to  penetrate  the  strata,  it  is  evident  that  the  epoch  at 
which  each  stratum  attains  its  maximum  and  minimum  temperatures 
will  be  different  from  those  at  which  the  other  strata  and  the  surface 
attain  them.    The  lower  the  strata  the  greater  will  be  the  differeooo 


TEBRBSTRIAL  HEAT.  87 

between  the  times  of  attainiDg  those  limits,  as  compared  with  tbe 
smface.  Thus,  it  is  fouod,  that  at  the  depth  of  twenty-five  feet  the 
maximnm  is  DOt  attaioed  until  the  sur&ce  has  attained  its  minimum. 
The  aeasons,  therefore,  at  this  depth  are  reversed,  the  temperature 
of  July  being  manifested  in  January,  and  vice  verid, 

2195.  Thermal  phenomena  below  the  stratum  of  uniform  fempc- 
raiure. — The  same  uniformity  of  temperature  which  prevails  in  the 
iovariable  stratum  is  also  observed  at  all  greater  depths;  but  the 
temperature  increases  with  the  depth.  Thus,  each  successive  stra- 
tum, in  descending,  has  a  characteristic  temperature,  which  never 
changes.  Tbe  rate  at  which  this  temperature  augments  with  the 
depth  below  tbe  invariable  stratum  is  extremely  different  in  different 
loodities.  In  some  there  is  an  increase  of  one  degree  for  every 
thirty  feet,  while  in  others  the  same  increase  corresponds  to  a  depth 
of  100  feet.  It  may  be  assumed,  in  general,  that  an  increase  of  one 
degree  of  temperature  will  take  place  for  every  fifty  or  sixty  feet  of 
depth. 

[The  existence  of  a  sensible  heat  in  deep  mines  had  long  attracted 
the  attention  of  observers ;  but  there  was  more  eagerness  to  explain 
the  fadB  than  to  observe  them  accurately.  It  was  explained  vari- 
ouslj ;  some,  as  Boyle,  attributed  it  to  the  decomposition  of  pyrites, 
or  rather,  to  a  kind  of  fermentation  to  which  recourse  was  often  had 
to  explain  embarrassing  facts ;  others  regarded  it  as  a  confirmation 
or  a  consequence  of  the  fiEunous  hypothesis  of  the  central  Jire — an 
hypothesis  which  had  been  framed  in  the  most  ancient  times,  and 
which  had  been  in  turn  adopted  or  rejected  by  philosophers.  Ocn- 
saone  appears  to  be  tbe  first  observer  who  carried  the  thermometer 
to  gradually  increasing  depths,  and  who  discovered  the  important 
hd  that  the  temperature  augments  with  the  depth.  These  experi- 
ments go  back  to  1740,  and  were  made  in  the  lead-mines  of  Giro- 
magny,  at  three  leagues  from  B^fort.] 

2196.  Temperature  of  springs. — The  permanency  of  the  tempe- 
ratures of  the  inferior  strata  is  rendered  manifest  by  the  uniformity 
of  the  temperature  of  springs,  of  which  the  water  rises  from  any 
considerable  depths.  At  all  seasons  of  the  year  the  water  of  such 
springs  maintains  [very  nearly]  the  same  uniform  temperature ;  [it 
attains  its  maximum  about  the  month  of  September,  and  its  mini- 
mum in  March ;  the  difference  between  these  two  epochs  reaching 
from  2°  to  4°.] 

It  may  be  assumed  that  the  [mean]  temperature  of  the  water  pro- 
ceeding from  such  springs  is  that  of  the  strata  from  which  they  rise. 
In  these  latitudes  it  is  found  in  general  to  be  a  little  above  the  mean 
temperature  of  the  air  for  ordinary  springs;  that  is  from  those  which 
probably  rise  from  strata  not  below  the  invariable  stratum.  In 
higher  latitudes  the  excess  of  temperature  is  greater  [from  6^  to 

in  4 


88  METEOROLOGY. 

8^];  a  fact  which  is  in  accordance  with  what  has  been  akedlj 
explained. 

It  has  not  been  certainly  ascertained  whether  the  hot  springs,  sone 
of  which  rise  to  a  temperature  little  less  than  that  of  boiling  water, 
derive  their  hnat  from  the  great  depth  of  the  strata  from  which  thej 
rise,  or  from  local  conditions  affecting  the  strata.  The  nnifornntj 
of  the  temperature  of  many  of  them  appears  to  favour  the  forma 
hypothesis ;  but  it  must  not  be  forgotten  that  other  geological  ocmi- 
ditions  besides  mere  depth  may  operate  with  the  same  permanency 
and  regularity. 

2197.  Thermal  conditions  of  seas  and  lakes, — The  anomaloiu 
quality  manifested  in  the  dilatation  of  water  when  its  temperatarfl 
falls  below  88^*8  Fahr.  (1395),  and  its  consequent  maximum  denaitji 
at  that  temperature,  is  attended  with  most  remarkable  and  importaol 
consequences  in  the  phenomena  of  the  waters  of  the  globe,  and  in 
the  economy  of  the  fribes  of  organised  creatures  which  inhabil 
them.  It  is  easy  to  show  that,  but  for  this  provision,  exceptional 
and  anomalous  as  it  seems,  diisturbances  would  take  place,  and 
changes  ensue,  which  would  be  attended  with  effects  of  the  most 
injurious  description  in  the  economy  of  nature. 

K  a  large  collection  of  water,  such  as  an  ocean,  a  sea,  or  a  laks^ 
be  exposed  to  continued  cold,  so  that  its  superficial  stratum  shall 
have  its  temperature  constantly  reduced^  the  following  effects  will  be 
manifested. 

The  superficial  stratum  falling  in  temperature,  will  become  heavier, 
volume  for  volume,  than  the  strata  below  it,  and  will  therefore  fink, 
the  inferior  strata  rising  and  taking  its  place.  These  in  their  turn 
being  cooled  will  sink,  and  in  this  manner  a  continual  system  of 
downward  and  upward  currents  will  be  maintained,  by  means  of 
which  the  temperature  of  the  entire  mass  of  liquid  will  be  continu- 
ally equalized  and  rendered  uniform  from  the  surface  to  the  bottooL 
This  will  continue  so  long  as  the  superficial  stratum  is  rendered 
heavier,  volume  for  volume,  than  those  below  it,  by  being  lowered 
in  temperature.  But  the  superficial  stratum,  and  all  the  inferior 
strata,  will  at  length  be  reduced  to  the  uniform  temperature  of  38^*8. 
After  this  the  system  of  currents  upwards  and  downwards  will  cease. 
The  several  strata  will  assume  a  state  of  repose.  When  the  supe^ 
ficial  stratum  is  reduced  to  a  temperature  lower  than  38^*8  (whicli 
is  that  of  the  maximum  density  of  water),  it  will  become  lighter^ 
volume  for  volume,  instead  of  being  heavier  than  the  inferior  strata 
It  will  therefore  float  upon  them.  The  stratum  immediately  belon 
it,  and  in  contact  with  it,  will  be  reduced  in  temperature,  but  in  i 
less  degree;  and  in  like  manner  a  succession  of  strata,  one  beloK 
the  other,  to  a  certain  depth,  will  be  lowered  in  temperature  by  th< 
oold  of  those  above  them,  but  each  stratum  being  lighter  than  thon 
will  remain  at  rest,  and  no  interchange  by  currents  will  tak^ 


TBBBB8TRIAL  HBAT.  99 

phue  between  stntom  and  stratam.  If  water  were  a  good  cod- 
doctor  of  best,  the  cooliog  effect  of  tbe  sarfaoe  woald  extend  down- 
wards to  a  considerable  deptb.  But  water  being,  on  tbe  contrary, 
in  extremelj  imperfect  conductor,  tbe  effect  of  the  saperficial  tem- 
peratnre  will  extend  only  to  a  very  limited  deptb ;  and  at  and  below 
that  limit,  the  uniform  temperature  of  38^*8,  that  of  the  greatest 
deoffityy  will  be  maintained. 

This  state  d  repose  will  oontinne  until  the  superficial  stratum  falls 
to  32^,*  after  which  it  will  be  congealed.  When  its  surfiiee  is  »>- 
lidified,  if  it  be  still  exposed  to  a  cold  lower  than  32'',  the  tempera- 
tne  of  the  surface  of  the  ice  will  continue  to  fiill,  and  this  reduced 
teaipcfmtnre  will  be  propagated  downward,  diminishing,  howerer,  in 
degree,  so  as  to  reduce  the  temperature  of  Uie  stratum  on  which  the 
lee  rests  to  32^,  and  therefore  to  continue  the  process  ci  congelation, 
nd  to  thicken  the  ice. 

If  iee  were  a  good  conductor  of  heat^  this  downward  process  of 
oongelalion  would  be  6ontinued  indefinitely,  and  it  would  not  be 
impossible  that  the  entire  mass  of  water  from  the  surface  to  the  bot- 
tom, whateyer  be  the  depth,  might  be  solidified.  Ice,  howeTer,  is 
nearly  as  bad  a  conductor  of  heat  as  water,  so  that  the  superficial 
temperature  can  be  propagated  only  to  a  very  inconsiderable  deptb  ; 
and  it  is  found  accordingly,  that  the  crust  of  ice  formed  even  on  the 
iar£ue  of  tbe  polar  seas,  does  not  exceed  the  SYcrsge  thi^VrKHw  of 
twenty  feet 

[2197*.  Temptratvre  and  congdation  of  riven, — ^In  rivers,  the 
disttibntion  of  heat  follows  other  laws,  on  account  of  the  motion  oi 
translation  of  the  liquid  molecules.  There  results  from  this,  in  fact, 
a  continual  mixture  of  the  upper  and  lower  strata,  which  tends  to 
establish  a  uniform  temperature  in  the  whole  mass.  Nevertheless, 
as  this  motion  is  different  at  the  sur&ce  and  at  the  bottom,  in  the 
middle  of  the  river  and  near  the  shores,  we  should  expect  many  ac- 
cidental phenomena  determined  by  these  drcumstancea.  Among 
these  phenomena,  those  of  congelation  alone  have  been  observed 
with  any  care.  It  has  been  established,  by  decisive  experiments, 
ftat,  in  certain  cases,  congelation  commences  at  the  surface,  and 
that,  in  other  cases,  on  the  contrary,  it  commences  at  the  bottom. 

When  rivers  are  covered  with  floating  ice^  we  may  say,  in  general, 
that  all  these  blocks,  which  dash  against  each  (Aher,  and  conse- 
ouently  assume  rounded  or  angular  forms,  were  originally  formed  at 
tbe  snr&ce :  some  were  detached  from  the  shores ;  but  others  were, 
at  first,  only  small  particles,  which  gained  axe  as  Uiey  floated  on  the 
water. 

The  formation  of  tbe  first  pieces  is  not  doubtful,  nnce  we  see  the 
shores  covered  with  a  layer  of  ice  which  b  constantly  beaten  and 

*  For  searwatcr  the  tntinag  point  is  28i<>. 


40  MBTBOBOLOOT. 

broken  by  tho  waves.  It  is  then  tLat  congelation  commences,  Im- 
cnuse  gecerallj  (he  water  is  there  leES  deep,  and  because  it  is  ia  oa- 
tact  with  liic  shore,  which  is  conBtaotly  cooled  by  the  air  and  radia- 
tion. The  ice  wiiicb  is  oltaehed  thereto,  is  cooled  in  its  turn  by  this 
double  cause,  and  becomea  then,  as  the  shore  itself,  a  cold  hoiiy,  ca- 
pable of  chilling  what  touches  it.  The  lump  or  even  impeioeptiUe 
fragment?,  into  wbicb  this  mass  is  broken,  float  by  their  specifie 
levity :  tbcy  become  cooler  than  the  water,  and  the  ixapa  whLoii  M 
on  tbeir  borders  congeal  iustaotly. 

The  formation  of  pieces  of  ice  at  the  tmriace,  and  far  from  tka 
ahores  nnd  all  solid  bodies,  has  been  called  in  question  by  WIM 
physicists :  and  it  is  difficult  to  prove  it  directly,  for  it  may  be  aaid 
that  the  pieces  which  are  found  there  were  detached  from  the  shom 
by  the  waves.  But  it  must  be  admitted  that  the  free  surfaoe  of  tbs 
water  may  be  indefinitely  cooled  below  32°,  and  that  tbns  fioiltj, 
notwithstanding  the  agitation,  it  must  give  birth  to  needles  of  ice 
which  subsequently  grow  oa  cooliog,  by  coiftaot  of  the  air  and  nuli- 

The  formation  of  ice  at  the  very  bottom  of  the  water  was  long 
contested ;  but  able  observers  have  obtained  direct  proof  of  it,  um 
it  remains  only  to  seek  the  cause.  The  agitated  waters  of  rivera 
may  doubtless  fall  several  degrees  below  32°  without  freezing; 
knd  when  the  depth  is  not  great,  the  whole  thickness  of  the  liquid 
stratum  may  participate  in  this  depression  of  temperature.  The 
solid  substaDccs  at  the  bottom  at  length  participate  in  it  themselvei 
by  their  prolonged  contact  with  the  water,  and  the  agitation  at  the 
bottom  is  less  than  at  the  surface.  The  inequalitJes  of  the  bed 
form  a  multitude  of  little  hollows  where  the  water  is  only  feebly 
a^tated ;  and  in  them  we  may  conceive  congelation  to  take  place, 
and  even  more  rapidly  than  at  the  surface.] 

2198.  Thermal  conth'tion  of  a  froixa  ua. — The  thermal  oondi- 
tion,  therefore,  of  a  frozen  sea,  is  a  state  of  molecnkr  repose,  as  ab- 
solute as  if  the  whole  moss  of  liquid  were  solid.  The  temperatot* 
at  the  surface  of  the  ico  being  below  the  freezing  point,  increaaes  in 
descending  until  it  rises  to  the  freezing  point,  at  the  s^tom  where 
the  ice  ceases,  and  the  liquid  water  commences.  Below  this  tba 
temperature  still  angmcnts  until  it  reaches  3d°'8,  the  temperatars 
of  maximum  density  of  water,  and  this  tempenture  is  continued 
uniform  to  the  bottom. 

2199.  Procoi  of  thawing,  —  Let  ua  now  consider  what  effeola 
will  be  produced,  if  the  superficial  strata  be  exposed  to  an  increase 
of  temperature.  After  the  fusion  of  tho  ice,  the  temperature  of  the 
surface  will  gradually  rise  from  32°  to  38°'8,  the  temperature  of 
greatest  density.  When  the  superficial  stratum  rises  above  32°,  it 
will  become  heavier  than  the  stratum  under  it,  and  an  interchange 
by  ciments,  and  a  consequent  eqaalixation  of  temperature,  will  tm 


TEBRESTRIAL  HEAT.  41 

place,  and  tliis  will  continne  until  the  superficial  Btratnm  attains  the 
tempenture  of  38^*8,  when  the  temperature  of  the  whole  mass  of 
water  from  the  mahoe  to  the  hottom  will  become  uniform. 

After  this  a  farther  elevation  of  the  tempraturc  of  the  superficial 
rtratom  will  render  it  lighter  than  those  below  it,  and  no  currents 
will  be  produoedy  the  liquid  remaining  at  rest;  and  this  state  of 
repose  will  continue  so  long  as  the  temperature  continues  to  rise. 

Every  fidl  of  the  superficial  temperature,  so  long  as  it  continues 
above  38^*8,  will  be  attended  with  an  interchange  of  currents  be- 
tween the  superficial  and  those  inferior  strata  whose  temperature  is 
above  38^*8,  and  a  constant  equalization  of  temperature. 

2200.  Depth  of  ttrcUum  of  constant  temperature  in  oceans  and 
sftu.  —  It  appears,  therefore,  to  result  as  a  necessary  consequence 
firom  what  has  been  explained,  and  this  inference  is  fully  confirmed 
by  experiment  and  observations,  that  there  exists  in  oceans,  seas,  and 
other  large  and  deep  collections  of  water,  a  certain  stratum,  which 
retains  permanently,  and  without  the  slightest  variation,  the  tempe- 
rature of  38^*8,  which  characterizes  the  state  of  greatest  density, 
and  that  all  the  inferior  strata  equally  share  this  temperature.  At 
the  lower  latitudes,  the  supeiior  strata  have  a  higher,  at  the  higher 
latitudes  a  lower  temperature,  and  at  a  certain  mean  latitude  the 
stratum  of  invariable  temperature  coincides  with  the  surface. 

In  accordance  with  this,  it  has  been  found  by  observation  that  in 
the  torrid  xone,  where  the  superficial  temperature  of  the  sea  is  about 
83^,  the  temperature  decreases  with  the  depth  until  we  attain  the 
stratum  of  invariable  temperature,  the  depth  of  which,  upon  the 
Line,  is  estimated  at  about  7000  feet  The  depth  of  this  stratum 
gradually  diminishes  as  the  latitude  increases,  and  the  limit  at  which 
it  coincides  with  the  surface  is  somewhere  between  55^  and  60^. 
Above  this  the  temperature  of  the  sea  increases  as  the  depth  of  the 
stratum  increases,  until  we  sink  to  the  stratum  of  invariable  tempe- 
rature, the  depth  of  which  at  the  highest  latitudes  (at  which  obser- 
vations have  been  made)  is  estimated  at  about  4500  feet. 

2201.  Effect  of  tuperficial  agitation  of  the  sea  extends  to  only  a 
tmall  depth.  —  It  might  be  imagined  that  the  temperature  of  the 
surfiuse  would  be  propagated  downwards,  and  that  a  thermal  equal- 
isation might  therefore  be  produced  by  the  intermixture  of  the  supe- 
rior with  the  inferior  strata,  arising  from  the  agitation  of  the  surface 
of  the  waters  by  atmospheric  commotions.  It  is  found,  however, 
that  these  effects,  even  in  the  case  of  the  most  violent  storms  and 
hurricanes,  extend  to  no  great  depth,  and  that  while  the  surface  of 
the  ocean  is  furrowed  by  waves  of  fhe  greatest  height  and  extent, 
the  inferior  strata  are  in  the  most  absolute  repose. 

2202.  Destmctive  effects  which  would  he  produced  if  water  liad 
not  a  paint  of  maadmum  density  above  its  point  of  congelation.  — 
If  water  followed  the  general  law,  in  virtue  of  which  all  bodies  become 

4* 


42  IfETBOROLOOT. 

more  dense  as  tbeir  temperatare  is  lowered,  i  oontiDaed  firoBt  ought 
coDgeal  the  ocean  from  its  Bur&ce  to  the  bottom ;  and  certainly  would 
do  90  in  the  polar  regions ;  for  in  that  case  the  system  of  Tertisil 
currents,  passing  upwards  and  downwards  and  producing  an  equaUa- 
tion  of  temperature,  which  has  been  shown  to  prevail  above  88**'8, 
would  equally  prevail  below  that  point,  and  consequently  the  same 
equalization  of  temperature  would  be  continued,  until  the  entire  dm 
of  water,  from  the  surface  to  the  bottom,  would  be  reduced  to  the 
point  of  congelation,  and  would  consequently  be  converted  into  a 
solid  mass,  all  the  organized  tribes  inhabiting  the  waters  beiog 
destroyed. 

The  existence  of  a  temperature  of  maximum  density  at  a  point  of 
the  thcrmomctric  scale  above  the  point  of  congelation  of  water,  com- 
bined with  the  very  feeble  conducting  power  of  wat«r,  whether  in 
the  liquid  or  solid  state,  renders  such  a  catastrophe  impossible. 

2203.  Variations  of  the  temperature  of  the  air  at  9ea  and  wn 
land. — The  air  is  subject  to  less  extreme  changes  of  temperature  at 
sea  than  on  land.  Thus,  in  the  torrid  zone,  while  the  temperatare 
on  land  suffers  a  diurnal  variation  amounting  to  10^,  the  extreme 
diurnal  variation  at  sea  does  not  exceed  3^^.  In  the  temperate  zone 
the  diurnal  variation  at  sea  is  limited  generally  to  about  51^,  while 
on  continents  it  is  very  various  and  everywhere  considerable.  In 
different  parts  of  Europe  it  varies  from  20*^  to  26®. 

At  sea  as  on  land  the  time  of  lowest  temperature  is  that  of  sun- 
rise, but  the  time  of  greatest  heat  is  about  noon,  while  on  land  it  is 
at  two  or  three  hours  after  noon. 

On  comparing  the  temperature  of  the  air  at  sea  with  the  supe^ 
ficial  temperature  of  the  water,  it  has  been  found  that  between  the 
tropics  the  air,  when  at  its  highest  temperature,  is  warmer  than  the 
water,  but  that  its  mean  diurnal  temperature  is  lower  than  that  of 
the  water.  [The  temperature  of  the  air  and  water  was  observed 
every  4  hours  by  Captain  Duperrey ;  and  in  1850  observations  made 
between  0°  and  20°  lat.  N.  and  S.,  during  his  voyage  round  the  world, 
the  sea  was  found  warmer  than  the  air  1371  times,  and  the  air 
warmer  than  the  sea  only  479  times.] 

In  latitudes  between  25°  and  50°  the  temperature  of  the  air  is 
very  rarely  higher  than  that  of  the  water,  and  in  the  polar  regions 
the  air  is  never  found  as  warm  as  the  surface  of  the  water.  It  is, 
on  the  contrary,  in  general  at  a  very  much  lower  temperature. 

2204.  Interchange  of  eqvatorial  and  polar  waters.  —  Much  un- 
certainty prevails  as  to  the  thermal  phenomena  manifested  in  the 
vast  collections  of  water  which'  cover  the  greater  part  of  the  Bur&ce 
of  the  fflobe.  It  appears,  however,  to  be  admitted  that  the  currents 
caused  by  the  difference  of  the  pressures  of  strata  at  the  same  level 
in  the  polar  and  equatorial  seas,  produce  an  interchange  of  waten, 
which  contributes  in  a  great  degree  to  moderate  the  extreme  thermal 


TERRESTRIAL  HEAT.  43 

efitBcts  of  ihese  regions,  the  corront  from  the  pole  redacing  the  tcm- 
peratnre  of  the  equatorial  waters,  and  that  from  the  line  raising  the 
temperatoie  of  the  polar  waters  and  contrihuting  to  the  fusion  of 
the  ice.  A  soperficud  current  directed  from  the  lino  towards  the 
polen  carries  to  the  colder  regions  the  heated  waters  of  the  tropics, 
while  a  counter  current  in  the  inferior  strata  carries  from  the  poles 
bwards  the  line  the  colder  waters.  Although  the  prevalence  of 
these  currents  may  be  regarded  as  establbhed,  they  are  nevertheless 
modified,  both  in  their  intensity  and  direction,  by  a  multitude  of 
cansea  connected  with  the  depth  and  form  of  the  bottom,  and  the  local 
influence  of  winds  and  tides. 

2205.  Polar  ice, — The  stupendous  mass  of  water  in  the  soh'd 
state  which  forms  an  eternal  crust  encasing  the  regions  of  the  globe 
immediately  around  the  poles,  presents  one  of  tlie  grandest  and  most 
imposing  classes  of  natural  phenomena.  The  observations  and  re- 
searches of  Captain  Scoresby  have  supplied  a  great  mass  of  valuable 
information  in  this  department  of  physical  geography. 

2206.  Extent  and  character  of  the  icefidih.  —  Upon  the  coasts 
of  Spitzbergen  and  Greenland  vast  fields  of  ice  are  found,  the  extent 
of  which  amounts  to  not  less  than  thirty  to  fifty  hundred  square 
miles,  the  thickness  varying  from  twenty  to  twenty -five  feet.  [Some 
of  the  fields  of  ice  observed  by  Captain  Scoresby  were  nearly  a  hun- 
dred miles  in  length,  and  more  than  half  that  breadth.]  The  sur- 
face b  sometimes  so  even  that  a  sledge  can  run  without  difficulty  for 
an  hundred  miles  in  the  same  direction.  It  is,  however,  in  some 
placefi,  on  the  contrary,  as  uneven  as  the  surface  of  land,  the  masses 
of  ice  collecting  in  columns  and  eminences  of  a  variety  of  forms, 
rising  to  heights  of  from  twenty  to  thirty  feet,  and  presenting  the 
most  striking  and  picturesque  appearances.  These  prodigious  crys- 
tals sometimes  exhibit  gorgeous  tints  of  greenish  blue,  resembling 
the  topaz,  and  sometimes  this  is  varied  by  a  thick  covering  of  snow 
upon  their  summits,  which  are  marked  by  an  endless  variety  of  form 
and  outline. 

2207.  Production  %f  xcehergs  by  (heir  frojcture.  —  These  vast  ice 
fields  are  sometimes  suddenly  broken,  by  the  pressure  of  the  sub- 
jacent waters,  into  fragments  presenting  a  surface  of  from  100  to 
200  square  yards.  These  being  dispersed,  are  carried  in  various 
directions  by  currents,  and  sometimes  by  the  effect  of  intersecting 
currents  they  are  brought  into  collision  with  a  fearful  crash.  A  ship 
which  might  chance  in  such  a  case  to  be  found  between  them  could 
no  more  resist  their  force  than  could  a  glass  vessel  the  effect  of  a 
cannon  ball.  Terrible  disasters  occur  from  time  to  time  from  this 
cause.  It  is  by  the  effects  of  these  currents  upon  the  floating  masses 
of  broken  ice  that  these  seas  are  opened  to  the  polar  navigators.  It 
u  ihaa  that  whaJen  are  enabled  to  reach  the  parallels  froui  IQ^  U> 


14  MBTEOROLOQT. 

80^,  which  are  tlie  fitvonrite  resort  of  those  monsters  of  the  dec^ 
which  they  pursue. 

2208.  Their  forms,  and  magnitude.  —  Sometimes  after  such  ool- 
lisions  new  icebergs  arise  from  the  fragments  which  are  heaped  one 
upon  another,  <'  Pelion  on  Ossa/'  more  stupendous  still  than  those 
which  have  been  broken.  In  such  cases  the  masses  which  resnlt 
assume  forms  infinitely  various,  rising  often  to  an  elevation  of  thirty 
to  fifty  feet  above  the  surface  of  the  water ;  and  since  the  weight  c^ 
ke  is  about  four-fifths  of  the  weight  of  its  own  bulk  of  water  (787), 
it  follows  that  the  magnitude  of  these  masses  submerged  is  four 
times  as  great  as  that  which  is  above  the  surface.  The  total  height 
of  these  floating  icebergs,  therefore,  including  the  part  submerged, 
must  be  from  150  to  250  feet. 

2209.  Sunken  icebergs.  —  It  happens  sometimes  that  two  sucb 
icebergs  resting  on  the  extremities  of  a  fragment  of  ice  100  or  120 
feet  in  length,  keep  it  sunk  at  a  certain  depth  below  the  surfue  of 
the  water.  A  vessel  in  such  cases  may  sail  between  the  icebergs 
and  over  the  sunken  ice;  but  such  a  course  is  attended  with  the 
greatest  danger,  for  if  any  accidental  cause  should  detach  either  of 
the  icebergs  which  keep  down  the  intermediate  mass  while  the  ship 
is  passing,  the  latter  by  its  buoyancy  will  rise  above  the  sur&ce,  and 
will  throw  up  the  ship  with  irresistible  force. 

2210.  Singular  effects  of  their  superficial  fusion. — ^Icebergs  are 
observed  in  Baffin's  Bay  of  much  greater  magnitude  than  off  the 
coast  of  Greenland.  They  rise  there  frequently  to  the  height  of 
100  to  130  feet  above  the  surface,  and  their  total  height,  including 
the  part  immersed,  must  therefore  amount  to  500  or  650  feet.  These 
masses  appear  generally  of  a  beautiful  blue  colour,  and  having  all 
the  transparency  of  crystals.  During  the  summer  months,  when 
the  sun  in  these  high  latitudes  never  sets,  a  superficial  fusion  is  pro- 
duced, which  causes  immense  cascades,  which,  descending  from  their 
summit  and  increasing  in  volume  as  they  descend,  are  precipitated 
into  the  sea  in  parabolic  curves.  Sometimes,  on  the  approach  of  the 
cold  season,  these  liquid  arches  are  seized  and  solidified  by  the  in- 
tensity of  the  cold  without  losing  their  form,  %nd  seem  as  if  caught 
in  their  flight  between  the  brink  firom  which  they  were  projected  and 
the  surface,  and  suddenly  congealed.  These  stupendous  arches, 
however,  do  not  always  possess  cohesion  in  proportion  to  their  weight 
and  after  augmenting  in  volume  to  a  certain  limit,  sink  under  tneir 
weight;  and,  breaking  with  a  terrific  crash,  fall  into  the  sea. 

-  2211.  Depth  of  polar  seas. — The  depth  of  the  seas  off  the  coast 
of  Greenland  is  not  considerable.  Whales,  being  harpooned,  often 
plunge  in  their  agony  to  the  bottom,  carrying  with  them  the  harpoon 
and  line  attached  to  it.  When  they  float  they  bear  upon  their  bodies 
evidence  of  having  reached  the  bottom  by  the  impression  they  rs- 
tun  of  it;  and  the  length  of  line  they  carry  with  them  in  such 


TBRBB8TBIAL  BBAT.  46 

lOWB  that  the  depth  does  not  exceed  SOOO  or  4000  feet.  About  the 
idillo  of  the  spatre  between  Spjizberfien  and  Orccnlnnd  tbc  sound- 
igs  liiLve  reached  800U  I'^ct  without  finOrn^;  iHitiotii. 

2212.  Colli  of  the  polur  reijium.  —  Tlic  degree  of  cold  of  rlic 
olftr  repoDB,  like  the  temperature  of  nil  oilier  purls  of  the  globe, 
epends  on  the  extent  and  depth  of  the  ^eaa.  If  there  be  eztctieivo 
[Beta  of  anrface  not  corercd  by  water,  or  covered  onlj  hy  a  Binull 
eptfa,  the  influence  of  the  water  in  moderating  and  equalizing  the 
emperatnre  is  sreatlj  diminished.  Hence  it  is  that  the  tempcraturo 
f  the  Math  polar  regions  is  more  moderate  than  that  of  the  north. 
^fler  pusing  the  latitude  of  the  New  Orcndes  and  the  New  Shct- 
knds,  which  form  t,  barrier  of  ice,  the  naTigator  entcra  an  open  cea, 
vhicb,  according  t«  all  appearance,  extends  to  the  pole.  Mueh,  hnw- 
ner,  gtill  remains  to  be  discovered  respecting  the  physical  condition 
)f  these  regions. 

2213.  Solar  and  celf glial  heat. — Whatever  may  be  the  sources 
of  iotcmal  heat,  the  globe  of  the  earth  would,  after  a  certiun  time, 
be  reduced  to  a  state  of  absoJnte  cold,  if  it  did  not  receive  from  cs- 
temal  sources  the  qoantily  of  heat  necessary  to  repair  its  losses.  If 
the  globe  were  suspended  in  space,  all  other  bodies  from  which  heat 
eonld  be  supplied  to  it  being  removed,  the  heat  which  now  pervades 
the  earth  and  its  surronnding  atmosphere  would  be  ncce^aarilj  dissi- 
pated \ty  radiation,  and  would  thus  escape  into  the  inSnitc  depths  of 
Rpnoe.  The  temperature  of  the  atmospbere,  and  those  of  the  siic- 
cndve  stral*,  extending  from  the  snrfaco  to  the  centre  of  the  globe, 
wonld  thus  be  continually  and  indefinitely  diminished. 

As  no  such  fall  of  temperature  takes  place,  and  ss,  on  the  con- 
Intry,  the  mean  temperature  of  the  globe  is  maintained  at  an  inva- 
riable standard,  the  variations  inoidenlol  to  season  and  climate  being 
■II  periodical,  and  producing  in  their  ultimate  result  a  mutual  com- 
pensation, it  remains  to  be  shown  fi-om  what  sources  the  heat  is 
derived  which  maintains  the  mean  temperature  of  the  globe  at  this 
invariable  standard,  notwithstanding  the  large  amount  of  beat  which 
it  loses  by  radiation  into  the  sniTounding  space. 

Alt  the  bodies  of  the  material  universe,  which  are  distributed  in 
coantless  numbera  throughout  the  infinitude  of  space,  are  sources  of 
beat}  and  centres  from  which  that  physical  agent  is  radiated  in  all 
directions.  The  effeot  produced  by  the  radiation  of  each  of  these 
diminishes  in  the  same  proportion  as  the  square  of  its  distance  in- 
creases. Tbe  fixed  Stan  are  bodies  analogous  to  our  snn,  and  at  dis 
tances  so  enormous  that  the  effect  of  the  radiation  of  any  individuaj 
star  is  altogether  insensible.  When,  however,  it  is  considered  that 
the  tsalUtude  of  these  stars  spread  over  tbe  firmament  is  so  prodi- 
^ons  that  in  some  places  many  thousand  are  crowded  together  witbin 
ft  space  no  greater  tiian  that  occupied  by  the  disc  of  the  full  moon, 
it  will  not  ba  matter  of  sarprise  that  the  feebleness  of  thermal  in- 


46  MBTEOBOLOGT.  ^ 

flnenoe,  dae  to  their  immense  distances,  is  compensated  to  a  | 
extent  by  their  countless  number ;  and  that,  consequently,  their 
rifio  effects  in  those  regions  of  space  through  which  the  earth  p 
in  its  annual  course  is,  as  will  presently  appear,  not  only  far 
being  insensible,  but  is  very  little  inferior  to  the  calorific  pow 
the  sun  itself. 

We  are,  then,  to  consider  the  waste  of  heat  which  the  earth  m 
by  radiation  as  repaired  by  the  heat  which  it  receives  from 
sources,  the  sun  and  the  stellar  universe ;  and  it  remains  to  ex 
what  is  the  actual  quantity  of  heat  thus  supplied  to  the  earth 
what  proportion  of  it  is  due  to  each  of  these  causes. 

2214.  Quantity  of  heat  emitted  hy  the  9un. — ^An  elaborate  i 
of  experiments  were  made  by  M.  Pouillet,  and  concluded  in  1 
with  the  view  of  obtaining,  by  means  independent  of  all  hypot 
as  to  the  physical  character  of  the  sun,  an  estimate  of  the  a 
calorific  power  of  that  luminary.  A  detailed  report  of  these  c 
vations  and  experiments,  and  an  elaborate  analysis  of  the  n 
derived  ^m  them,  appeared  in  the  Transactions  of  the  Acaden 
Sciences  of  Paris  for  that  year. 

It  would  be  incompatible  with  the  elementary  nature  and  the 
sequent  limits  of  this  work,  to  enter  into  the  details  of  thcs 
searches.  We  shall,  therefore,  confine  ourselves  here  briefly  to 
their  results. 

When  the  firmament  is  quite  unclouded,  the  atmosphere  ab 
about  one-fourth  of  the  heat  of  those  solar  rays  which  enter  i( 
tically.  A  greater  absorption  takes  place  for  rays  which  ent 
obliquely,  and  the  absorption  is  augmented  in  a  certain  ascerti 
proportion,  with  the  increase  of  obliquity.  It  results  from  the 
lysis  of  the  results  obtained  in  the  researches  of  M.  Pouillet, 
about  forty  per  cent,  of  all  the  heat  transmitted  by  the  sun  t< 
earth,  is  absorbed  by  the  atmosphere,  and  that  consequently 
sixty  per  cent,  of  this  heat  reaches  the  surface.  It  must,  how 
be  observed  that  a  part  of  the  radiant  heat,  intercepted  by  the  a 
sphere,  raising  the  temperature  of  the  air,  is  afterwards  transmi 
as  well  by  radiation  as  by  contact,  from  the  atmosphere  to  the  e 

By  means  of  direct  observation  and  experiment  made  with  in 
ments  contrived  by  him,  called  pyrheliometersj  by  means  of  v 
the  heat  of  the  solar  radiation  was  made  to  affect  a  known  weigl 
water  at  a  known  temperature,  M.  Pouillet  ascertained  the  a 
quantity  of  heat  which  the  solar  rays  would  impart  per  minute 
surface  of  a  given  magnitude,  on  which  they  would  fall  vertic 
This  being  determined,  it  was  easy  to  calculate  the  quantity  of 
imparted  by  the  sun  in  a  minute  to  the  hemisphere  of  the  earth  v 
is  presented  to  it,  fi)r  that  quantity  is  the  same  which  would  b 
parted  to  the  surface  of  the  great  circle  which  forms  the  base  of 
hemisphere,  if  the  solar  rays  were  incident  perpendicularly  upoi 


TERRESTRIAL  HEAT.  47 

2215.  Sofar  heat  at  the  earth  vovUl  melt  a  shell  of  ice  100  ftct 
thirk  in  a  year, — In  ibis  manDer  it  was  ascertained  by  31.  Pouillet, 
that  if  the  total  quantity  of  heat  wbicb  tbe  earth  receives  from  the 
nn  in  a  year  were  aniformly  diffascd  over  all  parts  of  the  surface, 
and  were  completely  absorbed  in  the  fusion  of  a  shell  of  ice  encrust- 
ing the  globe,  it  would  be  sufficient  to  liquefy  a  depth  of  100  feet 
cf  rach  shell. 

Since  a  cubic  foot  of  ice  weighs  54  lbs.,  it  follows  that  the  average 
annuml  Bupply  of  heat  received  from  the  sun  per  square  foot  of  the 
earth's  sar&oe  would  be  sufficient  to  dissolve  5400  lbs.  weight  of  ice. 

2216.  Calculation  of  the  actual  quantity  of  heat  emitted  by  the 
m».  —  This  &ct  being  ascertained  supplies  the  means  of  calculating 
the  quantity  of  heat  emitted  from  the  surface  of  the  sun,  independ- 
ently of  any  hypothesis  respecting  its  physical  constitution. 

It  is  evident  from  the  uniform  calorific  effects  produced  by  the 
solar  rays  at  the  earth,  while  the  sun  revolves  on  its  axis,  exposing 
sacocssively  every  side  to  the  earth  in  the  course  of  about  twenty- 
five  daysy  that  the  calorific  emanation  from  all  parts  of  the  solar  sur- 
£EMe  is  the  same.  Assuming  this,  then,  it  will  follow,  that  the  heat 
which  the  surfiMie  of  a  sphere  surrounding  the  sun  at  the  distance 
of  the  earth  would  receive  would  be  so  many  times  more  tlinn  the 
heat  received  hy  the  earth  as  the  entire  surface  of  such  sphere  wt^uld 
be  greater  than  that  part  of  it  which  the  earth  would  occupy.  The 
calculation  of  this  is  a  simple  problem  of  elementary  geometry. 

But  such  a  spherical  surfiice  surrounding  the  sun  and  conccutricnl 
with  ity  would  necessarily  receive  all  the  heat  radiated  by  that  lumi- 
nary, and  the  result  of  the  calculation  proves  that  the  quantity  of 
heat  emitted  by  the  sun  per  minute  is  such  as  would  suffice  to  dis- 
lolve  a  shell  of  ice  enveloping  the  sun,  and  having  a  thick n(>ss  of 
38 A  feet;  and  that  the  heat  emitted  per  day  would  dissolve  Kuch  a 
Bhell,  having  a  thickness  of  55748  feet,  or  about  10}  miles. 

2217.  Meat  at  sun's  surface  seven  times  as  intense  as  that  <f  a 
blast  furnace. — ^The  most  powerful  blast  furnaces  do  not  emit  for  a 
given  extent  of  fire  surface  more  than  the  seventh  part  of  this 
quantity  of  heat.  It  must  therefore  be  inferred  that  each  square 
foot  of  the  surface  of  the  sun  emits  about  seven  times  as  much  heat 
as  is  issued  by  a  square  foot  of  the  fire  surface  of  the  fiercest  blubt 
furnace. 

2218.  Temperature  of  the  celestial  spaces. — When  the  surface  of 
the  earth  during  the  night  is  exposed  to  an  unclouded  sky,  an  inter- 
change of  heat  takes  place  by  radiation.  It  radiates  a  certain  part 
of  the  heat  which  pervades  it,  and  it  receives,  on  the  other  hand, 
the  beat  radiated  from  two  sources,  Ist,  from  the  strata  of  atmo- 
sphere, extending  from  the  surface  of  the  earth  to  the  suinniit  of 
the  atmospheric  column^  and  2d^  from  the  celestial  spaces,  vrhich  lie 
aatpJde  this  limit,  mad  which  receive  their  beat  from  the  rad\a\\o\i 


48  XSTBOROLOGT. 

of  the  oonntless  nambers  of  suns  which  compose  the  stellar  nniten 
M.  PouiUet^  by  a  series  of  ingeniously  contrived  experiments  a 
observations,  made  with  the  aid  of  an  apparatus  contrived  by  hii 
called  an  (zctinameter,  has  beefb  enabled  to  obtain  an  appioxiou 
estimate  of  the  proportion  of  the  heat  received  by  the  earth  whi 
is  due  to  each  of  tnese  two  sources,  and  thereby  to  determine  t 
actual  temperature  of  the  region  of  space  through  which  the  eai 
and  planets  move.  The  objects  and  limits  of  this  work  do  not  p 
mit  us  to  give  the  details  of  these  researches,  and  we  must  therefc 
confine  ourselves  here  to  the  statement  of  their  results. 

It  appears  from  the  observations,  that  the  actual  temperature 
space  is  included  between  the  minor  limit  of  815^,  and  the  maj 
limit  of  207^  below  the  temperature  of  molting  ice,  or  between  — 28 
and  — 175°  Fahr.  At  what  point  between  these  limits  the  real  te 
perature  lies,  is  not  yet  satisfactorily  ascertained,  but  M.  Pouil 
thinks  that  it  cannot  differ  much  from  — 224°  Fahr. 

2219.  Heat  received  hy  earth  from  celestial  spoA^e  would  melt, 
a  year,  eighty-five  feet  thick  of  ice. — It  is  proved  from  those  resul 
that  the  quantity  of  heat  imparted  to  the  earth  in  a  year,  by  the  i 
diation  of  the  celestial  space,  is  such  as  would  liquefy  a  spheric 
shell  of  ice,  covering  the  entire  surface  of  the  earth,  the  thicknc 
of  which  would  be  eighty-five  feet,  and  that  forty  per  cent,  of  tl 
quantity  is  absorbed  by  the  atmosphere. 

Thus  the  total  quantity  of  heat  received  annually  by  the  earth 
such  as  would  liquefy  a  spherical  shell  of  ice  185  feet  thick,  of  whi 
100  feet  are  due  to  the  sun,  and  85  feet  to  the  heat  which  emanat 
from  the  stellar  universe. 

The  fact  that  the  celestial  spaces  supply  very  little  less  heat 
the  earth  annually  than  the  sun,  may  appear  strange,  when  the  ve 
low  temperature  of  these  spaces  is  considered,  a  temperature  ISi 
lower  than  the  cold  of  the  pole  during  the  presence  of  the  sun. 
must,  however,  be  remembered  that  while  the  space  from  which  i 
solar  radiation  emanates  is  only  that  part  of  the  firmament  occupi 
by  the  disc  of  the  sun,  that  from  which  the  celestial  radiation  pi 
ceeds  is  the  entire  celestial  sphere,  the  area  of  which  is  about  ti 
hundred  thousand  times  greater  than  the  solar  disc.  It  will  thei 
fore  cease  to  create  surprise,  that  the  collective  effect  of  an  area 
extensive  should  be  little  short  of  that  of  the  sun. 

The  caloric  effect  due  to  the  solar  radiation,  according  to  the  o 
culations  and  observations  of  M.  Pouillet,  exceeds  that  which  result 
from  the  formulse  of  Poisson.  These  formulso  were  obtained  fit 
the  consideration  of  the  variation  of  the  temperature  of  the  etn 
of  the  earth  at  different  depths  below  the  surface.  M.  PouiU 
thinks  that  the  results  proceeding  from  the  two  methods  would 
brought  into  accordance  if  the  iuflueucc  of  the  atmosphere  on  sol 
heat^  which,  as  appears  from  what  has  been  explained,  is  very  oc 


ATM08PHBBI0  P&BSSURB.  48 

aderable,  oomld  be  introdiioed  in  a  more  direct  manner  into  Pois- 
•oo'i  formals. 

2220.  SMmmary  of  the  thermal  effects. — In  fine,  therefore,  the 
leieaiches  of  M.  Pomllet  give  the  following  results,  which  must  be 
reoeiTed  aa  mere  approximations,  subject  to  correction  by  future 
obeenation : 

Ist  That  the  son  aapplies  the  earth  annually  with  as  much  heat 
ai  would  liqo^  100  feet  thick  of  ice  covering  the  entire  globe. 

2d.  Thai  the  celestial  spaces  supply  as  much  as  would  uqucfy  85 
feet  thick. 

3d.  That  40  per  oeni  of  the  one  and  the  other  supply  is  absorbed 
by  the  atmosphere,  and  60  per  cent  received  by  the  earth. 

4th.  That  of  the  heat  radiated  by  the  earth,  90  per  cent,  is  ioter- 
eq>ted  by  the  atmosphere,  and  10  per  cent,  dispersed  in  space. 

5th.  That  the  heat  evolved  on  the  surface  of  the  sun  in  a  day 
would  liquefy  a  shell  of  ice  10|  miles  thick,  enveloping  the  sun,  and 
the  intensi^  of  the  solar  fire  is  seven  times  greater  than  that  of  the 
fieroest  blast  furnace. 

6th.  That  the  temperature  of  space  outside  the  atmoflphere  of  the 
earth  ia  — 224°  Fahr.,  or  256°  below  that  of  melting  ice. 

7th.  That  the  solar  heat  alone  constitutes  only  two-thirds  of  the 
entire  qoantitj  of  heat  supplied  to  the  earth  to  repair  its  thermal 
losses  by  terrestrial  radiatfon ;  and  that  without  the  heat  supplied  by 
ftellar  radiation,  the  temperature  of  the  earth  would  fall  to  a  point 
iHiich  would  be  incompatible  with  organic  life. 


CHAP.  II. 

TBI  AIB  AMD  ATMOSPHERIC   VAPOURS. 

2221.  JF^riodical  changes  in  the  atmospheric  pressure.  —  The  pe- 
riodical ehanffCB  to  which  the  pressure  of  the  atmosphere  is  subject, 
and  the  principal  causes  which  produce  them,  have  been  already  briefly 
mdicated  (719.  et  seq.).  We  shall  now  explain  more  fully  some  of 
the  more  important  of  these  phenomena. 

It  has  been  ooatomary  in  these  climates  to  observe  and  register  the 
hoiffht  ci  the  barometric  column  four  times  a  day,  at  9  A.  m.,  at  noon, 
atfp.M.,  andat9  P.M. 

Hie  oiean  m<Mithly  and  mean  annual  heights  are  obtained  from  a 
comparison  of  the  noon  obeervations.  The  diurnal  period  is  obtained 
bom  a  comparison  of  the  morning  and  afternoon  observations. 

2222.  Jfecm  anmuU  freight  of  barometer.  —  The  mean  height  of 
Aa  barometer  at  P^uris,  obtained  from  observations  continued  fron: 

m.  5 


60  MBTEOROLOaT. 

1816  to  1836,  has  been  ascertained  to  be  29764  inehes  [756"*^]. 
The  mean  annual  beight  during  this  period  did  not  vary  so  nrnch  ai 
twelve  hundredths  of  an  inch. 

2223.  Efftcl  of  tcinds  on  the  barometric  column, — It  has  been 
found  that  the  barometric  column  is  affected  by  the  direction  and 
continuance  of  the  wind,  but  these  effects  are  not  the  same  in  all 
localities.  At  Paris,  the  height  is  greatest  when  the  wind  blows 
from  the  north  or  north-east,  and  least  when  from  the  south  and 
south-west.  The  extreme  difference  of  the  mean  heights  during 
such  winds  was  found  to  be  twenty-seven  hundredths  of  an  inch. 
ObservatioDS  made  at  Metz  [for  nine  years]  by  Schuster  gave  a  like 
result,  but  with  a  little  less  difference.  At  Marseilles,  however,  no 
such  effect  has  been  observed,  but  rather  a  tendency  to  a  eontraTj 
change,  the  height  being  generally  above  the  mean  in  southerly 
winds,  and  below  it  in  north-westerly. 

2224.  Diurnal  variations  of  the  barometer.  —  A  long  series  of 
observations  on  the  diurnal  changes  in  the  barometer  establish  the 
existence  of  two  periods,  a  period  of  decrease  from  9  A.  M.  to  8  P.  M., 
and  a  period  of  increase  from  3  p.  M.  to  9  P.  M.  The  mean  amount 
of  the  former,  taken  from  eleven  years'  observation  at  Paris,  was 
0*0294  in.,  and  of  the  latter  00146  in.  The  decrease  from  9  A.  M. 
to  8  P.  M.  is  therefore  less  than  the  thirtieth  of  an  inch,  and  the  in- 
crease from  3  p.  M.  to  9  p.m.  less  than  the 'sixtieth  of  an  inch. 

A  comparison  of  these  variations  in  different  seasons  of  the  year 
shows  that  the  increase  of  the  evening  is  subject  to  very  minute  and 
irregular  changes,  but  that  the  changes  of  the  decrease  in  the  morn- 
ing are  both  more  considerable  and  more  regular,  the  amount  of  the 
decrease  being  always  least  in  November,  December,  and  January, 
and  greatest  in  February,  March,  and  April,  [and  of  an  intermediate 
and  variable  value  during  the  remaining  six  months  of  the  year.] 

During  the  night  the  barometer  falls  from  9  P.  M.  to  4  A.M.,  and 
rises  from  4  A.  M.  to  9  A.  M.,  [when  it  attains  its  maximum.] 

2225.  The  winds.  —  No  meteorological  phenomenon  has  had  so 
many  observers,  and  there  is  none  of  which  the  theory  is  so  little 
understood,  as  the  winds.  The  art  of  navigation  has  produced  in 
every  seaman  an  observer,  profoundly  interested  in  the  discovery  of 
the  laws  which  govern  a  class  of  phenomena,  upon  the  knowledge 
of  which  depends  not  only  his  professional  success  but  his  personal 
security,  and  the  lives  and  property  committed  to  his  charge. 

The  chief  part  of  the  knowledge  which  has  been  collected  respect- 
ing the  causes  which  produce  these  atmospheric  currents  is  derived, 
nevertheless,  much  more  from  the  comparison  of  the  registers  of 
observatories  than  from  the  practical  experience  of  mariners. 

2226  Winds  propaf/ated  b^  compression  and  rare/act  ion. — Winds 
are  propagated  either  by  compression  or  by  rarefaction.  In  the 
former  case  they  are  developed  in  the  same  direction  in  which  they 


WINDS.  61 

blow ;  in  the  Utter  case  they  are  developed  in  the  contrary  direction. 
To  render  this  intelligible^  let  us  imagine  a  column  of  air  included  in 
a  tube.  If  a  piston  inserted  in  one  end  of  the  tube  be  driven  from 
the  mouth  inwards,  the  air  contiguous  to  it  will  be  compressed,  and 
this  portion  of  air  will  compress  the  succeeding  portion,  and  so  on ; 
the  compression  being  propagated  fit)m  the  end  at  which  the  piston 
enters  toward  the  opposite  end.  The  remote  end  being  open,  the  air 
wiU  flow  in  a  current  driven  before  the  piston  in  the  same  direction 
in  wkkfa  the  compression  is  propagated. 

If  we  imagine,  on  the  other  hand,  a  piston  inserted  in  the  tube  at 
some  distance  from  its  mouth,  to  be  drawn  outwards  toward  the 
noathy  the  air  behind  it  will  expand  into  the  space  deserted  by  the 
piston,  and  a  momentary  rarefaction  will  be  produced.  The  next 
portion  of  air  will  in  like  manner  follow  that  which  is  next  the 
piston,  the  rarefaction  which  begins  at  the  piston  being  propagated 
backwards  through  the  tube  in  a  direction  contrary  to  the  motion  of 
the  piston  and  that  of  the  current  of  air  which  follows  it. 

What  is  here  supposed  to  take  place  in  the  tube  is  exhibited  on  a 
larger  scale  in  the  atmosphere.  Any  physical  cause  which  produces 
a  compression  of  the  atmosphere  from  north  to  south  will  produce  a 
north  wind ;  and  any  cause  which  produces  a  rarefactiou  from  north 
to  south  will  produce  a  south  wind. 

2227.  Effect  of  sudden  condensation  of  vapour.  —  Of  all  the 
causes  by  which  winds  are  produced,  the  most  frequent  is  the  sudden 
condensation  of  vapour  suspended  in  the  atmosphere.  In  general 
the  atmosphere  above  us  consists  of  a  mixture  of  air  properly  so 
called,  and  water,  either  in  the  state  of  vapour,  or  in  a  vesicular 
stale,  the  nature  and  origin  of  which  has  not  yet  been  clearly  ascer- 
tained. In  either  case  its  sudden  conversion  into  the  liquid  state, 
md  its  consequent  precipitation  to  the  earth,  leaves  the  space  it  occu- 
pied in  the  atmosphere  a  vacuum,  and  a  corresponding  rarefaction  of 
the  air  previously  mixed  with  the  vapour  ensues.  The  adjacent 
strata  immediately  rush  in  to  re-establish  the  equilibrium  of  pncu- 
■latic  pressure,  and  winds  are  consequently  produced. 

The  propagation  of  winds  by  rarefaction  manifested  in  directions 
eoDtrary  to  that  of  the  winds  themselves,  is  common  in  the  North 
of  Enrope.  Wargentin  gives  various  examples  of  this.  When  a 
vest  wind  springs  up,  it  is  felt,  he  observes,  at  Moscow  before  it 
reaches  Abo,  although  the  latter  city  is  four  hundred  leagues  west 
of  MO0OOW,  and  it  does  not  reach  Sweden  until  after  it  has  passed 
over  Finland. 

[Dr.  Franklin  appears  to  have  been  the  first  to  observe  this  mode 
of  pn^wgation  of  winds  and  storms.  He  relates,  in  his  letters,  that, 
having  wished  to  observe  an  eclipse  of  the  moon  at  Philadelphia,  he 
was  prevented  by  a  nortli^easterly  storm,  which  commenced  about 
7  c^dock,  P.  M .     He  was  surprised,  some  days  after,  to  learn  that  at 


62  METEOROLOGY. 

BoBiOD^  situated  about  300  miles  to  the  northeast  of  Philadelphia, 
the  storm  did  not  commence  until  11  o'clock^  p.  M.,  long  after  the 
observation  of  the  first  phases  of  the  eclipse;  and,  comparing  toge- 
ther the  reports  collected  in  the  different  colonics,  he  found  that  this 
northeasterly  storm  was  propagated  for  the  south-west.'] 

2228.  Hurricanes,  —  The  intertropical  regions  are  the  theatre  of 
hnrricanes.  It  is  there  only  that  these  atmospheric  commotions  are 
displayed  in  all  their  terrors.  In  the  temperate  zone  tempests  are 
not  only  more  rare  in  their  occurrence  but  much  less  violent  in  their 
force.  In  the  circumpolar  zone  the  winds  seldom  acquire  the  force 
which  would  justify  the  title  of  a  storm. 

The  hurricanes  of  the  warm  climates  spread  over  a  considerable 
width,  and  extend  through  a  still  more  considerable  length.  Some 
are  recorded  which  have  swept  over  a  dbtance  of  four  or  five  hun- 
dred leagues,  with  a  nearly  uniform  violence. 

It  is  only  by  recounting  the  effects  produced  by  these  vast  com- 
motions of  the  atmospheric  ocean,  that  any  estimate  can  be  formed  of 
the  force  which  air,  attenuated  and  light  as  that  fluid  is,  may  acquire 
when  a  great  velocity  is  given  to  it.  In  hurricanes  such  as  that 
which  took  place  at  Guadaloupe  on  the  25th  July,  1825,  houses  the 
most  solidly  constructed  were  overthrown.  A  new  building  erected 
in  the  most  durable  manner  by  the  government  was  rased  to  the 
ground.  Tiles  carried  from  the  roof  were  projected  against  thick 
doors  with  such  force  as  to  pass  through  them  like  a  cannon  ball. 
A  plank  of  wood  8^  feet  long,  9  inches  wide,  and  an  inch  thidc, 
was  projected  with  such  force  as  to  cut  through  a  branch  of  palm 
wood  18  inches  in  diameter.  A  piece  of  wood  15  feet  Ions  voA  8 
inches  square  in  its  cross  section,  was  projected  upon  a  hard  paved 
road,  and  buried  to  a  depth  of  more  than  three  feet  in  it.  A  atrong 
iron  gate  in  front  of  the  governor's  house  was  carried  awaj,  ana 
three  twenty-four  pounders  erected  on  the  fort  were  dismounted. 

2229.  The  probable  causes  eorplained, — ^^These  effects,  prodi^ponB 
as  they  are,  all  arise  from  mechanical  causes.  There  is  no  agent 
engaged  in  hurricanes  more  subtle  than  the  mechanical  force  of  air 
in  motion,  and  since  the  weight  and  density  of  the  air  suffer  no  im- 
portant change,  the  vast  momentum  manifested  by  such  effects  as 
those  described  above,  must  be  ascribed  altogether  to  the  extraordi- 
nary velocity  imparted  to  the  air  by  the  magnitude  of  the  local 
vacuum  produced,  as  already  stated,  by  the  sudden  condensation  of 
vapour.  To  form  some  approximate  estimate  of  this  it  may  be  stated 
that,  in  the  intertropical  regions,  a  fall  of  rain  often  takes  place  over 
a  vast  extent  of  surface,  sujfficient  in  quantity  to  cover  it  with  a  stra- 
tum of  water  more  than  an  inch  in  depth.  If  such  a  fall  of  rain 
were  to  take  place  over  the  extent  of  a  hundred  square  leagues,  as 
sometimes  happens,  the  vapour  from  which  such  a  quantity  of  liquid 
would  be  produced  by  condensation  would,  at  the  temperature  of 


VATER  SPOUTS. 


6S 


Boly  Wy  occopj  ft  volame  100,000  IJmea  greater  than  that  of  the 
bqaid ;  and,  cofiEcqueotly,  in  the  atmosphere  over  the  surface  of 
100  aqoare  leagnee  it  wonld  fill  a  apace  9000  feet,  or  nearly  two 
mil«B  ID  length.  The  extent  of  the  vacuum  produced  b;  its  coudeo- 
ntioD  vonlabe  a  volame  nearly  equal  lo  200  cubic  miles,  or  to  the 
lolnme  of  a  column  trhose  base  is  a  square  mile  and  nhose  height 
U  200  mUea. 

2230.  Water  ipouU  and  land  ipouU.  —  These  phenomeoa,  called 
water  or  land  aponte  according  as  they  are  manifested  at  sea  or  on 
land,  coDBist  appareDtlj  of  dense  masses  of  aqneons  vapour  and  air, 
having  at  once  a  gyratory  and  progressive  motion,  and  resembling  in 
■fona  a  conical  cloud,  the  baae  of  which  is  presented  upvards,  and 
the  vertex  of  which  generally  rests  upon  the  ground,  but  sometimes 
tflEumes  a  contrary  position.  This  phenomeaon  is  attended  with  a 
■oand  like  that  of  a  wwgon  rolling  on  a  rough  pavement. 

Violent  mechanical  e^tg  aometimes  attend  these  meteors.  Large 
tnea  torn  up  by  the  roots,  stripped  of  their  leaves,  and  exhibiting 
all  the  appearances  of  having  been  struck  by  liglitning,  are  pro- 
jected to  great  distances.  Houses  are  often  thrown  down,  unroofed, 
and  otherwise  injured  or  destroyed,  when  they  lie  in  the  course  of 
these  meteon.  Rain,  hul,  and  frequently  globes  of  fire,  like  the 
ball  l^taing,  also  aocompany  tbem. 

The     various     appearances     ex- 
hibited by  water  spouts  are  rcpre- 
eentod  in  fy.  669. 
No  satisfactory   theory   has  yet 
I   ooanected  these  phenomena  with  the 

general  laws  of  physics. 
I  2231.  Evaporation  from  the  far- 
face  of  ioaier.  —  If  the  surface  of 
I  a  aea,  lake,  or  other  large  collection 
J  of  water,  were  exposed  to  the  atmo- 
j  aphere  consisting  of  pure  air  without 
I  any  admixture  of  vapour,  evapora- 
I  tion  would  immediately  conimeoce, 
'  and  the  vapour  developed  at  the  sur- 
&C0  of  the  water  wonld  ascend  into 
and  mix  with  the  atmosphere.  The 
«  of  the  atmosphere  would  then  be  (he  sum  of  the  pressures 
af  the  atmoephere,  properly  so  called,  and  of  the  vapour  suspended 
ia  it,  nnce  neither  of  these  elastic  fluids  cau  augment  or  dimioish 
tte  pRMnre  of  the  other. 

Th«  vapour  developed  from  the  autface  of  the  water  thus  min- 

Aig  with  the  atmoephere,  acquires  a  common  temperature  with  it 

Thia  TUKMU-,  theiafore,  receiving  thus  from  the  air  with  which  it  is 

5* 


Pig.  MS. 


M  HETSOROLOUT. 

intermixed  more  or  lees  hekt,  after  having  ptawd  into  the 
state,  ia  tuperheate<l  vapour  (149G.)     It  has,  therefore,  a  ^ 
temporaturo  than  that  wliich  cotTMponila  to  its  density,  or,  vhita 
the  same,  it  has  a  luss  deoaily  than  that  which  correspoDdB  to  it 
temperature.     Such  vapour  maj  therefore  lose  temperatnre  to  aar 
taia  extoDt  without  being  condcnaed. 

2232.  Air  may  he  saturated  with  vapour. — But  if  the  nm  A^ 
moHpbero  codUduo  to  bo  suspeoJed  over  the  aorface  of  water,  ihi 
process  of  cnpoiation  being  contioaed,  the  quantity  of  Tifon 
which  riacB  into  the  air  and  uiogU-s  with  it  will  be  oonlinuaUj  t» 
creased  until  it  acquires  tbe  greatest  deosit;  which  is  compatible  will 
its  temperature.  Evaporatiou  inuat  then  coase,  and  tbe  air  ii  aud 
to  be  laturaled  with  vapour. 

If  tbe  temperature  of  the  air  in  sueh  case  rise,  evaporation  will 
TGcommenco  and  will  cnutiiiuo  until  the  vapour  shall  acquire  tlit 

Scatest  density  cdmpatible  with  the  iccrCBsed  temperature,  and  will 
en  cease,  the  air  being,  as  before,  mliiratcd. 

2233.  1/  the  lcm}>oraliirn  of  saliiratnl  air /.ill,  '■oiideinntion  Kill 
lake  pfaee. — But  if  the  temperature  ftU,  the  greateat  denaityof 
vapour  compatible  wiih  it  being  less  than  at  tbe  higher  temperatorr, 
a  part  of  the  vapour  muflt  be  condensed,  and  this  oondenaation  mut 
continue  until  tlio  vapour  suspended  in  the  air  shall  be  reduced  lo 
that  state  of  density  wbicb  ia  the  greatest  compatible  with  the  re- 
duced temperature. 

2234.  Atmonphcre  rareJy  taturntcd.  ~  A  fluid  so  light  and  mobile 
as  tho  atmosphere,  can  never  remain  long  in  a  atate  of  repose,  and 
the  column  of  air  auapcnded  over  the  surface  of  any  oollection  of 
water,  however  extensive,  is  subject  to  frequent  change.  In  gennal, 
therefore,  before  any  such  portion  of  the  atmoaphere  beooma  aatu- 
rated  by  evapnratioo,  it  is  removed  and  replaced  by  another  portico. 
It  happens,  eooscquently,  that  the  atmosphere  rarely  beoomea  Mtn- 
rated  by  the  immediate  effect  of  evaporation. 

2235.  Mai/  become  so  hi/  redurrd  lemjieraliire  or  inferrnimgKtig 
ttrata.  —  The  state  of  saturation  is,  however,  often  attained  either 
by  loss  of  temperature,  or  by  the  intermixture  of  strata  of  air  of 
different  tempeistures  and  differently  charged  with  vapoura.  Thai>, 
if  air  which  is  below  the  point  of  saturation  suffer  a  loss  of  heat,  its 
temperature  may  fall  to  that  point  which  is  tbe  highest  compatible 
with  the  density  of  the  vapour  actually  suspended  in  it.  The  air 
will  then  become  saturated,  not  only  by  receiving  any  iucreaaed 
quantity  of  vapour,  but  by  losing  that  caloric  by  which  the  vapour 
it  contained  was  previously  svperhcattd. 

If  two  strata  of  air  at  different  tempenilurcs,  and  both  charged 
with  vapour  to  a  point  below  saturation,  be  intermingled,  they  will 
take  oil  intermediate  temperature;  that  which  had  the  higher  tempe- 
ntiire  mpartjag  a  portion  of  ita  licat  to  thaib  w\k\cV  ^«&  «.  \nw(n 


ATM08PHKBS.  55 

empentiire.  The  vapour  with  which  they  were  previously  charged 
rill  likewise  be  intermixed  aod  reduced  to  the  common  temperature. 
!(ow,  in  this  case  it  may  happen  that  the  common  temperature  to 
vhicli  the  entire  mass  is  reduced,  after  intermixture,  shall  be  either 
sqoal  to  or  less  than  the  greatest  temperature  compatible  with  the 
lensity  of  the  vapour  in  the  mass  of  air  thus  mixed.  If  it  be  equal 
;o  that  temperatore,  the  mass  of  air  after  intermixture  will  be  satu- 
raiedf  though  the  strata  before  intermixture  were  both  below  satura- 
don ;  and  if  less,  condensation  must  take  place  until  the  density  of 
the  vapour  suspended  in  the  mixture  be  reduced  to  the  greatest  density 
Bompatibld  with  the  temperature. 

2236.  Air  and  vapour  interminghj  (hough  of  different  tpecific 
gravities. — It  might  be  supposed  that  air  and  vapour  being  mixed 
together  without  combining  chemically,  would  arrange  themselves  in 
itrata,  the  lighter  floating  above  the  heavier  as  oil  floats  above  water. 
This  statical  law,  however,  which  prevails  in  liquids,  is  in  the  case 
of  elastic  fluids  subject  to  important  qualifications.  The  latter  class 
of  fluids  have  a  tendency  to  intermingle  and  diffuse  themselves 
throogh  and  among  each  other  in  opposition  to  their  specific  gravi- 
ties. Thus  if  a  stratum  of  hydrogen,  the  lightest  of  the  gases,  rest 
■pon  a  stratum  of  carbonic  acid,  which  is  the  heaviest,  they  will  by 
ilow  degrees  intermingle,  a  part  of  the  hydrogen  descending  among 
the  carbonic  acid,  and  a  part  of  the  carbonic  acid  ascending  among 
the  hydrogen,  and  this  will  continue  until  the  mixture  becomes  per- 
fiectly  uniform,  every  part  of  it  containing  the  two  gases  in  the  pro- 
portion of  their  entire  quantities. 

The  flame  law  prevails  in  the  case  of  vapours  mixed  with  gases ; 
and  thiiB  may  be  explained  the  fact,  that  although  the  aqueous  va- 
poar  Biispended  in  the  air,  and  having  the  same  temperature,  is 
always  lighter  bulk  for  bulk  than  the  air,  it  does  not  ascend  to  the 
apper  strata  of  the  atmosphere,  but  is  uniformly  diffused  through  it. 

2237.  The  pressure  of  air  retards,  hut  does  not  diminish  evapo- 
ralibm. — ^It  may  be  stat^  generally,  that  the  effect  of  a  column  of 
air  snperposed  upon  the  surface  of  water  is  only  to  retard,  but  not 
either  to  prevent  or  diminish,  the  evaporation.  The  same  quantity 
of  vapoor  will  be  developed  as  would  be  produced  at  the  same  tem- 
peratare  if  no  air  were  snperposed  on  the  water ;  but  while  in  the 
latter  case  the  entire  quantity  of  vapour  would  be  developed  instan- 
taneoviflly,  it  is  produoed  gradually,  and  completed  only  after  a  cer- 
tnn  interval  of  time  when  the  air  is  present.  The  quantity  of  va- 
pov  developed,  and  its  density  and  pressure,  are  however  exactl^^ 
the  same,  whether  the  space  through  which  it  is  diffused  be  a  vacuum, 
m  bs  filled  by  air,  no  matter  what  tiie  density  of  tiie  air  may  be. 


50  METEOROLOGY. 

The  properties  of  the  air,  therefore,  neither  modify  nor  are  modified 
by  those  of  the  vapour  which  is  diifased  through  it 

2288.  WTien  vapour  intermixes  with  air,  it  renders  it  meei/ieaJfy 
lighter.  —  Since,  at  the  same  temperature  and  pressure,  the  densi^ 
of  the  vapour  of  water  is  less  than  that  of  air  in  the  ratio  of  5  to  8| 
it  follows  that  when  air  becomes  charged  with  vapour  of  its  own 
temperature,  the  volume  will  be  augmented,  but  the  density  dimiB- 
ished.  If  a  certain  volume  of  air  weigh  8  grains,  an  equal  volniiie 
of  vapour  will  weigh  5  grains,  the  two  volumes  mixed  together  will 
weigh  13  grains,  and,  consequently,  an  equal  volume  of  the  mixture 
will  weigh  6|  grains.  In  this  case,  therefore,  the  density  of  the  air 
charged  with  vapour  is  less  than  the  density  of  dry  air  of  the 
temperature  in  the  ratio  of  6|  to  8. 


CHAP.  in. 

HTGROMETRT. 

2239.  Hygrometry.  —  This  is  the  name  given  to  that  branch  of 
meteorology  which  treats  of  the  methods  of  measuring  the  elaatie 
force  and  the  quantity  of  aqueous  vapour  which  is  suspended  in  the 
atmosphere,  and  in  which  the  influence  of  various  natural  bodies  and 
physical  agents  upon  this  vapour  is  explained. 

If  the  atmosphere  were  always  charged  with  vapour  to  saturation, 
the  pressure  and  density  of  the  vapour  contained  in  it  would  be  im- 
mediately determined  by  its  temperature,  for  there  would  then  be 
the  greatest  pressure  and  density  compatible  with  the  temperaturOi 
and  the  pressure  and  density  would  be  given  by  the  tables  (1494). 

2240.  The  dew  point.  —  But  when  the  air,  as  generally  happens, 
is  not  saturated,  it  becomes  necessary  to  contrive  means  by  which 
the  temperature  to  which  it  must  be  reduced,  in  order  to  become 
saturated  by  the  quantity  of  vapour  actually  suspended  in  it,  can  be 
determined. 

Such  temperature  is  called  the  dew  point,  inasmuch  as  after  re- 
duction below  that  temperature,  more  or  less  condensation,  and  the 
consequent  deposition  of  moisture  or  dew,  will  take  place. 

2241.  Method  of  determining  the  pressure  and  density  of  this 
vapour  suspended,  in  the  air, — When  the  actual  temperature  of  the 
air  and  the  dew  point  are  known,  the  pressure  and  density  of  the 
vapour  suspended  in  the  air  may  be  found. 

ijet  T  express  the  temperature  of  the  air,  t  the  dew  point,  p  the 
pressure  of  the  vapour  which  would  saturate  the  air  at  Uie  tempera* 


HYGROMBTRT.  57 

tan  TfP  die  prenure  of  the  vapour  which  would  satarate  it  at  the 
temperature  t,  and,  in  fine,  let  p'  express  the  pressure  of  the  vapour 
•etittlly  suspended  in  the  air. 

This  pressure  F^  is  greater  than  the  pressure  p,  which  the  same 
Tipour  having  the  same  density  has  at  the  temperature  t,  by  that . 
iaewse  of  pressure  which  is  due  to  the  increase  of  temperature  from 
f  lo  T.  If  the  increase  of  pressure  due  to  one  degree  of  augmented 
Impenitare  be  expressed  by  n,  the  increase  duo  to  (t  —  t)  degrees 
will  be  expressed  by  (t  —  t)X  n.     Hence,  we  shall  have 

I^  =pX  {I  +  (T—t)Xn\ 

So  that  when  p,  the  pressure  of  the  saturating  vapour  at  the  dew 
pointy  18  known,  p',  the  actual  pressure,  can  be  found. 

But  any  means  by  which  the  temperature  t  at  the  dew  point  can 
be  determined,  will  necessarily  also  determine  the  pressure  py  inas- 
Duch  as  this  pressure  is  that  which  corresponds  to  vapour  having  the 
greatest  density  compatible  with  the  temperature  /,  and  is  therefore 
liven  by  the  tables  (1494).  This  being  found,  p'  may  be  computed 
vj  the  preceding  formula. 

To  find  the  density  of  the  vapour  actually  suspended  in  the  air, 
or,  what  is  the  same,  the  weight  of  water  in  the  state  of  vapour  con- 
tamed  in  a  cubio  foot  of  air,  let  this  weight  be  expressed  by  y^,  and 
lei  w  express  the  weight  of  vapour  which  would  saturate  a  cubic 
Ibot  of  air  at  the  temperature  T. 

Sinoe  the  pressure  is  proportional  to  the  density  when  the  tempe- 
Blore  is  the  same,  we  shall  have 

P :  p^ : :  w :  w' ; 

Therelbrei 

p'     w 

Bj  this  formula,  therefore,  the  weight  w'  of  vapour  contained  in  a 
tMc  foot  of  air  can  be  found,  provided  the  weight  and  pressure  of 
tke  vapoar  which  would  saturate  it  at  the  same  temperature,  its  dew 
pointy  and  the  pressure  of  the  vapour  which  would  saturate  it  at.  that 
painty  are  sevendly  known. 

2242.  Table  of  pr&tsures  and  densities  of  saturating  vapours. — 
The  following  table,  in  which  are  given  the  pressure  and  weight  of 
the  Mtunting  vapour  in  a  cubic  foot  of  air,  at  the  several  tempera- 
tnes  expressed  in  the  first  column,  will  supply  all  the  data  necessary 
fcr  neh  ealcnlations,  provided  only  that  means  be  obtained  for  deter- 
by  experiment  the  dew  point. 


68 


METEOROLOGT. 


Tablb  showing  the  Pressure  and  Weight  of  satnntuig  Vapour  (MmtaiiMi 
a  Cubic  Foot  of  Air  at  Temperatures  yarjiog  from  — 4°  Fahr.  to  -f- 1 

Fabr. 


IhrcBwure: 

Weight  of  Vapour 

PreMure: 

Weight  of  Tu 
in  a  Cubic  n 

Tempeniure. 

Inrheis 

in  a  Cubic  Foot 

Temperature. 

Inrhea, 

Mercury. 

of  Air. 

Mereury. 

of  Air. 

o 

o 

Oraiu. 

—  40 

•05 

1 

66-2 

•64 

7 

60 

•08 

1 

680 

•68 

7 

140 

•10 

1 

69-8 

•72 

8 

23  0 

•16 

2 

71-6 

•76 

8 

820 

•20 

2 

78-4 

•81 

9 

88-8 

•22 

2 

75-2 

•86 

9 

85-6 

•28 

8 

77  0 

•91 

10 

87-4 

•24 

8 

78-8 

•96 

10 

89-2 

•26 

8 

80-6 

102 

11 

410 

•28 

8 

82-4 

108 

12 

42-8 

•80 

8 

84-2 

114 

12 

44-6 

•82 

4 

860 

1^21 

IS 

46-4 

•84 

4 

87-8 

1-28 

14 

48-2 

•86 

4 

89-6 

1-86 

14 

600 

•88 

4 

91-4 

148 

15 

61-8 

•40 

6 

93-2 

1-61 

16 

58-6 

•48 

6 

950 

159 

17 

65-4 

•45 

6 

96-8 

1-68 

18 

57-2 

•48 

6 

98-6 

1-77 

18 

690 

•61 

6 

100-4 

1-87 

19 

60-8 

•64 

6 

102-2 

1-97 

20 

62-6 

•58 

6 

1040 

209 

21 

64-4 

•61 

7 

2243.  Example  of  such  a  calculation,  —  As  an  example  of 
application  of  the  preceding  formulad,  let  us  suppose  that  the  t 
perature  of  the  air  is  77^,  and  that  the  dew  point  is  ascertaio'K 
be  54J°. 

By  the  preceding  table  then  we  obtain  the  following  data : 

T  =  77°,        p  =  0-91,        <  =  54J,       jp  =  0-44. 

But  it  appears  from  what  has  been  already  explained  (14$ 
that  n  =  ©•002037  =  ^^5. 
Hence  we  find 

p'  =  0-44 X  { 1  +  22 -5  X  0002037 }  =  0-46. 

It  follows,  therefore,  that  the  actual  pressure  of  the  vapour 
pended  in  the  air  is  46  per  cent,  of  the  pressure  of  the  vapour  wl 
would  saturate  it. 

We  have  also 

P  =  0-96,  w  =  10: 

And  therefore 

w'  =  6  05. 


HTGR0MBTBR8. 


59 


44.  MeAod  of  atceriaining  the  dew  poitU, — To  determine  the 
painty  let  a  thin  ghiss  or  decanter  be  filled  with  water,  and,  im- 
og  a  thermometer  in  it,  let  it  be  exposed  in  the  open  air.  Let 
»ld  water  be  poared  into  it  by  small  quantities  and  mixed  with 

as  to  reduce  its  temperature  by  slow  degrees  below  that  of  the 
imding  air.  A  temperature  will  at  length  be  attained  at  which 
idy  deposition  of  moisture  will  be  manifested  on  the  external 
oe  of  the  glass.  The  temperature  at  which  this  effect  first  be- 
to  be  manifested  is  the  dew  point. 

explain  this  it  must  be  considered  that  the  shell  of  air  in  im- 
lie  contact  with  the  glass  is  reduced  to  the  temperature  of  the 
,  and  when  that  temperature  has  been  reduced  so  low  that  the 
ir  suspended  in  the  air  saturates  it,  any  further  diminution  of 
eratore  is  attended  with  condensation,  which  is  in  effect  mani- 
i  by  the  dew  which  then  immediately  begins  to  collect  upon  the 
ce  of  the  glass. 

45.  DanielTs  -fl^^romc/er. —Hygrometers  have  been  constructed 

in  different  forms,  on  this  principle,  to  indicate 
the  dew  point.  That  of  Daniel  I  has  been  most 
generally  adopted.  This  instrument  consists 
of  a  glass  tube,  having  a  thin  bulb  blown  on 
each  end  of  it,  and  being  bent  into  the  rectan- 
gular form  represented  in  Jig,  670.  The  bulb 
a  is  filled  to  two-thirds  of  its  capacity  with 
ether,  which  being  boiled  produces  vapour  which 
fills  the  tube  t  and  the  bulb  6,  and  escapes 
through  a  small  opening  in  the  bottom  of  b. 
In  this  manner  the  air  is  expelled  from  the 
ether,  the  tube,  and  the  bulbs.  The  opening 
in  b  is  then  closed  with  the  blowpipe,  and  the 
heat  being  removed  from  the  bulb  a,  the  va- 
pour in  the  tube  and  bulb  b  is  condensed,  so 

the  space  within  the  instrument  above  the  surface  of  the  ether 
ins  only  the  vapour  of  ether,  which  corresponds  to  the  tempe- 
«  of  the  fluid  in  the  bulk  a.  A  thermometer  is  previously  in- 
d  in  the  tube  /,  the  bulb  of  which  is  plunged  in  the  ether,  and 
bulb  b  is  surrounded  by  a  linen  or  muslin  cloth,  which,  being 
mted  with  ether  by  means  of  a  small  phial  provided  with  a  fine 
Bgnlar  spout,  evaporation  takes  place,  by  which  the  bulb  b  is 
d.  The  vapour  of  the  ether  which  fills  the  bulb  b  is  thus 
ensed  in  it,  and  more  vapour  flows  in  to  fill  its  place  from  the 
L  The  surface  of  the  ether  in  a  being  thus  continually  released 
the  pressure  of  the  vapour  condensed,  further  evaporation  and 
meqaent  depression  of  the  temperature  of  the  fluid  in  the  bulb 
I,  and  thiB  continues  until  the  temperature  of  the  bulb  a  is 


670. 


60 


BCETEOBOLOGT. 


redueed  to  the  dew  point,  when  a  olondy  deposition  will  b 
fested  on  the  glass  of  the  bulb  a, 

2246.  AvguM^i  Ptyckrvmetei 
fessor  August  of  BerUn  has  ooi 
an  hygrometer,  the  indications  < 
depend  on  the  depression  of  tern 
produced  by  evaporation  in  a 
sphere  which  is  below  the  point 
ration.  Two  thermometers,  [q 
fig.  671,]  exactly  alike  in  all 
are  mounted  on  a  support  in  in 
juxtaposifion,  the  bulb  of  or 
enyeloped  in  a  cloth,  which  is  I 
stantly  wetted  with  distilled  wa 
the  atmosphere  were  already  s 
no  eyaporation  would  ensue ; 
be  not  saturated,  evaporation  v 
place  from  the  wet  cloth  sun 
the  bulb,  and  a  depression  of  i 
ture  will  be  indicated,  which  i 
a  certain  relation  to  the  rate 
evaporation.  The  thermomete 
fore,  enveloped  in  the  wet  cl( 
fall  below  the  other,  which  g 
true  temperature  of  the  air,  and  the  difference  between  the  t 
mometers  thus  becomes  a  measure  of  the  rate  of  evaporati 
the  cloth,  and  thereby  of  the  degree  of  dryness  of  the  ai 
greater  the  quantity  of  vapour  with  which  the  air  is  char 
less  will  be  the  difference  of  the  temperatures  indicated  by 
thermometers. 

When  the  air  is  extremely  dry,  the  difference  between 
thermometers  sometimes  amounts  to  from  14^  to  18^. 

Professor  August  has  constructed  tables  by  which  the  pre 
the  vapour  suspended  in  the  air,  which  corresponds  to  the 
indications  of  the  two  thermometers,  can  be  immediately  fou 
2247.  Sausmre*$  Hygrometer. — Hygrometric  substances  i 
porous  bodies  whose  affinity  for  moisture  is  so  strong,  that  wl 
are  exposed  to  an  atmosphere  in  which  more  or  less  vapour 
pended,  they  will  attract  this  vapour  and  condense  it  in  the: 
so  that  they  will  become  wet.  The  quantity  of  moisture  wh: 
imbibe  in  this  manner  is  more  or  less,  according  to  the  qua 
vapour  with  which  the  atmosphere  is  charged. 

The  varying  absorption  of  vapour  causes  in  some  bodies 
spending  variation  of  dimensions.  The  hygrometer  of  i 
[fig.  672,]  is  founded  on  this  property.  A  hair  well  prepa 
deprived  of  all  greasy  matter  is  attached  to  a  point  of  suspe 


Fig.  671. 


61 

S  Bnd  being  carried  nniid  &  small  wheel  is  kept  extended 

,i  I_  by  BUEpending  to  its  extremity  a  Boiall  weight/  Be, 
^^E^  ing  hjgrometric,  it  absorba  moiBture  from  ihe  atmo- 
^here,  by  which  if  is  made  to  expand  atid  incrcaae  its 
length.  This  cauees  the  wheel  round  which  it  is  coiled 
to  turn  through  a  oorreepoading  space,  which  in  sliowa 
by  an  index  d  fixed  upon  the  centre  of  the  wheel,  which 
plays  upon  a  graduated  arch  ih. 

As  the  vapour  snspended  in  the  air  increases  or  di- 
/,  mioishes,  the  oonbaction  of  the  hajr  rtirics  in  corre- 
sponding maDoer,  and  the  index  shows  the  changoH, 
indicating  extreme  dryness  at  one  extremity  of  the 
aoale,  and  extreme  humidity  at  the  other. 

Tables  have  been  constructed  by  which  the  indico- 
^_  tions  of  this  instrument  give  the  pressure  of  the  vapour 

Kg,  fix     suspended  ia  the  air. 

p247*.  General  connderatum  of  hygromeUn. — The  quantify 
d  wkterj  vapour  contained  in  the  atmoephcre,  at  any  given  moment, 
may  be  determined  either  by  what  is  called  the  chemicai  mcihoil,  or 
hj  meua  of  iDatrumeoU  called  hyi/romdcre.  The  chemical  method 
emuists  in  absorbing,  by  means  of  substances  which  have  a  great 
avidity  for  water,  the  vapour  contained  in  a  certaiu  volamo  of  air, 
and  in  determiniog  its  weight  by  the  balance.  The  air  ia  drawn  by 
mnna  of  an  aspirator  through  tubes  filled  with  coarse  fragmcnta  of 
pamiee-stone,  moistened  with  enlphuric  acid.  Experiment  has  shown 
that  tubea  of  this  kind  completely  retain  the  humidity  of  the  air. 
Hence,  the  increase  of  weight  in  the  tubes  rcprcacnts  the  weight  of 
the  water  which  existed  in  a  volume  of  air  equal  to  the  capacity  of 
the  aspirator.  This  method  docs  not  give  the  quantity  of  humidity 
which  exists  in  the  air  at  a  determinate  moment,  but  determines, 
«ith  great  precision,  the  mean  quantity  which  tJie  air  contained 
doHng  the  experiment.  But  it  is  an  experiment  of  the  laboratory, 
Kquinng  time  and  bulky  apparatus  for  its  performance ;  and,  conse- 
quently, does  not  admit  of  adoption  in  meteorological  observatories. 
It  ia,  however,  eminently  adapted  to  the  veri£cation  of  the  other 
methods;  and  for  this  purpose,  was  constantly  made  use  of  by  Itcg- 
naolt  in  his  hygrometrical  researches,  some  of  the  results  of  whi^ 
ue  given  below. 

HygromeUrs,  or  instruments  which  serve  to  measure  the  elastic 
force  a[  the  watery  vapour  contained  in  the  air,  ore  of  three  kinds, 
being  conatructed  on  difierent  principles.  Some  act  by  condensation, 
olhere  by  evaporation,  and  others  again  by  absorption.  The  first  are 
ailed  antderuini/  or  dew  point  hygrometers — the  second,  icel-und- 
d/g  tii/6  hygrometers  or  pst/cArotncler* — and  the  third,  alisorjiiion 
hygrometers. 


82  MBTBOROLOeT. 

Ist  Condensing  or  dew  point  hygrometers, — Hygrometera  of  thi^ 
kind  are  the  only  ones  whose  results  are  perfectly  exact  and  reliable* 
their  indications  being  influenced  neither  by  the  temperaturei  nor  by 
the  degree  of  humidity,  nor  by  the  variable  agitation  of  the  air. 

Le  Koy,  of  Montpellier,  was  the  first  to  propose  the  determination 
of  the  dew  point  by  the  rough  process  described  in  2244 ;  but  when 
the  air  is  very  dry,  a  deposit  of  dew  cannot  be  produced  in  thai 
way. 

The  process  of  Le  Roy  received  its  first  practical  application  bj 
the  construction  of  Daniell's  condensing  hygrometer  (2245) ;  which, 
however,  cannot  be  absolutely  relied  upon,  since  it  is  liable  to  the 
following  objections,  (a)  The  cooling  of  the  ether  in  the  bulb  a 
principally  takes  place  at  the  surface  of  the  liquid  where  the  evapo- 
ration occurs ;  and  as  liquids  are  bad  conductors  of  heat,  there  is  al- 
ways a  marked  difference  of  temperature  between  the  upper  and 
lower  layers  of  the  liquid.  However  delicate  the  thermometer  may 
be,  it  still  indicates  only  the  mean 'temperature  of  the  layers  in  which 
its  reservoir  is  immersed;  and  this  mean  temperature  may  dififei 
perceptibly  from  that  on  which  the  first  deposit  of  dew  depends, 
(b)  The  manipulation  requires  the  long-contmued  presence  of  the 
observer  near  the  apparatus ;  and  this  necessarily  influences  the  hy 
grometric  state  of  the  air  and  its  temperature,  especially  if  the  ob- 
server is  obliged  to  approach  very  near  to  read  off  the  thermometei 
and  to  observe  the  first  deposit  of  dew.  (c)  The  evaporation  of  t 
great  quantity  of  ether  takes  place  on  the  bulb  2>  in  a  space  eztremel} 
near  to  that  in  which  the  deposit  of  dew  upon  the  bulb  a  is  deter 
mined ;  and  the  lowering  of  temperature  caused  by  this  in  the  neigh 
bouring  strata,  must  occasion  a  very  sensible  change  in  the  hygro 
metric  state  of  the  air.  (d)  And  lastly,  the  ordinary  commercia! 
ether  contains  as  much  as  one-tenth  its  weight  of  water ;  and  thu 
water,  being  carried  in  great  part  by  the  vapour  of  ether  into  i 
space  very  close  to  that  in  which  the  deposit  of  dew  is  determined 
tends  again  to  change  the  hygrometric  state  of  the  air. 

Bache's  hygrometer.  Jig.  673,  which  is  free  from  most  of  the 
foregoing  objections,  consists  of  a  cubical  box  e,  filled  with  finely 
pounded  ice  and  salt,  into  which  is  inserted  a  metallic  bar  6,  havin| 
on  its  upper  surface  a  groove  containing  mercury,  into  which  dips  i 
delicate  thermometer  a  suspended  from  a  support  d;  the  thermo 
meter  being  movable  along  the  groove.  The  whole  rests  upon  i 
wooden  stand  c.  One  of  the  vertical  sides  of  the  bar  b  presents  i 
surface  of  polished  silver;  and  the  temperature  of  this  bar,  whicl 
is  about  zero  near  its  insertion  into  the  box,  gradually  rises  toward; 
the  other  end.  There  will  be  a  deposit  of  dew  on  this  polished  sur 
face,  terminating  abruptly  at  a  certain  vertical  line  whose  tempera 
ture  will  be  that  of  the  dew  point.  This  temperature  is  easily  as 
certained  by  placing  the  bulb  of  the  thermometer  opposite  that  line 


HTCmOVXTIRS. 


68 


Fig.  673. 

tnd  hence  this  instruroent  allows  of  the  dew  point  being  read  off  at 
loj  moment  by  the  observer. 

But  of  all  condensing  hygrometers,  that  of  Regnanlt,  Jigs.  674 
md  675,  is  the  most  perfect.  It  consists  of  a  thimble,  ahc  {fi<j. 
674),  made  of  silver,  very  thin,  and  perfectly  polished,  \  inch  in 
depth,  and  ^ths  of  an  inch  in  diameter,  which  is  fitted  tightly  upon 
a  riaas  tnbe  c  cf,  open  at  both  ends.  The  tube  has  a  small  lateral 
toDalare  i.  The  upper  opening  of  the  tube  is  closed  by  a  cork, 
wbieh  IB  traversed  by  the  stem  of  a  very  sensible  thermometer  occu- 
pying its  axis;  the  bulb  of  the  thermometer  is  in  the  centre  of  the 
lUver  thimble.  A  very  thin  glass  tube,  fg^  open  at  both  ends, 
traveTses  the  same  cork,  and  descends  to  the  bottom  of  the  thimble. 
Ether  is  poured  into  the  tube  as  high  as  m  7t,  and  the  tubulure  t  is 
placed  in  communication  by  means  of  a  leaden  tube  d^  with  an  as- 
pirator jar,  six  or  eicht  pints  in  capacity,  filled  with  water.  The 
aapirator  jar  is  placed  near  the  observer,  while  the  hygrometer  is 
kq)t  as  &r  from  his  person  as  is  desirable.  On  allowing  water  to 
nm  from  the  aspirator  jar,  air  enters  by  the  tube  gf^  passing  bubble 
by  babble  through  the  ether,  which  it  cools  by  carrying  away  va- 
poor:  the  refrigeration  is  the  more  rapid  the  more  freely  the  water 
M  allowed  to  flow ;  and  the  whole  mass  of  ether  presents  a  sensibly 
miform  temperature,  as  it  is  briskly  agitated  by  the  passage  of  the 
bubbles  of  air.     The  temperature  is  sufficiently  lowered  in  less  than 


HBTBOKOLOOT. 


Fig.  074. 


Fig.  flT5. 


a  minute  to  detennitie  a 
abuodant  deposit  of  dn. 
The  therniometer  t*  llMn 
observed  through  a  litllt 
tolcscopo.  SappDtathitH 
ia  read  off  at  60° ;  thii 
tiMupcrature  is  BTidenll; 
Eomcnbat  lower  than  wlwt 
correspondB  ezactlr  to  thg 
air's  homidity.  Bj  dot- 
itig  the  stopcock  of  tha 
Eispiiator,  the  pasmgg  of 
nit  is  stopped,  the  dev 
disappears  in  a  fev  to- 
CO  ads,  scd  tbe  thermo- 
meter again  liscs.  Sap- 
pose  that  it  marks  62°: 
this  degree  is  above  Ibt 
dow  point  The  stopcod: 
of  the  aspirator  ia  Um 
opened  very  slightly,  n 
as  to  dctcrmiDe  the  pw- 
sage  of  a  vei;  small 
stream  of  air-bnbblei 
throQgh  the  ether.  If 
the  thermometer  oot- 
daues,  notwithstandii^ 
to  rise,  the  stopcock  u 
opened  farther,  and  tin 
thermometer  brought 
dowa  to  Sl^-S  :  by  shi^ 
ting  the  stopcock  slight] j, 
it  is  easy  to  stop  the  &Ur 


iog  range,  and  make  the 
thermometer  remain  Etatiooaiy  at  51°-8,  as  Toog  as  is  desired.  If 
no  den  forma  after  the  lapse  of  a  few  seconda,  it  is  evident  that  51''8 
ia  higher  than  the  dew  point.  It  is  bronght  down  to  6I°-6,  and 
maintained  there  by  regulating  tbe  flow.  The  metallic  surface  being 
now  observed  to  become  dim  after  a  few  seconds,  it  is  concluded  that 
Bl^-S  is  too  low,  while  tl°-8  is  too  high.  A  still  greater  approxi- 
mation may  be  made,  by  now  finding  whether  51°'7  is  above  or  be> 
low  the  point  of  condensation.  These  operations  may  bo  executed 
in  a  very  short  time,  after  a  little  practice;  three  or  four  minutes 
being  fonnd  sufficient,  by  M.  Eegnault,  to  determine  the  dew  point 
to  within  about  j\,th  of  a  degree,  Fahr.  A  more  considerable  &11 
of  temperatore  may  be  obtained  by  moans  of  this  than  the  origtnal 


HYQBOMBTBRS.  65 

of  DankUy  with  the  coiisamption  of  a  much  less  quantity 
flf  ether;  indeed,  that  liquid  may  he  dispensed  with  entirely,  and 
aloohol  mhstitated  for  it.  The  thermometer  t^,  to  observe  the  tem- 
pentnre  of  the  air  daring  the  experiment,  is  placed  in  a  second 
■Bilar  glass  tuhe  and  thimble  d  h\  also  under  die  influence  of  the 
w^mSuxtj  bat  containing  no  ether. 

It  IS  evident  from  this  description  that  Regnault's  hygrometer 
•bviates  all  of  the  objections  to  which  that  of  Daniell  is  open.  The 
thermometer  indicates  exactly  the  same  temperature  as  the  ether, 
nd  all  the  layers  of  this  liquid  present  a  uniform  temperature,  from 
the  eontiniud  a^tation  produced  by  the  passage  of  the  bubbles  of 
■r;  the  metallio  side  on  which  the  dew  is  deposited  has  also  the 
■Be  temperature  as  the  ether,  because  it  is  very  thin,  and  is  in 
iaiie&te  contact  with  this  liquid.  The  manipulation  does  not 
nqore  the  observer  to  be  close  by ;  he  may,  on  the  contrary,  be  at 
the  distance  of  sever^  yards,  and  observe  the  instrument  with  a 
tdeseope.  No  vapour  is  found  near  the  point  at  which  the  hygro- 
■etiic  state  is  determined ;  and  much  lower  temperatures  may  be 
obluned  than  with  Daniell's  hygrometer.  Thus,  during  the  greatest 
lammer  heat,  Regnault  succeeded  in  lowering  the  thermometer  of 
the  condenser  several  degrees  below  32^,  and  covering  the  metallic 
nde  with  a  thick  layer  fA  hoar  frost. 

2d.  The  psychrometer  of  August,  which  is  more  generally 
known  in  this  country  as  the  tcet-and-dry  hulb  hi/grometer,  is  per- 
haps the  most  extensively  employed  of  all  hygrometrical  instru- 
meots.  This  has  resulted,  probably,  from  the  fuct,  that  it  doe^  not 
easily  get  out  of  order,  and  from  its  demanding  no  practical  skill  on 
the  part  of  the  observer. 

The  two  following  were  the  formulae  constructed  by  Professor 
August  for  the  determination  of  the  elastic  force  of  the  watery 
▼apoor  contained  in  the  air. 

-       _g— 0-558  (<  — 0  6 
^  '*'■"  5l2=7  ' 

^        _e  — 0-558ft  — <')6 
^^-  "^^  572=7  ' 

I  being  the  tension  required  of  the  vapour  in  the  atmosphere  in 
the  Paris  lines ;  e  the  tension  in  Paris  lines  which  corresponds  with 
the  temperature  of  the  moist  thermometer ;  t  the  temperature  of  the 
dry,  and  /  that  of  the  moist  thermometer,  in  degrees  of  lleauraur's 
scale;  and  lastly,  h  the  altitude  of  the  barometer  in  Paris  lines. 
Formula  L  serves  lor  temperatures  above  32^,  and  II.  when  the 
damp  tbennometer  is  covered  with  ice,  t.  e.,  for  temperatures  under 

BeCBMill  liaa  shown  (Annate*  de  Chimie  et  dt  Physique.^  Tome 

a  * 


60  HETSOHOLOOT. 

xzxrii.,  Man,  1853),  tbat  thcso  formuIiB  cannot  be  regurded  u  t 
true  ezprsBBion  of  tbe  facts ;  for  they  lake  no  account  of  f^everel  ci^ 
oumelancea  which  exert  a  great  influcnc«  on  the  indications  of  the 
instrument.  TIid  relitive  temperstnrca  of  the  dry  »nd  moist  tbei^ 
monieters  do  oot  depend  only  on  the  atate  of  saturation  of  the  sir; 
they  depend  dIeo  ou  ita  different  states  of  agitaUon,  and  on  the  Ivtd 
conditiona  in  which  ii  is  placed.  Thesa  thermometers  indkaU,  k 
fact,  reaultants  dependent  on  the  proper  temperature  of  the  aninnit 
nir,  oQ  the  variable  calorific  ndiation  of  the  BnrroondiDg  bodies,  aid 
besides,  for  the  moist  thermometer,  on  the  evaporating  power  (lAidi, 
perhaps,  varies  with  the  temperature)  which  the  air  exerts  on  wttar, 
in  the  conditions  of  temperature,  saturation,  and  motion,  in  whiah 
the  instrument  is  placed.  By  giving  to  the  psychrometer  a  i^nd 
motion  of  circular  translation  about  a  vertical  axis,  we  mav  dimiiuth 
the  iDflucnce  of  the  variable  agitation  of  the  air  and  that  of  the 
local  conditions:  but  wo  will  thus  destroy  the  simplicity  of  tha 
instrument,  which  constitutes  its  principal  merit. 

Kcgnault  coniiidors  it  useless  to  seek  formula)  which  will  repr^ 
sent  psychrometrical  observations  better  than  those  of  Angoit, 
because  evidently  no  aooount  can  be  taken  of  the  local  and  nocidenliLl 
circum^itHnces  which  influence  the  instrument :  and  hence  ik 
vsi/ckriim'ii'r  m'ixt  be  rrr/arded  a*  a  mere  empirical  inttnime^ 
k/iusc  inilicaliont  are  without  scientific  value.  It  is  therefore  to  be 
desired  that  observers  should  be  well  convinced  of  this  fiict,  in  order 
tbat  they  may  not  continue  to  make  use  of  instrnmente  on  whose 
iodicatioDS  they  possess  no  certain  data,  and  to  accumulate  donbtful 
observations  which  will  be  much  more  injurious  than  useful  to  the 
progress  of  meteorology. 

3d.  The  ^iV  hyi/romctfr  of  Sanssuro,  which  is  tho  only  kind 
of  absorption  hygrometer  ever  employed  to  any  extent,  is  entirdj 
unreliable ;  for  the  numcroua  experiments  of  Kcgnault  haro  demon- 
atrated  that  no  two  instruments  furnish  indications  which  admit  of 
comparison,  and  that  they  do  not  possess  the  high  degree  of  sens- 
bility  which  was  formerly  assigned  to  them.  In  iuct,  uicy  aro  ofien 
quite  long  in  arriving  at  their  state  of  eriuilibrium.  Henoo,  thii 
iDstrumcnt  also  should  be  totally  abandoned.] 

2248.  Deic. — The  evaporation  produced  during  the  day  by  the 
action  of  solar  heat  on  the  suritice  of  water,  and  on  all  bodies 
chai^d  with  mobture,  causes  the  atmosphere  at  the  time  of  sunset 
to  be  more  or  less  charged  with  vapour,  especially  in  the  wans 
season.  On  hot  days,  and  in  the  absence  of  winds,  the  atmosphere 
St  snnset  is  generally  at  or  near  the  point  of  saturation. 

Immediately  after  sunset  the  temperature  of  the  air  falb.  If  it 
were  previonsly  in  a  stato  of  saturation,  condensation  must  ensue, 
which  will  bo  con^derable  if  the  heat  of  the  day  and  the  consequent 
ehange  of  tempcraturo  afler  sunset  bo  great      In  snch  esse,  the 


DXW  EXPLAINED.  67 

ympaar  condcnflcd  oft«n  assumes  the  appearance  of  a  fine  rain  or  mist^ 
tikiDg  the  liquid  form  before  its  actual  deposition  on  the  surface. 

The  deposition  of  dew,  however,  also  tidccs  place  even  where  the 
atmosphere  is  not  reduced  to  its  point  of  saturation.  When  the 
finnament  is  unclouded  after  sunset,  all  objects  which  are  good  radi- 
ators of  heat,  among  which  the  foliage  and  flowers  of  vegetables  arc 
the  foremost,  lose  by  radiation  the  heat  which  they  had  received  * 
before  sunset  without  receiving  any  heat  from  the  firmameut  suffi- 
ooit  to  replace  it.  The  temperature  of  such  objects,  therefore,  falls 
moch  below  that  of  the  air,  on  which  they  produce  an  effect  pre- 
dtely  similar  to  that  which  a  glass  of  very  cold  water  produces  when 
exposed  to  a  warm  atmosphere  charged  with  vapour.  The  air  con- 
tieuous  to  their  surface  being  reduced  to  the  dew  point  by  contact 
with  them,  a  part  of  the  vapour  which  it  holds  in  suspension  is  con- 
densed, and  collects  upon  them  in  the  form  of  dew. 

It  follows  from  this  reasoning,  that  the  dew  produced  by  the  fall 
nf  temperature  of  the  air  below  the  point  of  saturation  will  bo 
deposited  equally  and  indifferently  on  the  surfaces  of  all  objects 
exposed  in  the  open  air;  but  that  which  is  produced  by  the  loss  of 
temperature  of  objects  which  radiate  freely,  will  only  be  deposited 
OD  those  surfaces  which  are  good  radiators.  Foreign  writers  on 
physics  accordingly  class  these  depositions  as  different  phenomena, 
the  former  being  called  by  French  meteorologists  serein,  and  the 
ktter  roi^e  or  dew.  We  are  not  aware  that  there  is  in  English  any 
term  corresponding  to  serein. 

Dew  will  fail  to  be  deposited  even  on  objects  which  are  good  radi- 
itors,  when  the  firmament  is  clouded.  For  although  heat  be  radiated 
18  abundantly  from  objects  on  the  surface  of  the  earth  as  when  the 
Bkj  is  unclouded,  yet  the  clouds  being  also  good  radiators,  transmit 
hat,  which  being  absorbed  by  the  bodies  on  the  earth,  compensates 
for  the  heat  they  lose  by  radiation,  and  prevents  their  temperature 
from  falling  so  much  below  that  of  the  air  as  to  produce  the  con- 
densation of  vapour  in  contact  with  them. 

Wind  aiso  prevents  the  deposition  of  dew,  by  carrying  off  the  air 
fnm  contact  with  the  surface  of  the  cold  object  before  condensation 
has  time  to  take  place.  Meanwhile,  by  the  contact  of  succeeding 
poitioos  of  air,  the  radiator  recovers  its  temperature. 

la  general,  therefore,  the  conditions  necessary  to  insure  the  depo- 
■tioD  of  dew  are,  1st,  a  warm  day  to  charge  the  air  with  vapour ; 
2d,  ID  unclouded  night;  3d,  a  calm  atmosphere;  and,  4th,  objects 
expoicd  to  it  which  are  good  radiators  of  heat. 

In  the  close  and  sheltered  streets  of  cities  the  deposition  of  dew 
ii  iirely  observed,  because  there  the  objects  are  necessarily  exposed 
l»  ewh  other's  influence,  and  an  interchange  of  heat  by  radiutiou 
t4ei  pboe  so  as  to  maintain  their  temperature ;  besides  which,  the 


68  HETBOROLOCIT. 

objects  found  tbere  &re  not  aa  atrong  ndUton  u  tha  fbli^a  Mil 
flowers  of  vcgotablcB.  J 

2249.  Hoar  feral.  —  Whan  the  cold  which  follows  the  oondeiufrj 
tion  of  vnpnur  falls  below  32°,  what  wonid  otbcnrise  be  Dtw  h^  i 
comcB  BOAR  FROST.  For  the  same  reason  that  dew  is  depOKtrij 
when  the  temperature  of  tbo  air  is  above  the  point  of  satonlii^  I 
.  boar  frost  maj  be  msDifeated  when  the  temperature  of  tba  air  s] 
manj  degrees  above  the  point  of  oongelation ;  for  in  tliis  cue,  ■■  k] 
that  of  dew,  the  objects  on  which  the  boar  frost  colleote  low  ao  BHiki 
beat  bj  their  strong  radiation,  that  while  the  atmoephere  mmj  \n 
above  40°  they  will  fall  below  32°.  In  snoh  cases,  a  dew  is  flat 
deposited  upon  them  which  eoon  pongeals,  and  forma  the  needlei  ntk 
crystals  with  which  every  observer  is  familiar. 

The  boar  frost  is  sparingly  or  not  at  a]l  formed  upon  the  nakal 
earth,-  or  on  stones  or  wood,  while  it  is  profusely  collected  oo  leam 
and  flowers.     The  latter  are  strong,  the  former  feeble  radiators. 

Glass  is  a  good  radiator.  The  panes  of  a  window  fall  during  dii 
night  to  a  teitipcrikturc  below  32°,  although  tbc  air  of  the  room  la 
at  a  much  higher  tcnipcmtarc.  Condensation  and  a  profnv 
deposition  of  moisture  takes  platw  on  tlicir  inner  surfaces,  which 
soon  congeals  and  exhibits  the  cryatuUized  coating  so  often  wit- 
nessed. 

The  frost!)  of  spring  and  autumo,  which  so  frequently  are  it- 
tended  with  injury  to  the  crops  of  the  farmer  and  ganlcner,  proceed 
generally  not  from  the  congelation  of  moisture  deposited  frwa  tto 
atmosphere,  but  from  the  congelation  of  their  own  proper  moiston 
by  the  radiation  of  their  temperature  caused  by  the  nocturnal  ra^ 
ation,  which  in  other  cases  produces  dew  or  hoar  frost.  The  yoing 
buds  of  leaves  and  flowers  in  spring,  and  the  grain  and  fruit  io 
autumn,  being  reduced  by  radiation  below  32°,  while  the  atmoapben 
is  man;  degrees  above  that  temperature,  the  water  which  forms  (art 
of  their  composition  is  frozen,  and  blight  ensues. 

These  principles,  which  serve  to  explain  the  eanse  of  the  evil,  alia 
suggest  its  remedy.  It  is  only  necessary  to  ihelter  the  object  from 
exposure  to  the  unclouded  skj,  which  may  bo  done  by  matting 
gauze,  and  vsrious  other  expedients. 

2^50.  Fabrication  of  ice  in  hot  climatfs. — In  tropical  climatv 
the  principle  of  nocturnal  radiation  has  supplied  the  means  of  tfa« 
artitcial  produolion  of  ice.  This  process,  which  is  conducted  on  i 
coDaiderable  scale  in  Bengal,  where  some  establishments  for  tb«  pn- 
pose  employ  Beveral  hundred  men,  consists  in  placing  wftter  ia 
shallow  pans  of  unglazed  pottery  in  a  situation  which  is  exposed  to 
the  clear  sky  and  sheltered  from  currents  of  air.  Evaporation  ii 
promoted  by  the  porous  quality  of  the  pans  which  become  aoaked 
with  water,  and  radiation  takes  place  at  the  same  time  both  from  tki 
water  and  the  pani.    Both  these  oauses  oombise  in  lowering  Ihi 


FOGS  Ain)   CLOCDa. 


3251.  Fiyn  and  chiuh.  —  Wlien  the  steam  isfiuing  from  tlie  sur- 
ke  of  wsrm  water  asccuds  into  air  whicb  is  at  a  lower  tcmpcraliire, 
im  Qondenaed,  but  tbe  particles  of  water  formed  by  Bucb  codiIcds:!- 
fioB  ue  so  minatej  that  thc^  float  in  tbe  air  aa  would  the  Diinuto 
lAtielee  of  «a  extremely  fine  dost  Tbcse  particles  lose  tbeir  trans- 
pRDCj  by  Tcason  of  their  ntintitenGaa,  acconliag  to  a  geticral  law  of 
fijwiil  optics.  The  Tapour  of  water  is  tracsparent  and  colourlesa. 
It  ii  only  when  it  losea  tbe  character  and  qualities  of  true  vnpnur, 
Aat  it  lequires  the  cloudy  and  semi-opake  appcantDoe  just  men- 
faned. 

Fogs  an  nothing  more  tbao  such  condensed  vapour  produced  from 
die  snr&ce  of  seas,  lakes,  or  rivers,  when  the  water  hu  a  higher 
bnperatnrc  than  the  stratum  of  air  which  rests  upon  it  These  fogs 
He  more  thick  and  frequent  when  the  air,  besides  having  a  lower 
temperatore  than  tbe  water,  is  already  saturated  with  vapour,  because 
in  that  case  all  tbe  vapour  developed  must  be  immediately  condensed, 
whereas,  if  the  air  be  not  saturated,  it  will  absorb  more  or  less  of  tho 
npoor  which  rises  from  the  water. 

[Fogs  are  quite  frequently  observed  in  drcnmstanees  which  seem, 
tt  first  sight,  very  difierent  from  the  foregoing.  For  example,  at  tbe 
lime  of  a  thaw,  when  the  tempemtare  of  the  air  is  sensibly  higher 
than  that  of  the  water,  very  dense  fogs  still  form  on  rivers,  even 
riien  ^ey  arc  covered  with  ice :  but  appearances  only  arc  changed, 
the  piiociple  is  the  same.  In  fact,  in  this  case,  the  warm  air  is  satu- 
lated  with  humidity,  and,  when  it  comes  to  be  mixed  with  the  air 
vlucb  bas  been  cooled  by  contact  with  the  ice  or  other  cold  bodies, 
in  Tapoor  is  condensed.] 

Cloods  ue  nothing  bnt  fc^  suspended  in  the  more  elevated  strata 
of  the  atmosphere.  Clouds  are  most  frequently  produced  by  the 
intermixtare  of  two  strata  of  air,  having  different  temperatures  and 
^tknotly  charged  with  vapour,  the  mixture  being  supersaturated, 
and  therefore  being  attended  with  pardal  condensation  as  already 
explained  (2235). 

[It  u  generally  admitted  that  the  vapours  which  constitute  .clonds 
an  reticular  vapours;  that  is  to  say,  aggregations  of  little  globules 
filled  with  moist  air,  altogether  analogous  to  sonp-bubblcs.  These 
globoles  are  very  easily  distinguished  by  the  naked  eye  in  fogs  whicb 
rise  on  warm  water,  and  particularly  on  tho  surftice  of  a  black  solu- 
tion, as  coffee.  Their  density  is  essentially  greater  than  that  of  tho 
■ir,  on  acconnt  of  the  liquid  pellicle  which  forms  their  envelope  ;  and 
it  is  somewhat  difficult  to  explain  how  they  can,  notwithstanding  this 
exoen  of  danuly,  remain  suspended  in  the  ait.     Qay-Lussao  was  of 


70  METEOROLOGT. 

opinion  that  tlie  currents  of  warm  air  which  rise  inoessantlj  from  the 
earth  during  the  d;iy,  have  a  great  influence  in  determining  the 
ascension  and  iiiaintiiining  the  suspension  of  clouds.  Frcsnel  sup- 
posed that  the  solar  heat,  hcing  absorbed  by  the  clouds,  forms  oat 
of  them  a  species  of  air-balloons  which  rise  to  heights  proportioDil 
to  the  excess  of  temperature.  These  two  causes  are  without  donbt 
very  efficacious ;  but  we  are  as  yet  in  possession  of  too  few  data  on  the 
true  constitution  of  clouds  and  on  tne  properties  of  the  vapoars  or 
different  elements  which  compose  them,  to  attempt  a  complete  explt- 
uation  of  the  phenomenon.  Wo  are  still  less  able  to  present  any 
thing  but  conjectures,  more  or  less  hazardous,  on  the  causes  which 
determine  the  form  of  clouds,  their  extent,  their  elevation,  thnr 
colour,  and  all  their  various  appearances,  whose  study  is  the  object 
of  the  meteorologist.] 

2252.  Rain.  —  When  condensation  of  vapour  takes  place  in  tbe 
upper  strata  of  the  atmosphere,  a  fog  or  mist  is  first  produced,  after 
which  the  aqueous  particles  coalescing  form  themselves  in  virtue  nf 
the  attraction  of  cohui^ion  into  spherules,  and  fall  by  their  gravity  to 
the  earth,  producing  the  phenomenon  of  rain. 

2253.  Rain  gnwfc.  —  An  instrument  by  which  the  quantity  of 
rain  which  falls  upon  an  area  of  given  magnitude,  at  a  given  place, 
within  a  given  time,  is  called  a  IIain  gauge  or  Udometer.  [The 
terms  Pluvimeter  and  Ombrometer  are  employed  by  some  ob- 
servers to  denote  the  same  instrument.] 

These  instruments,  which  vary  in  form,  in  magnitude,  and  in  the 
provisions  by  which  the  quantity  falling  is  measured  and  registered, 
consist,  in  general,  of  a  cylindrical  reservoir  of  known  diameter,  the 
bottom  of  which  being  funnel-shaped,  terminates  in  a  discharge-pipe, 
through  which  the  contents  pass  into  a  close  vessel.  The  qnantttj 
received  from  time  to  time  by  this  vessel  is  measured  and  indioatea 
by  a  great  variety  of  expedients. 

2254.  Quantity  of  rain  falling  in  various  j^laces. — ^The  quantity 
of  rain  which  falls  in  a  given  time  at  a  given  place,  is  expressed  by 
stating  the  depth  which  it  would  have  if  it  were  received  upon  i 
plane  and  level  surface,  into  which  no  part  of  it  would  penetrate. 

At  Paris,  the  average  annual  quantity  of  rain  which  falls,  obtained 
from  observations  continued  for  thirty  years  at  the  Observatory,  ii 
23  G  inches.  There  is,  however,  considerable  variation  in  the  quan- 
tities from  which  this  average  is  deduced;  the  smallest  quantitj 
observed  being  16*9  inches,  and  the  greatest  27*9  inches. 

The  greatest  annual  fall  of  rain  is  that  observed  at  Maranham, 
lat.  2^°  S.,  which  is  stated  by  Uumboldt  to  amount  to  277  inchee, 
more  than  double  the  annual  quantity  hitherto  observed  elsewhere. 
The  following  are  the  annual  quantities  at  the  under-named  places :— 


BAIN  —  SHOW  —  HAIL. 


10-0 
41-8 
8B-& 
861 


17-0 
89-0 
M-0 


Bordcanz  (7  jean)... 
Obftlona  (48  jmn).... 
Dijon  (34  7»Ta> 


jvrn*  ffl  je>n) 

RuDMt  (8  jMia) 

8t  Lo  (S  7«ui) 

TonlonM  (8  7«wn)... 
Badn  of  tb*  Stoat  {• 

Kudal 

DoidIHm 


LiTeipool... 


London  (Dalton) 

"      (Howmrd)  .. 

York 

Edinburgh  —..■•. 


8S-6 
23-6 

27-6 
82 '5 
26-0 
()4'5 
29-5 
60-0 
S8'6 
81 '6 
260 
85-0 
b3-H 
86-02 
8614 


24-90 

25-70 
26-00 


the  following  nky  be 


mg  the  czceptioonl  pluvial  pben 

orft — 

Sombaj,  Bis  iocbes  of  rein  fell  in  a  aingle  day. 

^yenne,  ten  inches  fell  in  ten  hours. 

JeDoa,  on  the  25th  of  Oct  1822,  thirty  inches  of  rain  fell  on 

nneDce  of  a  water  apout.     Thb  is  the  greatest  &11  of  rain  on 

}.  Snoio.  — The  physical  conditions  which  dctennine  the  pro- 
I  of  snow  are  not  ascertained.  It  is  not  known  whether  the 
u  they  bll  are  immediately  produced  by  the  congelation  of 
aed  vapour  in  the  cloud  whence  they  first  proceed,  or  whether, 
at  first  minute  pardclea  of  frozen  vapour,  they  coalesce  with 
Ttoen  particles  in  felling  through  the  successive  strata  of  tho 
d  thus  finally  attain  the  magnitude  which  they  have  on  reach- 
I  gronnd. 
only  eiact  observations  which  have  been  made  on  snow  refer 
forma  of  the  crystals  composing  it,  which  Captain  Scoresby 
served  with  very  great  accuracy  in  his  Polar  Voyages,  and  of 
he  has  given  drawings.  The  flakes  appear  to  consist  of  fine 
I,  grouped  with  singular  symmetry.  A  few  of  the  most 
cable  forms  are  represented  in/^.  675. 

e  rtd  noie  which  is  met  with  in  polar  regions  and  wherever 
)ws  an  permanent,  owes  its  colour  to  a  small  fungus  or  mush- 
which  has  the  property  of  vegetating  in  snow.] 

t.  /All/. — The  phjuical  cuuees  which  produce  this  Eomu^XAa 


72  JIBTEOROLOQT. 

■oouT^  of  tho  agriculturist  are  uncertain.  UypothoBCS  b&ve  been 
advanced  to  exp&in  it  which  are  more  or  lees  plausible,  but  which 
do  not  fulGl  the  oonditionB  that  would  entitle  them  to  Uie  place  of 


phjfsical  causes.     Volla  prop...»J  _  .! !j,  .'.-.cL  hiia  obtained  Bona 

celebrity,  and  which  is  cbaracterized  by  the  iugcnuity  that  marked 
every  physical  investigation  of  that  great  philosopher.  Two  strata 
of  clouds,  each  charged  with  vapour,  and  with  opposite  clectriciticf^ 
arc  supposed  to  be  curried  by  different  atmospheric  currenU  at  difiia^ 
cnt  elevations  to  such  a  position,  that  one  is  vertically  above  the 
other,  and  ecparatcd  from  it  by  a  stratum  of  the  atmosphere  of  ■ 
cert^n  thickness.  Assuming  that  condensation  and  congelation  an 
produced  in  the  superior  cloud,  and  that  haibtoncs  of  small  magni- 
tude result  directly  from  the  congelation  of  particles  of  water,  theaa 
fall  in  a  shower  upon  the  inferior  cloud,  where  their  elcctridty  ia 
first  neutralized  by  an  equal  charge  of  the  contrary  Suid,  and  tb^ 
are  then  charged  with  that  fluid,  when  they  are  repelled  upwaidi, 
and  rise  again  to  the  superior  cloud,  where  like  effects  ensue,  ud 
they  fall  agun  to  the  iofcrior  cloud,  and  so  continue  to  rise  and  fidl 
between  the  two  clouds  upon  the  same  principle  as  the  pith-halli 
more  in  the  cipcriuient  described  in  (1794).  The  gradual  iacreiis 
of  magnitude  of  the  hailstones  during  this  reverberation  between  Uu 
two  clouds  is  tbua  ezplaiued  by  Volta :  —  When  they  fall  from  the 
superior  upon  the  inferior  cloud  tbcy  penetmt«  Jt  to  a  certain  deptli, 
and  because  of  thi-ir  low  temperature,  the  vapour  condenses  and  eon- 
geals  upon  their  ^uiTucu,  thua  iueruu^iii^  their  voimae.  The  same 
effect  ia  produced  whk;u  Ihi-y  ri:-c  ii^niu  to  the  biiiieriur  cloud,  and  ii 


HAILSTORMS.  73 

repeated  eaeh  time  that  they  pass  to  and  firo  from  cloud  to  cloud, 
ODtil  the  weight  of  the  stones  becomes  so  great  that  it  resists  the 
electric  mttraction,  and  they  then  fall  to  the  earth. 

Volta  also  explained  how  two  clouds  might  thus  be  charged  with 
contraiy  eleetridtiefl,  by  the  effect  of  solar  heat  in  producing  evapora- 
tion, and  by  the  assumption  that  vaporization  develops  positive  and 
condennftion  negative  electricity.  This  explanation  is  inadmissible, 
inasmuch  as  it  is  now  established  that  evaporation  and  condensation 
are  only  attended  with  the  development  of  electricity  when  they 
cause  deoompoflition.  However,  as  it  is  well  ascertained  that  clouds 
are  frequently  charged  with  opposite  electricities,  this  part  of  the 
hypotheab  of  Volta  might  be  received  without  objection  as  a  possi- 
bility. But  even  admitting  this,  the  hypothesis  cannot  be  regarded 
as  more  than  an  ingenious  conjecture. 

[In  the  explanation  of  hall  there  are  two  difficulties,  both  of 
which  have  mtherto  transcended  all  the  efforts  of  physicists  to 
resolve  them. 

We  require  to  know,  1st,  how  the  cold  which  congeals  the  water, 
is  produced  ;  and  2d,  how  a  hailstone  which  has  acquired  sufficient 
size  to  fall  by  its  own  weight,  remains  suspended  in  the  air  until  it 
aLi|uires  a  circumference  of  12  or  15  inches. 

The  theory  of  Volta  just  given  answers  only  the  second  of  these 
questions  :  it  has  been  attempted  to  answer  the  first  by  saying  that 
the  cold  is  produced  by  wind.  There  are  winds  which  are  always 
aecompanied  by  a  greater  or  less  depression  of  temperature :  such 
arc  those  which  are  propagated  by  rarefaction  (2220).  Observation 
has  shown  that  they  may  produce,  at  the  surface  of  the  earth,  a 
fJi  of  thirty  degrees;  and  there  is  no  doubt  that,  in  the  higher 
rc'piiona  of  the  atmosphere,  they  may  cause  a  still  greater  cold.  Me- 
t«orrjlogi:»t8  ought  then  to  pay  attention  to  this  point,  in  order  to 
ai^crtain  whether  the  winds  which  bring  hnilstorins  are  or  are  not 
winds  propagated  by  rarefaction.  If  the  cold  has  not  this 'origin, 
the  whule  difficulty  remains,  and  other  means  must  be  sought  for  its 
j^'lution.  The  theory  which  Volta  proposed  in  answer  to  the  secoud 
(juestiun  is  liable  to  some  grave  objections :  and  it  is  perhaps  moro 
tJirect  to  suppose  that,  the  cold  being  produced  by  the  wind,  it  is 
also  the  power  of  the  wind  which  carries  the  hailstones  horizontally 
'•r  at  least  very  obliquely  in  the  atmosphere ;  that  they  thus  traverse 
fifteen  or  twenty  leagues,  and  that  they  have  no  need  of  being  sus- 
pended for  a  very  long  time,  in  the  midst  of  very  dense  and  cold 
cljuda,  to  attain  the  enormous  size  which  they  sometimes  have.] 

2257.  The  pheno7ncna  atf^jmfinj  hailstorms. — In  the  absence  of 
iny  satiiifactory  explanation  of  the  phenonicuon,  it  is  imp^Ttant  to 
x^ccrtain  with  precision  and  certainty  the  circumstances  whicU  attend 
it,  and  the  conditions  under  which  it  is  produced. 

It  may  then,  in  the  first  place,  be  considered  as  certain  that  the 

iif  7 


74  MJSTE0B0L0Q7. 

formation  of  hail  is  an  effect  of  sndden  electrical  changes  in  eloodi 
charged  with  vapour;  for  [hail  ordinarily  precedes  thundexstormSi 
sometimes  accompanjiog  them,  but  hardly  ever  following  themj 
especially  if  the  storms  are  of  any  duration.] 

Before  the  fall  of  hail,  during  an  interval  more  or  leas,  bat  some* 
limes  of  several  minutes'  duration,  a  rattling  noise  is  generally  heard 
in  the  air,  which  has  been  compared  to  that  produced  by  shaking 
violently  bags  of  nuts. 

Hail  falls  much  more  frequently  by  day  than  by  night.  Hail 
clouds  have  generally  great  extent  and  thickness,  as  is  indicated  by 
the  obscuration  they  produce.  They  are  observed  also  to  have  a 
peculiar  colour,  a  grey  having  sometimes  a  reddish  tint  Their  form 
IS  also  peculiar,  their  inferior  surfaces  having  enormous  protu- 
berances, and  their  edges  being  indented  and  ragged. 

These  clouds  are  often  at  very  low  elevations.  Observers  on 
mountains  very  frequently  see  a  hail  cloud  below  them. 

It  appears,  from  an  examination  of  the  structure  of  hailstones, 
that  at  their  centre  there  is  generally  an  opaque  nucleus,  resembling 
the  spongy  snow  that  forms  sfcet.  flound  this  is  formed  a  congealed 
mass,  which  is  semi-transparent.  Sometimes  this  mass  consists  of 
a  succession  of  layers  or  strata.  These  layers  are  sometimes  all 
transparent,  but  in  different  degrees.  Sometimes  they  are  alter- 
nately opaque  and  semi- tran spare ut. 

[Pouillet  found  that  the  tcD>perature  of  hailstones  varied  from 
31°  to  25°  Fahr.] 

2258.  Ejctraor (Unary  examples  of  haihtones.  —  Extraordinary 
reports  of  the  magnitude  of  hailstones,  which  have  fallen  during 
storms  so  memorable  as  to  find  a  place  iu  gcncnd  history,  have  come 
down  from  periods  of  antiquity  more  or  less  remote.  According  to 
the  Chronicles,  a  hailstorm  occurred  in  the  reign  of  Charlemagne, 
in  which  hailstones  fell  which  measured  fifteen  feet  in  length  by  six 
feet  in  breadth,  and  eleven  feet  in  thickness;  and  under  the  reign  of 
'J'ippoo  Saib,  hailstones  equal  in  magnitude  to  elephants  are  said  to 
have  fallen.  Setting  aside  these  and  like  recitals,  as  partaking  rather 
of  the  churaeter  of  fable  than  of  history,  we  shall  find  sufficient  to 
create;  abtonislnnent  iu  well  authenticated  observations  on  this 
subject. 

In  a  hailstorm  which  took  place  in  Flintshire  on  the  9th  April, 
1C97,  Halley  saw  hailstones  which  weighed  five  ounces. 

On  the  4th  May,  1G97,  llobert  Taylor  saw  fall  hailstones  mea- 
suring fourteen  inches  in  circumference. 

In  the  storm  which  ravaged  Como  on  20th  August,  1787,  Volta 
saw  hailstones  which  weighed  nine  ounces. 

Oil  22(1  May,  1822,  Dr.  Noggerath  saw  fall  at  Bonn  hailstones 
which  weighed  from  twelve  to  thirteen  ounces. 

It  appears,  therefore^  certain  that  in  different  countries  hailstorms 


ATK 08FHBBIC  KLICTRICITT.  75 

bm  oeetmed  m  wbich  etonea  weighing  from  half  to  three  quarters 
tf  ■  ponnd  bare  bllen. 

r5ii58*.  Duaitroia  haxltlorm  in  France  and  Holland,  in  1788. 
~To  gire  Bomc  idea  of  how  far  this  terrible  scourge  tnaj  eztcncl, 
nd  with  what  rclocitj  it  may  be  propagated,  BOroe  oetaiU  will  hero 
be  reported  of  the  famous  Btorm  wbich  traversed  France  and  Hol- 
Imd  on  the  13th  of  JDI7,  1788.  This  storm  was,  without  doubt, 
the  moBt  disastroos  and  frightful,  as  well  aa  the  best  observed,  on 

The  Btcrm  was  propagated  simnltaaeoasly  in  two  bands,  nearly 
paiallel,  and  extending  from  the  southwest  to  the  northeast.  The 
eastern  band  was  the  narrowest,  having  the  average  breadth  of  two 
leagues  and  a  quarter :  that  of  the  western  was  four  leagues.  They 
were  separated  bj  a  band,  of  about  five  leagues  in  average  breadth, 
which  received  only  an  abundant  rain.  To  the  east  of  the  eastern 
band,  and  to  the  west  of  the  western  band,  there  was  also  much  rain, 
but  over  an  extent  not  well  deteriniucd.  Each  baud  bad  a  total 
length  of  more  than  200  leagues.  All  points  in  this  immense  ex- 
tent were  not  stmck  at  once ;  but  it  was  found,  on  comparing  the 
times,  that  the  storm  advanced  at  the  rote  of  about  50  miles  per 
hour  from  the  I'yrcnees,  where  it  seemed  to  have  originated,  to  the 
Baltic  Sea,  where  all  trace  of  it  was  lost.  At  each  point,  the  bail 
&1I  only  for  about  seven  or  eight  minutes. 

The  number  of  parishes  laid  waste  in  France  was  1039 ;  the  total 
loss  was  found  on  official  inquiry  to  be  24,690,000  francs. 

This  phcuomenou  presenU  the  most  prodigious  example  both  of 
Ibe  forces  which  act  in  collecting  watery  vapour  and  maintaining  it 
•upended  in  the  air,  and  of  those  which  produce,  amid  the  heats  of 
■nmmer,  a  sudden  depression  of  temperature  in  widely-extended 
itmoepheric  rc^ons.] 


CHAP.  IV. 

ATMOEPHEBTG  ELEOTBICITT. 


2259.  Tht  air  gnuraUy  charged  Tcilh  positive  eleclricily. — The 
terrestrial  globe  which  we  inhabit  is  invested  with  an  ocean  of  nir  the 
depth  of  which  is  about  the  200th  part  of  its  diameter.  It  may 
therefore  be  conceived  by  imagining  a  coating  of  air,  the  tenth  of  an 
inch  thick,  investing  a  twcniy-ineh  globe.  Tliia  aerial  ocean,  rela- 
tively shallow  as  it  is,  at  the  bottom  of  which  the  tribes  of  organized 
nature  have  ibar  dwelUng,  is  nevertheleaa  ibo  theatre  of  Blupcwiom 
eieotrM^  pbenomeoB. 


76  METEOROLOQT. 

It  nit;  be  stated  as  a.  gcDcral  fact,  that  the  atmonphere  ithioh 
coTcra  tbo  globe  is  cliortfiil  nitli  positive  electricity,  which,  acting  M 

induction  on  ttic   EupcrliL:ial  stratum  uf  t!io   glubi;  on  which  it 

decomposes  the  natursl  electricity,  ottrecting  the  nontive  flmt  M 
tbe  surface  and  repelling  tbe  positive  fluid  to  the  mferiw  rink 
Tba  globe  and  its  atmosphere  maj  therefore  be  oot  inaptly  ompml 
to  a  Lejdcn  phial,  tbo  outer  ooatiDg  of  wbicb  being  plaosd  ta  <^ 
neiion  with  tbe  prime  conductor  of  a  macbine,  is  chw^  n& 
positive  eleetricitj,  and  the  inner  coating  being  ia  oonneziaB  nA 
the  ground,  is  charged  by  indaction  with  negative  olectricitf.  IW 
outer  coating  represents  uie  atmosphero,  and  the  inner  tlie  sopeifinl 
stntam  of  tbo  globe. 

2260.  Thit  ttale  tubject  lo  oariatioru  and  exceptiont.  —  lis 
normal  stale  of  the  general  atmoepherio  ocean  is  subject  to  raiiatiai 
and  ezccptions;  variations  of  intensity  and  ezoeptinns  id  qatHtf « 
name.  The  Tariations  are  periodical  and  accidental.  Tbt  txxt^ 
tioDS  local;  patches  of  the  general  atmosphere  in  which  dottdsflot 
being  occasionally  charged  with  negative  electricity. 

2261.  Diurnal  variatiom  of  cleclrical  inlentili/. — Tho  inteuitf 
of  the  electricity  with  which  the  atmosphere  is  charged  variei,  ia  da 
conrsa  of  twenty-four  hours,  altomatuly  increasing  and  decretan^ 
It  begins  to  decrease  at  a  few  minutes  after  sunrise,  and  continnM  t» 
decrease  until  two  or  thseo  o'clock  in  the  aflernoon,  wbea  it  Bttsni 
a  minimum.  It  then  increases  and  continues  ia  inoreaso  until  soms 
minutes  after  sunset,  when  it  attains  a  maximum.  AfW  that  it 
again  decreases,  attaining  a  minimum  at  a  certain  time  in  tbe  ^oAi, 
wfaich  varies  in  different  places  and  different  seasons,  after  whicK  it 
again  increases  and  attains  a  majumum  at  a  few  minutes  after  aim- 
rise. 

In  general,  in  winter,  tho  electricity  of  tlto  air  is  mora  inteon 
than  in 


2-2G2.  Oliscrvtitiojts  of  Qarl-rlet.—'Ihtse  were  the  general  resoHl 
of  the  extensive  scries  of  obsenations  on  atmospberio  electrieiQ 
made  by  Saussure.  Alorc  recently  tbey  have  been  confirmed  by  IM 
observations  of  M.  Quctelct,  wbicb  have  been  continued  withent 
ioterniptJun  daily  at  tho  Observatory  of  Brussels  for  tbe  last  tea 
years.  N.  Quctelct  found  that  tbo  first  maximum  was  manifested 
about  8  A.  M.,  and  the  second  about  d  P.  M.  Tbe  minimum  in  tbt 
day  was  at  3  P.  M.  He  found  also  that  the  mean  intonu^  mi 
greatest  in  January  and  least  in  June. 

Such  ore  the  normal  changes  which  the  electrical  condiljoa  of  tha 
air  undergoes  when  the  atmosphere  is  clear  and  unclouded.  Wben, 
however,  the  firuiament  is  covered  with  clouds,  tbe  electricity  is  sob- 
ject  during  tbe  day  to  frequent  and  irregular  changes  not  only  in 
intensity  but  in  name;  the  elcctrioity  being  often  negative,  owing  to 


and  finiiu-liiiies  ncgiitivc,  varying  wifli  the  iliroction  of  l!io 
S'urili  ffiiiiU  jrive  positive,  and  snutli  winds  nepilivc  depDsits. 
.  Miihijilt  of  iJitereiiiff  almorpherie  eleetritily.  —  The  elec- 
r  the  ktmosphore  U  oWrvcd  by  crcctiog  in  it,  to  aoj  desired 
1,  pointed  mutallio  conductors,  from  tbo  lover  extremities  of 
'ires  sre  carried  to  electroscopes  of  various  forms,  according 
Dtensitj  of  the  electricity  to  bo  observed.  All  the  asn^ 
if  ftrtifioial  electricity  may  be  reproduced  by  such  means; 
Dkj  be  taken,  light  bodies  attracted  and  repelled,  electrical 
eh  as  tbnee  described  in  (1792),  affected;  and,  in  fine,  all 
J  effects  of  the  fluid  produced.  So  immediate  is  the  inoreaso 
ncal  tension  in  rising  through  the  strata  of  the  air,  that  a 
r  electroscope  properly  adapted  to  the  purpose,  and  reduced 
ataral  state,  vhca  placed  horiEontally  on  the  ground,  will 
icnsible  divergence  whea  raised  to  the  level  of  the  eyes. 
.  Mfthmh  of  atccrtnining  the  electrical  condition  of  (A« 
Urala. — To  ascertain  the  electrical  condition  of  strata  too 

to  be  reached  by  a  fixed  conductor,  the  extremity  of  a  flez- 
>,  to  which  a  metallic  point  is  attached,  is  connected  with  a 
ill,  wbich  is  projected  into  the  air  by  a  gun  or  pistol,  or  to 
IT  projected  by  a  bow.  The  projectile,  when  it  attains  the 
'  its  flight,  detaches  the  wire  from  the  electroscope,  which 
iicatcs  the  electrical  state  of  the  air  at  the  highest  point 

by  the  projectile. 
:zpedient  of  a  kite,  used  with  so  much  aoecess  bj  Franklin, 

and  othen,  to  drew  electricity  from  the  clouds,  may  also  be 


78  MBTEOROLOOT. 

oord  at  some  distance  from  the  lower  extremiiy,  where  it  mm  turned 
aside  and  brought  into  connexion  with  an  electroscope,  or  other 
experimental  means  of  testing  the  quantity  and  quality  of  the  elec- 
tricity with  which  it  was  charged.  Komas  drew  from  the  extremi^ 
of  this  conducting  wire  not  only  strong  electric  sparks,  but  blades 
of  fire  nine  or  ten  feet  in  length  and  an  inch  in  thickneas,  the  dii 
charge  of  which  was  attended  with  a  report  as  loud  as  that  of  a  pistol 
In  less  time  than  an  hour,  not  less  than  thirty  flashes  of  this  magni- 
tude and  intensity  were  often  drawn  from  the  oonduetor^  beaidei 
many  of  six  or  seven  feet  and  of  less  length. 

2267.  Electrical  charge  o/cknuls  varies.  —  It  has  been  shown  by 
means  of  kites  thus  applied,  that  the  clouds  are  charged  some  with 
positive  and  some  with  negative  electricity,  while  some  are  observed 
to  be  in  their  natural  state.  These  circumstances  serve  to  explain 
some  phenomena  observed  in  the  motions  of  the  clouds  which  are 
manifested  in  stormy  weather.  Clouds  which  are  similarly  electrified 
repel,  and  those  which  are  oppositely  electrified  attract  each  other. 
Hence  arise  motions  among  such  clouds  of  the  most  opposite  and 
complicated  kind.  While  they  are  thus  reciprocally  attracted  and 
repelled  in  virtue  of  the  electricity  with  which  they  are  charged,  they 
are  also  transported  in  various  directions  by  the  currents  wmch  pre* 
vail  in  the  atmospheric  strata  in  which  they  float,  these  currents 
often  having  themselves  different  directions. 

22G8.  Thunder  anil  lightning.  —  Such  appearances  are  the  bdtb 
prognostics  of  a  thunderstorm.  Clouds  charged  with  contrary  elec- 
tricities affect  each  other  by  induction,  and  mutually  attract,  whether 
they  float  in  the  same  stratum  or  in  strata  at  different  elevationa. 
When  they  come  within  striking  distance^  that  is  to  say,  such  a  dis- 
tance that  the  force  of  the  fluids  with  which  they  are  charged  sup* 
passes  the  resistance  of  the  intervening  air,  the  contrary  fluids  nub 
to  each  other,  and  an  electrical  discharge  takes  place,  upon  the  same 
principle  as  the  same  phenomenon  on  a  smaller  scale  is  produced 
when  the  charges  of  the  internal  and  external  coatings  of  a  Leyden 
jar,  overcoming  the  resistance  of  the  uncoatcd  part,  rush  together 
and  a  spontaneous  discharge  is  made. 

The  sound  and  the  flash,  the  thunder  and  the  lightning,  are  only 
the  reproduction  on  a  more  vast  scale  of  the  cxplotdou  and  spark  A 
the  jar. 

The  clouds,  however,  unlike  the  metallic  coatings  of  the  jar,  are 
very  imperfect  conductors,  and  consequently,  when  discharged  at  one 
part  of  their  vast  extent,  they  preserve  elsewhere  their  electricity  in 
its  original  intensity.  Thus,  the  first  discharge,  instead  of  establish- 
ing equilibrium,  rather  disturbs  it;  for  the  part  of  the  cloud  which  is 
still  charged  is  alone  attracted  by  the  part  of  the  other  cloud  in  which 
the  fiuid  has  not  yet  been  neutralized.  Hence  arise  various  and 
complicated  motions  and  variations  of  form  of  the  clouds,  and  a  ano- 


ATMOSPHERIC  ELECTBICITT.  79 

of  discharges  between  the  sunc  cloads  most  take  place  before 
Ike  electrical  equiiibriuin  is  established.  This  is  necesiuirilr  at  traded 
bj  a  corxespondiDg  succcsssion  uf  fla:»he5  of  lij^htuing  aud  claps  of 
thunder. 

2269.  Ibrm  and  extent  of  the  JUuh  of  UglUnmg. — The  f>nn  of 
the  flash  in  the  ease  of  lightning,  like  that  of  the  spark  taken  from 
in  electrified  condnctor,  is  zigzag.  The  doublings  or  acote  angles 
formed  at  the  snccessive  points  when  the  flash  changes  its  direction 
Tary  in  number  and  proximity.  The  cause  of  this  zigzag  course, 
w lie t her  of  the  electric  spark  or  of  lightning,  has  not  been  explained 
is  any  clear  or  satisfactory  manner. 

The  length  of  the  flashes  of  lightning  also  varies ;  in  f^me  cas^s 
they  have  been  ascertained  to  extend  to  from  two  and  a  half  to  throe 
miles.  It  is  probable,  if  not  certain,  that  the  line  of  light  exhib:!>?d 
by  flashes  of  forked  lightning  are  not  in  reality  one  continue^l  Wuft 
mmnltaneously  luminous,  but  that  on  the  contrary  the  li;:h:  is 
developed  successively  as  the  electricity  proceeds  in  its  cours^': ;  tLc 
appearance  of  a  continuous  line  of  light  being  an  optical  ^rff'jct  slhi- 
logons  to  the  continuous  line  of  light  exhibited  when  a  lij^hvyl  etiik 
is  moved  rapidly  in  a  circle,  the  same  explanation  being  appli'.-aLIe 
to  the  case  of  lightning  (1143). 

2270.  Cause*  of  the  roHinfj  of  thunthr, — As  the  sound  of  iLmnder 
is  produced  by  the  passage  of  the  electric  fluid  through  the  air  which 
it  suddenly  compresses,  it  is  evolved  progrc<»ivc-Iy  along  the  entire 
qiace  along  which  the  lightning  moves.  But  &:nce  sound  lu'^ve-s 
only  at  the  rate  of  1100  feet  per  second,  while  the  transmluion  fi 
light  is  90  rapid  that  in  this  case  it  may  be  considered  as  practically 
instantaneous,  the  sound  will  not  reach  the  ear  for  an  interval  greater 
or  less  after  the  perception  of  the  light,  ju<t  as  the  fla=h  of  a  gun  is 
Been  before  the  report  is  heard  rS31  j. 

By  noting  the  interval,  therefore,  which  elapses  between  the  per- 
eeptioa  of  the  flash  and  that  of  the  sound,  the  distance  of  the  p^iint 
where  the  discharge  takes  place  can  be  compute<l  approximat^/iy  by 
allowing  1100  feet  for  every  second  in  the  interval. 

But  since  a  separate  sound  is  produt.'e*!  at  every  point  through 
which  the  flash  passes,  and  as  thcsC  pjiut.s  arc  at  distances  from  the 
observer  which  vary  according  to  the  position,  length,  direction,  and 
furm  of  the  flash,  it  will  follow  necessarily  that  the  sonnds  pr^yJiiee'l 
by  the  same  flash,  though  practically  simultaneous,  because  of  the 
great  velocity  with  which  the  electricity  moves,  arrive  at  the  ear  in 
comparatively  slow  succession.  Thus,  if  the  flash  be  transmitted  in 
the  exact  direction  in  which  the  observer  Is  placed,  and  its  length  be 
11,000  feet,  the  distances  of  the  points  where  the  first  and  last 
ioands  are  produced  will  differ  by  ten  times  the  space  thrrmgh  which 
souxui  movei  in  one  second.    The  first  sound  will,  therefore,  be  heard 


80  MHTBOBOIiOOT. 

ten  geconds  before  tha  ks^  Bod  (be  inteiuMdiftte  soundfl  vili  be  bwd 
during  the  inteiral. 

The  varying  loudoees  of  the  anoceraivB  lomida  heird  in  Hia  viSaf 
of  thunder  proceeda  in  p&rt  from  the  uma  oaosea  u  tbe  mTiag 
iotensity  of  the  light  of  the  flaah.  Bat  il  may,  perit^w,  be  won 
sntiHfactorily  explained  by  the  oombinKtioD  of  tha  niooeanTa  fi» 
(^barges  of  tbe  Bamo  cIoDd  rapidly  eacoeeding  euh  other,  and  eo»- 
biniDg  their  cfiects'with  thoge  arising  &om  the  varying  dutKBOii  if 
difTurent  parts  of  the  same  flash. 

2271.  Affected  by  the  zigzag  form  of  lightning.— It  afniean  to 
that  the  varying  intensity  of  the  rolliog  of  tbander  may  auo  be  n 
clearly  and  satis&ctorily  ezplmaed  by  the  ligzag  form  tX  tha  flu 
combined  with  the  effect  of  the  varying  distance ;  and  it  ueois  exb 
ordinary  that  an  explanation  so  obvious  haa  not  been  raMsak 
Let  A,  B,  0,  D,  fig.  G76.,  be  a  part  of  a  sigiag  flash  seeitVj  ' 


observer  nt  0.  Taking  o  as  a  centre,  suppose  arcs  O  c  and  B  6  of 
circles  to  be  drawn,  with  o  c  and  o  b  as  radii.     It  is  clear  that  the 

pointA  c  and  r,  and  b  and  h,  being  respectively  equally  distant  ^m 
the  observer,  the  sounds  produced  there  will  be  heard  eimnitane- 
ounly,  and,  supposing  them  equal,  will  produce  the  perception  of  ■ 
sound  twice  as  loud  as  cither  heard  alone  would  do.  All  the  points 
on  the  zigzag  c  B  c  &  are  so  placed  that  three  of  them  are  equ- 
di!^taat  from  o.  Thus,  if  with  o  as  centre,  and  o  m  as  i*din«, 
a  iiireukr  arc  bo  described,  it  will  intersect  the  path  of  the  light- 
ning at  the  three  points  m,  ni',  and  m',  and  theso  three  pcnnti 
being,  therefore,  at  the  same  distance  from  o,  the  sounds  prodneod 
at  them  will  reach  the  observer  at  the  same  moment,  and  if  they  bo 
equally  intense  wilt  produce  on  the  ear  the  same  effect  as  a  single 
sound  three  times  as  loud.  The  same  will  be  true  for  all  the  points 
of  the  zigzag  between  c  and  h.  Thus,  in  this  case,  supposing  the 
intensity  of  the  lightning  to  be  uniform  from  A  (o  D,  there  will  be 
three  degrees  of  loudness  in  the  sound  produced,  the  least  between 
A  and  c  and  between  b  and  S,  the  greatest  between  e  and  b  aloDg 
the  ligxag,  and  the  tntermediate  at  the  points  c  c  and  B  h. 


ATHOSPHBKIO  BLB0TSICIT7.  81 

It  b  erident,  thkt  from  tho  infinite  Tariet;r  of  form  and  position 
lith  Telation  to  the  obeetrer,  of  vhicb  the  coorw  of  the  lightaing 
k  meeptible,  the  Tariationa  of  intenaity  of  the  rolling  of  Uiauder 
*hieh  IBs;  be  expluned  in  this  way  have  no  limit. 

2272.  Affected  by  the  varying  diilance  of  different  parts  of  the 
Jlptk. — Siooe  the  kmdoeaa  of  a  sound  diminishes  as  the  square  of 
the  distance  of  the  obeerrer  is  increased  (844),  it  is  clear  that  this 
afibcda  aoother  means  (d  explaining  the  rarying  loudness  of  the 
roUing  of  thander. 

2273.  Affected  by  echo  and  by  v/derferenee.  —  Aa  the  rolling  of 
thunder  u  mnoh  more  nried  and  of  longer  continuance  in  moun- 
teinona  redone  than  in  open  plane  oountries,  it  ia,  no  doubt,  also 
affected  by  reverbention  from  every  sur&ce  which  it  encounters 
whib  capable  of  reflecting  sound.  A  part  therefore  of  the  rolling 
mnat  be  in  such  cases  the  effect  of  echo. 

It  baa  been  also  coujectured  that  the  acoustio  effects  are  modified 
by  the  effects  of  interference  (836). 

2*274.  Inductive  action  of  duadt  on  the  earth. — A  cloud  charged 
with  electricity,  whatever  be  the  quality  of  the  fioid  or  the  state  of 
the  atmoaphere  around  it,  exercises  by  induction  an  action  on  all 
bodies  ujion  the  earth's  surface  immediately  under  it.  It  bos  a 
tendency  to  decompose  their  natural  electricity,  repelling  the  fiuid 
of  the  same  name,  and  attracting  to  the  highest  points  we  6uid  of 
a  contrary  name.  The  effects  thus  actually  produced  upon  objects 
exposed  to  such  indnction  will  depend  on  the  intensity  and  quality 
of  the  electricity  with  which  the  cloud  is  charged,  its  distance,  tho 
condnctibility  of  the  oiaterials  of  which  the  bodies  affected  consist, 
their  magnitude,  position,  and,  above  all,  their  form. 

Water  being  a  mnch  belter  conducter  than  earth  in  any  state  of 
tgmgtiioo,  thunder  clouds  act  with  greater  energy  on  the  sea,  lakes, 
■od  oUier  largo  collections  of  water.  The  flash  has  a  tendency  to 
pasB  between  the  cloud  and  the  water,  just  as  the  spark  passes  bc- 
tweeo  the  conductor  of  an  electric  machine  and  tho  hand  presented 
to  iL  If  the  water  were  covered  with  a  thin  ahcet  of  glass,  the 
lightning  would  still  pass,  breaking  through  tho  glass ;  because, 
although  the  glass  be  a  non-oonduclor,  it  does  not  intercept  the  con- 
ductive action  of  the  cloud,  any  more  than  a  thin  glove  of  varnished 
silk  on  the  hand  wonld  intercept  the  spark  from  the  conductor. 

2273.  FormatioTi  o/fulgurita  exjilained.— This  explains  the  foot 
that  lightning  sometimes  penetrates  strata  of  tho  solid  ground  under 
which  eabterranean  reservoirs  of  water  are  found.  The  water  of 
■ach  reservcars  is  affected  by  the  inductive  action  of  an  electrified 
cloud,  and  in  its  turn  rcaots  upon  the  cloud  as  one  coating  of  a 
Ijeydeo  jar  reacts  upon  the  other.  When  this  mutual  action  is  suf- 
fimently  strong  to  overcome  the  resistance  of  the  subjacent  atmo- 
sphere and  the  stnta  of  soil  under  which  the  subterranean  kbot- 


82  MBTEOROLOGT. 

▼oir  lies,  a  discbarge  takes  place,  and  the  lightmsg  penetntefl  tiie 
strata,  fusing  the  materials  of  T^hich  it  is  composed,  and  leaTiDg  a 
tabular  bole  witb  a  bard  vitreficd  coating. 

Tubes  tbus  formed  bave  been  called  fulgurites^  or  thunder  titba. 

2276.  Accidents  of  the  surface  which  ottrtKt  lightning. — The 
properties  of  points,  edges,  and  other  projecting  parts,  of  oondnctan, 
which  bave  been  already  stated  (1776),  will  render  easily  intelligible 
the  influence  of  mountains,  peaked  hills,  projecting  rocks,  trees, 
lofty  edifices,  and  other  objects,  natural  and  artificial,  which  project 
upwards  from  the  general  surface  of  the  ground.  Lightning  never 
strikes  the  bottom  of  deep  and  close  valleys.  In  Switserland,  on 
the  slopes  of  the  Alps  and  JPyrenees,  and  in  other  mountainous  coun- 
tries, muhdtades  of  cultivated  valleys  are  found,  the  inhabitants  of 
which  know  by  secular  tradition  that  they  have  nothing  to  fear  from 
thunderstorms.  K,  however,  the  width  of  the  valleys  were  so  great 
as  twenty  or  thirty  times  their  depth,  clouds  would  occasionally 
descend  upon  thom  in  masses  sufficiently  considerable,  and  lightning 
would  strike. 

Solitary  hills,  or  elevated  buildings  rising  in  the  centre  of  an  ex- 
tensive plain,  are  peculiarly  exposed  to  lightning,  since  there  ar«  no 
other  projecting  objects  near  them  to  divert  its  course. 

Trees,  especially  if  they  stand  singly  apart  from  others,  are  likely 
to  be  struck.  Being  from  their  nature  more  or  less  impregnated 
with  sap,  which  is  a  conductor  of  electricity,  they  attract  the  fluid, 
and  are  struck. 

The  effects  of  such  objects  are,  however,  sometimes  modified  by 
the  agency  of  unseen  causes  below  the  surface.  The  condition  of 
the  soil,  subsoil,  and  even  the  inferior  strata,  the  depth  of  the  roots 
and  their  dimensions,  also  exercise  considerable  influence  on  the 
phenomena,  so  that  in  the  places  where  there  is  the  greatest  appa- 
rent safety  there  is  often  the  greatest  danger.  It  is,  nevertheless,  a 
good  general  maxim  not  to  take  a  position  in  a  thunderstorm  either 
under  a  tree  or  close  to  an  elevated  building,  but  to  keep  as  much 
as  possible  in  the  open  plain. 

2277.  Lightning  follows  conductors  hy  preference, — Its  effects  on 
buddings.  —  Lightning  foiling  upon  buildings  chooses  by  preference 
the  points  which  are  the  best  conductors.  It  sometimes  strikes  and 
destroys  objects  which  are  non-conductors,  but  this  happens  generally 
when  such  bodies  lie  in  its  direct  course  towards  conductors.  Thus 
lightning  has  been  found  to  penetrate  a  wall,  attracted  by  a  mass  of 
metal  placed  within  it. 

Metallic  roofs,  beams,  braces,  and  other  parts  in  buildings,  are 
liable  thus  to  attract  lightning.  The  heated  and  rarefied  air  in 
chimneys  acquires  conductibility.  Hence  it  happens  often  that 
lightning   descends   chimneys,  and   thus   passes  into   rooms.     It 


ATMOSPHSRIC  ELBCTRICITT. 


8a 


bws  bell-wireS;  metallic  mouldings  of  walls  and  famitnre,  and 
les  gilding. 

2278.  Conductors  or  paratonnerres  [lightning-rods]  for  tTiepro- 
tian  of  buildings,  —  The  purpose  of  paratonnerres  [lightning-rods] 
oondoctors  erected  for  the  protection  of  buildings,  is  not  to  repel, 
i  rather  to  attract  lightning,  and  divert  it  into  a  course  in  which 
vill  be  inooxioas. 

A  paratonnerre  is  a  pointed  metallic  rod,  the 
length  of  which  varies  with  the  building  on  which 
it  is  placed,  but  which  is  generally  from  thirty 
to  forty  feet.  It  is  erected  vertic^ly  over  tho 
object  it  is  intended  to  protect.  From  its  base 
an  unbroken  series  of  metallic  bars,  soldered  or 
welded  together  end  to  end,  are  continued  to  the 
eround,  where  they  are  buried  in  moist  soil,  or, 
better  still,  immersed  in  water,  so  as  to  facilitate 
the  escape  of  the  fluid  which  descends  upon  them. 
If  water,  or  moist  soil,  cannot  be  conveniently 
found,  it  should  be  connected  with  a  sheet  of 
metal  of  considerable  superficial  magnitude, 
buried  in  a  pit  filled  with  pounded  charcoal, 
or,  better  still,  with  braise  [small  coal]. 

The  parts  of  a  well-constructed  paratonnerre 
are  represented  in  fig.  Qll.  The  rod,  which  is 
of  iron,  is  round  at  its  base,  then  square,  and 
decreases  gradually  in  thickness  to  the  summit. 
It  is  composed  commonly  of  three  pieces  closely 
joined  together,  and  secured  by  pins  passed  trans- 
versely through  them.  In  the  figure  are  repre- 
sented only  the  two  extremities  of  tho  lowest, 
and  those  of  the  intermediate  piece,  to  avoid 
^ving  inconvenient  magnitude  to  the  diagram. 
The  superior  piece,  g^  is  represented  complete. 
It  is  a  rod  of  brass  or  copper,  about  two  feet  in 
length,  terminating  in  a  platinum  point,  about 
three  inches  long,  attached  to  the  rod  by  silver 
solder,  which  is  further  secured  by  a  brass  ferule, 
which  gives  the  projecting  appearance  in  the  dia- 
gram below  the  point. 

Three  of  the  methods,  reputed  the  most  effi- 
cient for  attaching  the  paratonnerre  to  the  roof,  are 
represented  in  fig.  678.,  at  p,  /,  and  /.  At  p 
the  rod  is  supported  against  a  vertical  piece,  to 
which  it  is  attached  by  stirrups ;  at  Z  it  is  bolted 
upon  a  diagonal  brace ;  and  at  /  it  is  simply 
secured  by  bolts  to  a  horizontal  beam  through 


flf.  677. 


KBTBOROLOaT. 


vhich  i<  ptsMs.    The  Ust  is  evidentlj  the  letat  ac^  met&ol  rf 

filing  it. 


Fig  era 

Tbo  conductor  is  coDtiuued  downwarda  along  the  wall  of  the  e£- 
ficc,  or  ia  auy  other  coDvenieut  conrae,  to  the  ground,  either  bj  ban 
of  iron,  rouod  or  square,  or  by  a  cable  of  iron  or  copper  wires,  suA 
as  is  sometimes  used  for  the  lighter  sort  of  suspension  bridges.  Tlui 
is  attached,  at  its  upper  extremity,  to  the  base  j)f  the  panttouneire  bj 
a  joint,  which  is  hermetically  closed,  so  as  to  prevent  oxidation, 
which  would  produce  a  dangerous  solution  of  cootinoity. 

To  comprehend  the  protective  influence  of  this  apparatus,  it  most 
bo  considered  that  the  inductive  action  of  a  thander-cloud  decotnpoees 
the  natural  electricity  of  the  rod  more  energetically  than  that  of  sni- 
rounding  objects,  both  on  account  of  the  matcri^  and  tha  form  of 
the  rod  (177C).  The  point  becoming  surcharged  with  the  fluid  of  a 
contrary  name  from  that  of  the  cloud  suspended  over  it,  disehargca 
this  fluid  ID  a  jot  towards  the  cloud,  where  it  combines  with  and 
noutnlizes  an  equal  quantity  of  the  electricity  with  which  the  cloud 
is  charged,  and,  by  the  continuance  of  this  process,  ultimately  reduces 
the  cloud  to  its  natural  state. 

It  is  therefore  more  correct  to  say  thai  the  paratonneiro  draws 
electricity  from  the  ground  and  projects  it  to  the  cloud,  than  that  it 
draws  it  from  the  cloud  and  transmits  it  to  the  earth. 

It  is  evidently  desirable  that  all  conducting  bodies  to  be  protected 
by  the  paratonncrre  should  be  placed  in  metallic  connexion  with  it, 
since  in  that  case  their  electricity,  decomposed  by  the  inductive  aotioD 
of  the  clouds,  will  necessarily  escape  by  the  conductor  either  to  the 
earth  or  to  the  cloud  by  the  point. 

It  is  considered  generally  that  the  range  of  protection  of  a  para- 
tonnerro  is  a  circle  round  its  base,  whose  radios  ia  two  or  three  tiiaea 
its  length. 


ATH03PHKBIC   BLBCTRICITT.  85 

2270.  E^m  oflightnirig  on  bodiei  wkteh  it  ttrihei. — Theeffccta 
of  lightaing,  like  those  of  doctricity  evolved  by  artificial  meaDs,  aro 
threefold:  pbjnoloflcal,  physical,  and  mechnnical. 

When  ligfabaiDg  killa,  the  parts  where  it  haa  struck  bear  the  marks 
of  seven  baming;  the  bones  are  often  broken  and  crashed,  as  if  they 
had  been  snljected  to  violent  mechanical  pressare.  When  it  acta 
on  the  Bjstem  by  iadootion  only,  which  is  called  the  secondary  or 
indirect  ahock,  it  doea  not  immediately  kill,  but  inflicts  nervous 
■hocks  so  severe  as  sometimes  to  leave  effects  which  are  incnrable. 

The  physical  efiecta  of  lightning  produced  upon  condnctors  is  to 
nite  tbeir  temperature.  This  elevation  is  sometimes  so  great  that 
Ihey  are  rendered  incandesoent,  fased,  and  even  burned.  This  bap- 
pens  occanonally  with  bell-wires,  especially  in  exposed  and  unpro- 
tected posodoDa,  as  in  courts  or  gardens.  The  drops  of  molten  metal 
jnoduoed  iu  saoh  cases  set  fire  to  any  combustible  matter  on  which 
thej  may  chaooe  to  &11.  Wood,  straw,  and  snch  non-conducting 
bodies,  are  ignited  generally  by  the  lightniug  drawn  through  tbem 
by  the  attraction  of  other  bodies  near  them  which  are  good  con- 
ductoiB- 

The  mechanical  efiects  of  lightning,  the  phyncal  canso  of  which 
bas  not  been  satisfactorily  explained,  are  very  extraordinary.  Enor- 
Bona  maases  of  metal  are  torn  from  their  supports,  vast  blocks  of 
■tone  are  broken,  and  massive  buildings  are  razed  to  the  ground. 

2280.  The  Aurora  Borealii  —  the  phenomenon  unexplained.  — 
Ho  theory  or  hypothesis  which  has  commanded  general  acceptation, 
has  jet  been  SDggeated  for  the  explanation  of  this  meteor.  All  the 
appeanooss  which  attend  the  phenomenon  are,  however,  electrical; 
and  its  Cmni,  direodons,  and  positions,  though  ever  varying,  always 
bear  a  nonarkable  relation  to  the  magnetic  meridians  and  poles. 
WkateTer,  therefore,  be  its  phyrioal  cause,  it  is  evident  that  the 
theatre  of  ita  action  is  the  atmosphere;  that  the  agent  to  which  the 
development  is  due  is  electricity,  influenced  in  some  unascertained 
nunner  by  terrestrial  magnetism.  In  the  absence  of  any  satisfactory 
theorj  for  the  explanation  of  the  phenomenon,  wo  shall  con&ne  our- 
telvea  here  to  a  short  description  of  it,  derived  from  the  most  citen- 
mve  and  exact  series  of  observations  which  have  been  made  in  those 
regions  where  the  meteor  has  been  seen  with  the  most  marked  char- 
acters and  in  the  greatest  splendour. 

2281.  General  (Aaraeter  of  iJte  mcUxtr. — The  aurora  borealls  is 
a  Inminons  phenomenon,  which  appcara  in  the  heavens,  and  is  seen 
in  high  latitudes  in  both  hemispheres.  Tho  term  aurora  boroalis,  or 
northern  lights,  has  been  applied  to  it  because  the  opportunities  of 
witnessing  it  aro,  from  the  ficographical  character  of  the  globe,  much 
mora  frequent  in  the  northern  than  in  the  southern  ncmisphcre. 
The  term  aurora  polarii  would  bo  a  more  proper  designation. 

Thia  phenomenon  oonusts  of  luminous  rays  of  various  ooloors, 
lU.  8 


86  HETEOROLOOT. 

Ismitig  from  erery  direction,  but  oonverging  to  the  aame  p<Hnt,vlnA 
appear  after  sututot,  gcncrallj  toward  tba  north,  occasionally  tomd 
the  west,  and  aouietimes,  but  rarely,  toward  tbe  south.  It  fraqngiillj 
appears  near  the  horizon,  ae  a  vague  and  difTnse  ligbt,  something  likt 
the  faint  streaks  which  harbinger  tho  rising  sun  and  form  the  dun. 
Hence  the  pbcDomcnon  has  derived  its  name,  the  northern  momiiig. 
Souetimcs,  honcver,  it  is  presented  under  tbe  form  of  a  Bomhre  dmd, 
from  which  lumiuous  jets  issac,  which  aro  often  vaiioDsly  colotind,  i 
and  illuminate  the  entire  atmosphere. 

Tlio  more  consjiiououa  auroms  coinmcDcc  to  be  formed  BOon  afta 
the  close  of  twilight.  At  first  a  dark  mist  or  toggj  cftud  ii  p» 
ceivcd  ID  the  north,  and  a  littio  more  brightness  towards  tiie  wM 
than  in  the  other  parts  of  tbe  heavens.  Tho  mist  gradually  toko 
the  form  of  a  circalar  segment,  resting  at  each  comer  on  tba  horina. 
The  visible  part  of  the  aro  soon  becomes  surronnded  with  a  pals 
light,  which  is  followed  by  the  formation  of  one  or  several  Inminoni 
arcs.  Then  come  jets  and  rays  of  light  variously  coloured,  which 
issue  from  (lie  dark  part  of  the  segment,  the  continuity  of  which  ii 
broken  by  bright  cmanalions,  indicating  a  movement  of  the  mat, 
which  seems  a^tnted  by  internal  shocks  dnriog  tlie  formation  of 
these  lumiuoua  radiations,  that  issue  from  it  as  flames  do  from  a  ent- 
flagration.  When  this  species  of  fire  has  ceased,  and  the  anron  hu 
become  extended,  a  erown  is  formed  at  the  zenith,  to  which  thew 
rays  converge.  From  this  time  the  phenomenon  diminishes  in  its 
intensity,  eihibiting,  nevertheless,  from  time  to  time,  sometimes  «i 
one  side  of  tho  heavens  and  sometimes  on  another,  jets  of  light,  ■ 
erown,  and  colours  more  or  less  vivid.  Finally  the  motion  ceases; 
the  light  approaches  gradually  to  tho  horizon  ;  the  cloud  (juitting  the 
otiier  partM  of  the  firmament  settles  in  the  north.  Tho  dark  part  of 
tho  Hegiucnt  becomes  luminous,  its  brightness  being  greatest  near  tbe 
horixon,  and  becoming  more  feeble  as  the  altitude  augments,  until  H 
loses  its  light  altogether. 

The  aurora  is  sometimes  composed  of  two  luminous  segments, 
which  are  concentric,  and  separated  from  eoeh  other  by  one  dark 
space,  and  from  tho  earth  by  another.  Sometimes,  though  rarely, 
there  is  only  one  dark  segment,  which  is  symmetrically  pierced 
rouiid  its  border  by  openings,  through  which  light  or  fire  is  seen. 

'2'18'2.  Bncriptiim  of  nvroriit  seen  in  the  jm/ar  riyiom  hy  M. 
Jioltin.  —  One  of  the  most  recent  and  enact  descriptions  of  this 
meteor  is  the  following,  supplied  by  31.  Lottin,  an  officer  of  the 
French  navy,  and  a  member  of  tho  Scientific  Commission,  sent  some 
years  ago  to  the  North  Seas.  Between  Scptenibor,  183S,  and  April, 
183!),  this  savant  observed  nearly  l.'iO  meteors  of  this  class.  They 
were  most  fret[uent  from  the  17th  November  to  tho  25th  January, 
being  tho  interval  during  which  the  sun  rcmaiDcd  constantly  below 
tho  horizon.    During  this  period  there  were  sixty-four  aurcnas  visifalt, 


ATMOSPHERIC  BLBCTEICnT.  87 

I  manj  which  &  clouded  ekj  conccttled  from  the  eye,  but  the 

Be  of  which  was  indical^d  by  tho  disturbancea  they  produced 

he  insgDetic  needle. 

I  snccesNon  of  appearances  and  changes  presented  by  these 

V  *re  thns  described  by  M.  Lottin  :  — 

ween  fonr  and  eight  o'clock,  p.  h.,  a  light  fog,  rising  to  the 

le  of  six  degrees,  became  coloured  on  its  upper  edge,  being 

1  with  the  light  of  the  meteor  rising  behind  it     This  border 

ing  gradually  more  regular  took  tho  form  of  an  are,  of  a  pale 

'  eoloor,  the  edges  of  which  were  diffuse,  the  extremities  rest- 

I  the  horison.     This  bow  swelled  sIow]y  upwards,  its  vertex 

eonatantly  on  the  magnetdo  meridian.  Bkckish  streaks 
d  r^nlarly  the  luminous  are,  and  resolved  it  into  a  e3mtem  of 
these  rays  were  alternately  extended  and  contracted;  some* 
alow  ly,  sometimes  instantaneously;  sometimes  they  would  dart 
icreasing  and  diminishing  suddenly  in  splendour.  The  inferior 
or  the  feet  of  the  rays,  presented  always  tho  roost  vivid  light, 
rmed  an  arc  more  or  less  regular.  The  length  of  those .  rays 
rry  various,  bnt  they  all  converged  to  that  point  of  the  heavens 
td  by  the  direction  of  the  southern  pole  of  the  dipping  needle. 
imes  they  were  prolonged  to  tho  point  whero  their  directions 
eted,  and  formed  the  summit  of  an  enormous  dome  of  light. 
I  bow  then  would  continue  to  ascend  toward  the  senith :  it 

suffer  an  undulatoiy  motion  in  its  light  —  that  is  to  say, 
one  extremity  to  the  other  the  brightness  of  the  rays  would 
K  suecessively  in  intensity.  This  luminous  current  would 
:  several  times  in  quick  succession,  and  it  would  pass  much 
ft«qucntly  from  west  to  east  than  in  tho  opposite  direction. 
imes,  but  rarely,  a  retrograde  motion  would  take  place  imme- 
i  afterward ;  and  as  soon  as  this  wave  of  light  had  run  succes* 

over  all  the  rays  of  tho  aurora  from  west  to  east,  it  would 

ID  the  contrary  direction  to  the  point  of  its  departure,  pro- 
;  such  an  effect  that  it  was  impossible  to  say  whether  tho  raya 
aires  were  actually  affected  by  a  motion  of  translation  in  a  direo- 
»rly  horizontal,  or  whether  this  more  vivid  light  was  transferred 
ray  to  ray,  the  system  of  rays  themselves  suffering  no  change 
ition.  The  bow,  thus  presenting  the  appearance  of  an  alter- 
lotion  in  a  direction  nearly  horizontal,  had  usually  the  appcar- 
)f  the  undulations  or  folds  of  a  ribbon  or  flag  agitated  by  tho 
Sometimes  one  and  sometimes  both  of  its  extremities  would 

the  horizon,  and  then  its  folds  would  become  more  numerous 
iiarkcd,  the  bow  would  change  its  character,  and  as-sume  tho 
>f  a  long  sheet  of  rays  rcturuing  into  iUcIf,  and  consisting  of 
1  parts  forming  graceful  curves.     The  brightness  of  the  rays 

vary  suddenly,  sometimes  surpassing  in  splendour  stars  of  the 
isgnitndo ;  these  rays  would  rapidly  dart  out,  and  curves  would 


88  MBTEOBOtOaT. 

1m  formed  and  developed  like  the  folds  of  a  serpent;  thoa  tli*  IM 
voald  affect  various  coionrs :  the  base  would  be  red,  tb«  mmt  i 
green,  and  the  rcitiuindur  vruul  J  preserve  its  clear  jollov  hue.  Bmk  - 
was  the  arRLDgcnieut  whicli  the  colours  always  proserved ;  they  wn 
of  admtrnblo  traosprircocy,  the  base  ezbibiting  blood-red,  asd  At 
grccD  of  the  middlo  being  that  of  the  pale  emenld;  the  bTuhbni 
would  diiniDiah,  the  colours  disappear,  and  all  be  extingmshed,  k>1 
times  suddenly,  and  sometimea  by  slow  d^reea.  AAer  this  ^mfr 
pearance,  fragments  of  tho  bow  would  be  reproduoed,  would  oonliBM 
their  upward  movoment,  and  approach  the  aenith ;  the  i*yB,  ij  tke 
effect  of  perspective,  would  be  gradually  shortened;  the  Uaekom- 
of  the  arc,  which  presented  tben  tho  appeannoe  of  a  lane  aoMOf 
parallel  rays,  would  be  estimated ;  then  the  vertex  of  the  bow  vdoli 
reach  the  magnetic  zenith,  or  the  point  to  which  the  south  pole  d 
the  dipping  needle  is  directed.  At  that  moment  the  raya  wwld  be 
seen  in  tho  direction  of  their  feet.  If  they  were  coloured,  thar 
would  appear  as  a  large  red  baud,  through  which  the  green  linta  of 
their  superior  parts  could  bo  distinguished ;  and  if  the  ware  of  ligbt 
above  mentioned  pas,scd  along  tbem,  their  feet  would  fonn  a  king 
sinuous  undulating  zone;  niiile,  throughout  all  these  changes,  the 
rays  would  never  suffer  any  oscillation  in  the  dircotioa  of  their  azi^ 
and  would  constantlj  preserve  their  mutual  parallelisms. 

While  these  appeawinoea  are  manifested,  new  bows  aro  formed, 
either  commencing  in  the  same  diffuse  manner,  or  with  vivid  and 
ready-formed  rays  :  they  succeed  each  other,  passing  through  neaily 
the  same  phases,  and  arrange  themselves  at  certain  distances  front 
each  other.  As  many  as  nine  have  been  counted,  forming  as  many 
bows,  having  their  ends  supported  on  tho  earth,  and,  in  their  amnga- 
mcn^  rescmltling  the  short  curtains  suspended  one  behind  the  oths 
over  the  scene  of  a  theatre,  and  Intended  to  represent  th«  sky. 
Sometimes  the  intervals  between  these  bows  diminish,  and  two  « 
more  of  them  close  upon  each  other,  forming  one  large  lone,  trave» 
ing  the  heavens,  and  disappearing  toward  the  south,  becoming  rapidly 
feeble  aft«r  passing  the  zenith.  But  sometimes,  also,  when  thia  loia 
extends  over  tho  summit  of  tho  firmament  from  east  to  weat,  the 
moss  of  rays  which  have  already  passed  beyond  the  magnatio  aenith 
appear  suddenly  to  come  from  the  south,  and  to  form  with  theaa 
from  the  north  tho  real  boreal  corona,  all  tho  rays  of  which  oonrerga 
to  the  zenith.  This  appearance  of  a  crown,  therefore,  la  doabtlMS 
the  mere  effect  of  perspective ;  and  an  observer,  placed  at  Hm  aama 
instant  at  a  ocrtaia  distance  to  the  north  or  to  the  south,  would  per- 
ceive only  an  arc. 

Tho  total  zone  measuring  less  in  the  direction  north  and  lonth 
than  in  the  direction  east  and  west,  since  it  often  leans  upon  the 
earth,  the  corona  would  be  expected  to  have  an  elliptical  form;  but 
that  does  not  always  happcu :  it  has  been  seen  circular,  the  ^iTn^mil 


ATMOSPHERIC  ELBCTSIcnT.  89 

■tending  to  a  greater  distance  tban  ttom  eight  to  twelve 
im  the  lenith,  vhile  at  other  times  they  reach  the  horizon, 
then,  be  imagined,  that  all  these  vivid  rajs  of  tight  issue 

^lendonr,  sabject  to  continual  and  sudden  Tariations  in 
h  and  brightneaa ;  that  these  beautifal  red  and  green  tints 
im  at  intervals;  that  waves  of  light  undulate  over  them; 
ata  of  light  succeed  each  other;  and,  in  fine,  that  the  vast 

presents  one  immense  and  magnificent  dome  of  light, 
n  the  snow-oovered  base  sapplied  by  the  gronnd — which 
as  aa  a  daxiling  frame  for  a  sea,  calm  and  black  as  a  pitcbv 

BOme  idea,  though  an  imperfect  one,  may  be  obtained  of 
lid  spectacle  which  presents  itself  to  him  who  witnessei 
,  from  the  bay  of  Alten. 
rana,  when  it  is  formed,  only  lasts  for  some  minutes :  it 

forms  suddenly,  without  any  previous  bow.  There  are 
re  than  two  on  the  same  night;  and  many  of  the  anronw 
ed  with  no  crown  at  all. 

'ona  becomes  gradually  faint,  the  whole  phenomenon  being 
th  of  the  zenith,  forming  bows  grado^ly  paler,  and  gene- 
)pe&riog  before  they  reach  the  southern  horizon.  All  this 
nonly  takes  place  in  the  first  half  of  the  night,  after  which 
\  appears  to  have  lost  ita  intensity :  the  pencils  of  rays,  the 

the  fragment  of  bows,  appear  and  disappear  at  ioter?aIs; 
vys  become  more  and  more  diffused,  and  ultimately  merge 
agne  and  feeble  light  which  is  spread  over  the  heavens, 
ike  little  clouds,  and  designated  by  the  name  of  auroral 
'ague*  auroralei).  Their  milky  light  frequently  undergoes 
langes  in  its  brightness,  like  motions  of  dilatation  and  con- 
rhich  are  propagated  reciprocally  between  the  centre  and 
iferencc,  like  those  which  are  observed  in  marine  animals 
dusse.  The  phenomena  become  gradually  more  faint,  and 
disappear  altogether  on  the  appearance  of  twilight,  Some- 
rever,  the  aurera  continues  after  the  commencement  of  day- 


M  MKTEOROLOOT. 

broak,  whim  the  light  ia  so  Btrong  that  a  printed  book  nuy  be  mt  : 
It  tben  disappears,  sometimeB  Baddenlj;  bat  it  often  happens  tlii^  g 
ta  the  daylight  Kugiuente,  tbo  aurora  becomeB  gradotllj  vu 
andcfiacd,  tikkcH  a  whitish  aolonr,  and  is  nltimatelv  m  minn 
the  cirrho-stratus  clonds  th^  it  is  impoanble  to  aistiogi ' 
them. 


Some  of  the  appearances  bore  doscribed  a 
379,  680,  681,  682.,  copied  from  the  menioii 
There  is  great  difficult;  in  detcnnining  tbo  exact  height  of  the 


ATHOSPnBttlO  ELBCTRrCITT.  91 

%  bomlia  ibove  the  cartb,  and  accortliogly  the  opinions  given 
is  sabject  by  different  obscrYcra  are  widely  discordant.  Mairan 
Med  the  mean  height  to  be  175  French  leagues;  Bergman  Bays 
Kod  Euler  seTenl  thousand  miles.  From  the  comparison  of  a 
XT  of  observations  of  an  aurora  that  appeared  in  March,  1826, 

at  different  places  in  the  north  of  England  and  south  of  Seot- 

Dr.  Dalton,  in  a  paper  presented  to  the  Bojal  Society,  com- 
I  its  height  to  be  about  100  miles.  But  a  t^culation  of  this 
in  whica  it  is  of  necessity  suf^MMed  that  the  meteor  is  seen  in 
ly  the  same  pUoe  by  the  different  observers,  is  subject  to  very 

nnoertainty.  The  observsUons  of  Br.  Richardson,  Frsnklin, 
I,  Parry,  and  others,  seem  to  prove  that  the  place  of  the  aurora 
-  within  the  limits  of  the  atmosphere,  and  scarcely  above  the 
n  of  the  clonda;  in  fact,  as  the  diurnal  rotation  of  the  earth 
ices  no  change  in  ila  apparent  position,  it  muat  necessarily  par* 

of  that  motion,  and  oooaeqtieaUy  be  regarded  as  an  atmo- 
rical  iihcnomenon. 


BOOK   THE  SECOND. 

ASTRONOMY. 


CHAPTER  L 

METHODS  01*  INVESTIGATION  AND  MEANS  OF  OBSERVATION. 

2288.  The  solar  system,  —  The  earthy  which  in  the  economy  of 
the  uuiverse  has  become  the  habitation  of  the  races  of  men,  is  a 
globular  mass  of  matter,  and  one  of  an  assemblage  of  bodies  of  liko 
form  and  analogous  magnitude,  which  revolve  in  paths  nearly  oiicolar 
round  a  common  centre,  in  which  the  sun,  a  globe  having  dimen- 
sions vastly  greater  than  all  the  others,  is  established,  maintaining 
physical  order  among  them  by  hb  predominant  attraction,  and  minis- 
tering to  the  well-being  of  the  tribes  which  inhabit  them  by  a  fit 
and  regulated  supply  of  light  and  heat. 

This  group  of  bodies  is  the  Solar  System. 

2284.  The  stellar  universe.  —  In  the  vast  regions  of  space  which 
surround  this  system  other  bodies  similar  to  the  sun  are  placed, 
countless  in  number,  and  most  of  them,  according  to  all  probability, 
superior  in  magnitude  and  splendour  to  that  luminary.  With  these 
bodies,  which  seem  to  bo  scattered  throughout  the  depths  of  im- 
mensity without  any  discoverable  limit,  we  acquire  some  acquaintance 
by  the  mere  powers  of  natural  vision,  aided  by  those  of  the  under- 
standing; but  this  knowledge  has  received,  especially  in  modem 
times,  prodigious  extension  from  the  augmented  range  given  to  the 
eye  by  the  telescope,  and  by  the  great  advances  which  have  been 
made  in  mathematical  science,  which  may  be  considered  as  conferring 
upon  the  mind  the  same  sort  of  enlarged  power  as  the  telescope  has 
conferred  upon  the  eye. 

2285.  Subject  of  astronomy — origin  of  the  name, — The  inves- 
tigation of  the  magnitudes,  distances,  motions,  local  arrangements, 
and,  so  far  as  it  can  be  ascertained,  the  physical  condition  of  these 
great  bodies  composing  the  Universe,  constitutes  the  subject  of 
that  branch  of  science  called  Astronomy,  a  term  derived  from  the 
Greek  words  aetti^  (aster),  a  star  (under  which  all  the  heavenly 
bodies  were  included),  and  vofjuot;  (nomos),  A  law — the  science  which 
expounds  the  laws  which  govern  the  motions  of  the  stars. 

(92) 


MBTHODS  OF  INVESTIGATION.  96 

6.  h  treaU  of  imuxemhle  chjeeU.  —  It  is  erident,  tbereforei 
Btronomj  is  distinguished  from  all  other  divisions  of  natural 
I  by  this  peculiarity,  that  the  bodies  which  are  the  subjects  of 
Uion  and  enquiry  are  all  of  them  inaccessible.  Even  the 
itself,  which  the  astronomer  regards  as  a  celestial  object — an 
—is  to  him,  in  a  certain  sense,  even  more  inaccessible  than  the 
;  for  the  very  fact  of  his  place  of  observation  being  confined 
'  to  its  surface,  an  insignificant  part  of  which  alone  can  be 
3d  by  him  at  any  one  moment,  renders  it  impossible  for  him 
nine,  by  direct  observation,  the  earth  as  a  whole — the  only 

which  he  desires  to  consider  it, — and  obliges  him  to  resort  to 
3ty  of  indirect  expedients  to  acquire  that  knowledge  of  its 
donB,  form,  and  motions,  which,  with  regard  to  other  and 
listant  objects,  results  from  direct  and  immediate  observation. 

7.  Hence  arise  peculiar  methods  of  investigation  and  peculiar 
nents  of  observation,  —  This  circumstance  of  having  to  deal 
iTely  with  inaccessible  objects  has  obliged  the  astronomer  to 
peculiar  modes  of  reasoning  and  peculiar  instruments  of  ob- 
on,  adapted  to  the  solution  of  such  problems,  and  to  the  dis- 

of  the  necessary  data.  Much  needless  repetition  will  then 
ed  by  explaining  once  for  all,  with  as  much  brevity  as  is  com- 
!  with  clearness,  the  most  important  classes  of  those  problems 
determine  the  circumstances  of  each  particular  celestial  object, 
'  describing  the  principal  instruments  of  observation  by  which 
cessary  data  are  obtuned. 

8.  Direction  and  hearing  of  visible  objects,  —  The  eye  esti- 
only  the  direction  or  relative  bearings  of  objects  within  the 
of  vision,  but  supplies  no  direct  means  of  determining  their 
368  firom  each  other,  or  from  the  eye  itself  (1168,  et  seq.). 

'■  absolute  direction  of  a  visible  object  is  that  of  a  straight  line 
from  the  eye  to  the  object. 

relative  direction  or  bearing  of  an  object  is  determined  by 
igle  formed  by  the  absolute  direction  with  some  other  fixed  or 
I  direction,  such  as  that  of  a  line  drawn  to  the  north,  south, 
r  west 

9.  They  supply  the  means  of  ascertaining  the  distances  and 
yns  of  inaccessible  objects,  —  By  comparing  the  relative  bear- 
f  inaccessible  objects,  taken  from  two  or  more  accessible  points 

distance  from  each  other  is  known,  or  can  be  ascertained  by 
measurement,  the  distances  of  such  inaccessible  objects  from 
ceseible  objects,  from  the  observer,  and  from  each  other,  may 
termined  by  computation.  Such  distances  being  once  known, 
e  the  data  by  which  the  mutual  distances  of  other  inaccessible 
8  from  the  former,  and  from  each  other,  may  be  in  like  manner 
ited;  80  that,  by  starting  in  this  manner  from  two  objects 
!  mntittl  difltaiioe  can  be  actually  measured^  we  may  prooeedi 


94 


ASTRONOICT. 


Fig.  683. 


by  a  chun  of  computations,  to  determine  tbe  relative  distanees  and 
positions  of  all  other  objects^  however  inaccessible;  that  Ml  within 
the  range  of  vision. 

2290.  Angular  magnitude  —  its  importance,  —  It  will  be  appa- 
rent, therefore,  that  anqular  magnitude  plays  a  most  prominent 
part  in  astronomical  investigations,  and  it  is,  before  all;  nocessaiy 
that  the  student  should  be  rendered  familiar  with  it. 

2291.  Division  of  the  circle  —  its  nomenclature,  —  A  circle  is 

divided  into  four  equal  arcs,  called  quadrants, 
by  two  diameters  aa'  and  bb'  intersecting 
at  right  angles  at  the  centre  c,  fig,  683. 

The  circumference  being  supposed  to  be 
divided  into  860  equal  parts,  each  of  which  is 
called  a  deqreE;  a  quadrant  will  consist  of 
90  degrees. 

Angles  are  subdivided  in  the  same  manner 
as  the  arcs  which  measure  them ;  and  aooofd- 
ingly  a  right  angle,  such  as  A  o  B,  being  divided 
into  90  equal  angles,   each   of  these  is  a 

DEGREE. 

If  an  angle  or  arc  of  one  degree  be  divided 
into  GO  equal  parts,  each  of  these  is  called  a  minute. 

If  an  angle  or  arc  of  one  minute  be  divided  into  60  equal  part8| 
each  such  part  is  called  a  second. 

Angles  less  than  a  second  are  usually  expressed  in  decimal  parts 
of  a  second. 

Degrees,  minutes,  and  seconds,  are  usually  expressed  by  the  signSi 
®, ', " ;  thus,  25°  SCy  40"-9  means  an  angle  or  arc  which  measures 
25  degrees,  80  minutes,  40  seconds,  and  910th8  of  a  second. 

The  letters  m  and  s  have  sometimes  been  used  to  express  minutes 
and  seconds ;  but  since  it  is  frequently  necessary  to  express  TIMS  as 
well  as  space,  it  will  be  more  convenient  to  reserve  these  letters  for 
that  purpose.  Thus,  25*  80"*  40'-9  expresses  an  interval  of  time 
consisting  of  25  hours,  80  minutes^  40  seconds^  and  9-10th8  of  a 
second. 

2292.  Relative  magnitudes  of  arcs  of  1°,  1',  and  1",  and  tkt 
radius. — It  is  proved  in  geometry  that  the  length  of  the  entire  cir- 
cumference of  a  circle  whose  radius  is  expressed  by  1*000  exceeds 
6*288  by  less  than  the  5000th  part  of  the  radius.  As  the  exact 
length  of  the  circumference  does  not  admit  of  any  numerical  ex- 
pression, it  will  therefore  be  sufficient  for  all  practical  purpoees  to 
take  6-288  to  express  it. 

If  d,  771,  and  «,  express  respectively  the  actual  lengths  or  Untar 
values  of  a  degree,  a  minute,  and  a  second  of  a  circle  the  length  of 
whose  radius  is  expressed  by  r,  we  shall  therefore  have  the  following 
numerical  relations  between  these  several  lengths:^- 


MBTHODS  OF  INVESTIGATION.  95 

eOX9=mf        60xm=rf,        3600xs  =  <f, 
360  d  =  6-283  r,        360x  60xwi  =  21600  xw  =  6-283  x  r, 
21600x60x«=  1296000x«  =  6-283r; 
tnd  from  these  may  be  deduced  the  folIowiDg : 

r  =  57-3  xd  =  3437-8  xm  =  206265  x  «. 

Bj  these  fommlaB  respectively  the  length  of  the  radius  may  be 
computed  when  the  linear  value  of  an  arc  of  1**,  1',  or  l"^is  known. 

In  like  manner,  if  the  length  of  the  radius  r  be  given,  the  linear 
Talue  of  an  are  of  1®,  1',  or  1"  may  be  computed  by  the  formula) 

1  _      1  _      1 

''"~57¥^'''  '^""8437^^'''         '"206265  ^'** 

2293.  The  linear  and  angtdar  mcu/nitiKle  of  an  arc. — By  the 
<mear  magnitude  of  an  arc  is  to  be  understood  its  actual  length  if 
extended  in  a  straight  line,  or  the  number  expressing  ite  length  in 
imits  of  some  known  modulus  of  length,  such  as  an  inchy  a  foot,  or 
a  mile.  By  its  angular  magnitude  is  to  be  understood  the  angle 
formed  by  two  lines  or  radii  drawn  to  its  extremities  from  the  centre 
of  the  circle  of  which  it  forms  a  part,  or  the  number  expressing  the 
magnitude  of  this  angle  in  angular  units  of  known  value,  as  degrees, 
minutes,  and  seconds. 

2294.  0/  the  three  /oUomng  quantitieSy — the  linear  value  of  aji 
arc,  its  angular  valtLe,  and  the  length  of  the  radius, — any  two  being 
fjicen,  the  third  may  he  computed. —  Let  a  express  the  angular  and  a 
the  hnear  value  of  the  arc,  and  r  the  radius. 

1^.  Let  a  and  a  be  given  to  compute  r.  By  dividing  a  by  o  we 
shall  find  the  linear  value  of  1°,  1',  or  1",  according  as  a  is  expressed 
'0  degrees,  minutes  or  seconds,  and  r  may  then  be  computed  by 

2292).     Thus,  according  to  the  angular  units  in  which  a  is  ex- 

ire^sed,  we  shall  have 

,-  =  -^  X  57-3  =  4  X  3437-8  =  -^  X  206265. 


a®  a  o 


t       2^.  Let  a  and  r  be  given  to  compute  o.     By  (2292)  the  linear 
{     values  of  1°,  1',  or  1"  may  be  computed,  since  r  is  given,  and  by 

dividiDg  a  by  one  or  other  of  these  values  a  will  be  found  :  thus  we 

shill  have 

o"  =  — :; ,  a= ; : ,  a    — 


3^.  Let  A  and  r  be  given  to  compute  a.  By  (2292),  as  before, 
the  linear  values  of  1°,  1'  or  1"  may  be  found,  and  by  multiplying 
one  or  other  of  theso  by  «  the  value  of  a  will  be  obtained.  Thus 
we  shall  have 


ASTBOSOUT. 


2'2S^.   The  arc,  the  ihonl,  and  the  litie  may  be  wntulmti, 
equal  vJun  the  anyle  it  mait. — K  ACB,jfy.  634,  be  ths 
A  B  the  &TC,  tod  A  0  =  o  B  the  ndina,  »  Una  a  d  drawn  tm 
oztremit;  (^  Uie  uo  perpendicnlir  to  tbe  ndiu  cb,  vhiok. 
thiougli  the  other  ezlreioiW  ot  the 
c  its  tine ;  and  the  Btnisht  Una  a  e 

extremities  of  the  uo  u  railed  its 
It  will  be  evideot  by  marely 
cliagram   with    a  gradiully  dccreamu 
that  the  three  IcngthH,  the  sioc  ad,  Im, 
A  B,  and  the  are  A  B,  will  approach  to  ^ 
as  the  are  dimiDishes.     Even  vrbcre  t^ 
BO  large  as  80°,  it  does  not  txceed  tha 
of  the  chord  by  more  than  three-to 

degree ;  and  therefbie,  for  all  angles . 

thia,  the  chord  and  an  may  be  oonddend 
equal  where  the  tnoet  extreme  precision  is 
required. 

In  like  msiiner,  if  the  angle  A  o  b  be  IS", 
the  sme  A  d  will  be  less  than  the  arc  b;  onl 
two>tenthB  of  a  degree,  that  is,  by  the  T.^ 
part  of  the  entire  length  of  the  arc.  lu  all  aeet, 
therefore,  where  greater  prediMoD  than  this  a 
not  required,  the  sine  A  n,  the  chord,  and  Ik 
arc  may  bo  coDBidercd  for  such  angles  as  interchangeable. 

When  tlio  angles  are  bo  amall  as  a  degree  or  two,  these  qnastitM 
nay  for  all  practical  purposes  be  considered  to  be  equal. 

2296.  To  ameriain  Ae  dittanee  of  a 
n  inacceuible  object  from  tuto  arremUe  ito- 
tiojtt. — This,  which  is  a  problem  of  tki 
highest  importance,  being  in  fact  tba  bin 
of  all  the  knowledge  wc  poasess  of  the  dis- 
tances, dimensions,  and  motions  of  the 
great  bodies  of  the  oniTergc,  admits  of  esq  I 
solntion.  1 

Lctsands't/j;.  685,tc  ihotwoBtationi,   1 
and  o  the  object  of  obsirv.ition j  and  let   I 
tbe  TisQsl  angles  subtendod  by  o  and  e*  at    I 
_  J,'     B,  and  by  o  and  s  at  8*,  bo  observed,  and 
tho  distance  8  s'  measured. 

Take  a  line  s/,  consisting  of  as  many 
inches  BS  there  are  miles  in  bb',  and  di«« 
two  lines  « o  and  i'  o  from  t  and   i*,  making  with  t  i  the  f^TI" 


Fig.  084. 


Fig.  (BS. 


MBTHODS  OF  nTTESTiaATION.  97 

as  8  o  and  s'  o  are  ascertained  bj  obserratioQ  to  make  with 
In  that  case  the  triangle  zod  will  be  in  all  respects  similar  to 
angle  s  o  s^,  only  drawn  on  a  smaller  scale,  an  inch  in  any  of 
68  corresponding  to  a  mile  in  one  of  the  sides  of  the  great 
«  8  o  s'.  If  the  sides  s  o  and  s'  o  be  therefore  measured,  they 
msffit  of  as  many  inches  as  there  are  miles  in  the  correspond- 
les  8  o  and  s'  o  of  the  great  triangle.  Now,  since  the  small 
le  is  always  accessible  to  du*ect  measurement,  and  as  the 
o  of  its  scale  to  that  of  the  great  trianele  is  known,  the 
tade  of  the  sides  of  the  great  triangle  may  be  ascertained, 
fchout  being  identical  in  its  actual  details  with  the  process  by 
this  problem  is  solved,  the  preceding  reasoning  is  the  same  in 
pie  and  spirit  Trigonometrical  tables  supply  much  more 
te  ^means  of  determining  the  proportion  of  the  sides  of  tho 
le,  but  such  tables  are  nothing  more  than  the  arithmetical 
sntation  of  such  diagrams  as^.  685. 

T.    Com  in  which  the  distance  of  the  object  is  great  reUuiveltf 
distance  between  the  stations.  —  If  in  this  case  the  stations  be 
so  selected  with  reference   to   the   object  that  tho 
y  directions  of  the  object  as  seen  from  them  shall  form 

angles  with  the  line  joining  the  stations  which  shall 
be  equal  or  nearly  so,  this  latter  line  may  be  consi- 
dered as  the  chord  of  the  arc  described,  with  the 
object  as  a  centre  and  the  distance  as  a  radius  \  and 
if  the  direction  of  the  object  from  either  station  be 
at  right  angles  to  the  line  joining  the  stations,  this 
latter  line  may  be  considered  as  the  sine  of  the  arc. 
In  either  case,  the  distance  of  the  object  bearing  a 
high  ratio  to  the  distance  between  the  stations,  th^ 
angle  formed  by  the  two  directions  of  the  object,  as 
seen  from  the  stations,  will  be  so  small  that  the 
chord  or  sine  may  be  considered  as  equal  to  the  arc, 
and  the  solution  of  the  problem  will  be  simplified  by 
the  principles  established  in  (2295). 

Let  8  and  s',  fig,  686,  be  the  stations,  and  o  the 

object;  under  the  conditions  supposed,  the  angle  o 

will  necessarily  be  small.      Its   magnitude   may  be 

ascertained   by  measuring   the   visual  angles   o  s  s' 

and  o  s'  8 ;  which  may  be  done,  since  both  stations  s 

and    s'   are  accessible,  and  each  of  them  is  visible 

J.  686.       from  the    other.       By  a  well-known  principle  esta 

blished  in  elementary  geometry,  the  three  angles  of 

triangle  added  together  make  180°.     If,  therefore,  the  sum 

two  observed  angles  at  s  and  s'  be  subtracted  from  180°,  the 

ider  will  be  the  angle  o.     Now  if  this  angle  be  expressed  by 

wonds,  we  shall  have  (2294) 

9 


M  AST&ONOMY. 

206265'^ 


8  0  =  SS'X 


•" 


2298.  Given  the  apparent  distance  between  two  disiani  ohjectt^ 
such  distance  being  at  right  angles,  or  nearly  so,  to  their  visual 
directions,  and  their  distance  from  the  observers,  to  find  the  actual 
distance  between  them.  —  This  problem  is  only  a  particular  applica- 
tioD  of  the  general  principle  explained  in  (2294),  a  being  the 
apparent  distance  of  the  objects,  a  the  real  distance  between  Uiem, 
and  r  their  distance  from  the  observer. 

This  method  may  be  applied  without  practical  error,  if  the 
apparent  distance  between  the  objects  be  not  greater  than  two  or 
three  degrees,  and  it  may  be  used  as  a  rough  approximation  in  cases 
where  the  apparent  distance  is  even  so  great  as  30^.  When  ^e 
apparent  distance  amounts  to  so  much  as  60^,  the  actual  distance 
computed  in  this  way  will  not  exceed  the  true  distance  by  more  than 
a  24th  part  of  its  whole  amount;  for  the  chord  of  60^  is  equal  to 
the  radius,  and  therefore  to  an  arc  of  57^*3,  being  less  than  ttke  an 
by  only  2°  7,  or  about  a  24th  part  of  its  length. 

2299.  Given  the  apparent  diameter  of  a  spherical  object  and  its 
distance  from  the  observer,  to  find  its  real  diameter.  — This  is  also 
a  particular  application  of  the  general  problem  (2294),  a  being  the 
apparent  diameter  and  r  the  distance,  and  in  all  cases  which  oocar 
in  astronomy  the  apparent  diameters  are  so  small  that  the  results 
of  the  computation  may  be  considered  as  perfectly  exact 

2300.  Methods  of  ascertaining  the  direction  of  a  visible  and 
distant  object.  —  It  might  appear  an  easy  matter  to  observe  the 
exact  direction  of  any  point  placed  within  the  range  of  vision,  since 
that  direction  must  be  that  of  a  straight  line  passing  directly  from 
the  eye  of  the  observer  to  the  point  to  be  observed.  If  the  eye  were 
supplied  with  the  appendages  necessary  to  record  and  measure  the 
directions  of  visible  objects,  this  would  be  true,  and  the  organ  of 
sight  would  be  in  fact  a  philosophical  instrament.  The  eye  is,  how- 
ever, adapted  to  other  and  different  uses,  and  constructed  to  play  a 
different  part  in  the  animal  economy ;  and  invention  has  been  stim- 
ulated to  supply  expedients,  by  means  of  which  the  exact  directions 
of  visible  distant  points  can  be  ascertained,  observed,  and  compared 
one  with  another,  so  as  to  supply  the  various  data  necessary  in  the 
classes  of  problems  which  have  just  been  noticed,  and  others  which 
we  shall  have  occasion  hereafter  to  advert  to. 

2301.  Use  of  sights.  —  The  most  simple  expedient  by  which  the 
visual  direction  of  a  distant  point  can  be  determined  is  by  sights, 
which  are  small  holes  or  narrow  slits  made  in  two  thin  opaque  plates 
placed  at  right  angles,  or  nearly  so,  to  the  line  of  vision,  and  so 
arranged,  that  when  the  eye  is  placed  behind  the  posterior  opening 
the  object  of  observation   shall   be  visible   through  the   anterior 


METHODS  OP  INVBSTIOATIOir.  99 

opening.  Every  one  is  rendered  familiar  with  this  expedient,  hy  its 
tpplication  to  fire-arms  as  a  method  of  "  taking  aim." 

This  cootrivance  is,  however,  too  rude  and  susceptible  of  error 
within  too  wide  limits,  to  be  available  for  astronomical  purposes. 

2302.  AppHcation  of  the  telescope  to  indicate  the  visual  direction 
of  micrometric  wires. — The  telescope  (1212)  supplies  means  of 
determining  the  direction  of  the  visual  ray  with  all  the  necessary 
precision. 

If  T  t',  fy.  687,  represent  the  tube  of  a  telescope,  t  the  ex- 


Xl 


#•- 


0 


Fig.  687. 

tremity  in  which  the  object-glass  is  fixed,  and  t'  the  end  where  the 
images  of  distant  objects  to  which  the  tube  is  directed  are  formed, 
the  visual  direction  of  any  object  will  be  that  of  the  line  t^  c  drawn 
from  the  image  of  such  object,  formed  in  the  Jield  of  view  of  the 
telescope,  to  the  centre  c  of  the  object-glass;  for  if  this  line  be  con- 
tinned  it  will  pass  through  the  object  s. 

But  since  the  field  of  view  of  the  telescope  is  a  circular  space 
of  definite  extent,  within  which  many  objects  in  different  directions 
may  at  the  same  time  be  visible,  some  expedient  is  necessary, 
by  which  one  or  more  fixed  points  in  it  may  be  permanently  marked, 
or  by  which  the  entire  field  may  be  spaced  out  as  a  map  is  by  the 
lines  of  latitude  and  longitude. 

This  is  accomplished  by  a  system  of  fibres,  or  wires  (38)  so  thin 
that  even  when  magnified  they  will  appear  like  hairs.  These  are 
extended  in  a  frame  fixed  within  the  eye-piece  of  the  telescope,  so 
that  they  appear  when  seen  through  the  eye-glass  like  fine  lines 
drawn  across  the  field  of  view.  They  are  differently  arranged,  accord- 
ing to  the  sort  of  observation  to  which  the  instrument  is  to  be  applied. 

2303.  Line  of  collimatian.  —  In  some  cases  two  wires  intersect 
at  right  angles  at  the  centre  of  the  field  of  view,  dividing  it  into 
quadrants,  as  represented  in  fg,  683.  The  wires  are  so  adjusted 
that  their  point  of  intersection  o  coincides  with  the  axis  of  the 
telescope  tube;  and  when  the  instrument  is  so  adjusted  that  the 
point  of  observation,  a  star  for  example,  is  seen  precisely  upon  the 
intersection  c  of  the  wires,  the  line  of  direction,  or  visual  ray  of 
that  star,  will  be  the  line  t^  c,  fy.  687,  joining  the  intersection  c, 
fifj.  683,  of  the  wires  with  the  centre  c,  fy.  687,  of  the  object-glass. 

The  line  d  c^fuj.  687,  is  technically  called  the  line  of  collimaiion. 

2304.  ApplicaXion  of  the  telescope  to  a  graduated  instrument.  — 
The  teleioope  Urns  prepared  is  attached  to  a  graduated  instrument 


74 


(i?0^ 


100 


ASTBONOmr. 


by  which  angular  magnitades  can  be  obaerred  and  measiured.  Such 
iostrumcDts  vary  infinitely  in  form,  magnitude,  and  mode  of  mount- 
ing and  adjustment,  according  to  the  purposes  to  which  they  are 
applied,  and  to  the  degree  of  precision  necessary  in  the  obeervatioDs 
to  be  made  with  them.  To  explain  and  illustrate  the  general  prin- 
ciples on  which  they  are  constructed,  we  shall  take  the  example  of 
one,  which  consists  of  a  complete  circle  graduated  in  the  oaiial 
manner,  being  the  most  common  form  of  instrument  used  in  ai- 
tronomy  for  the  measurement  of  angular  distances. 

Such  an  apparatus  is  represented  in  fig.  688.     The  circle  A  B  C  D, 


Fig.  688. 

on  which  the  divisions  of  the  graduation  are  accurately  engrayed, 
is  connected  with  its  centre  by  a  series  of  spokes  xy  z.  At  its 
centre  is  a  circular  hole,  in  which  an  axle  is  inserted  so  as  to  turn 
smoothly  in  it,  and  while  it  turns  to  be  always  concentric  with  the 
circle  A  b  o  d.  To  this  axle  the  telescope  a  2)  is  attached  in  such  a 
manner  that  the  imaginary  line  d  c,  fig.  687,  which  joins  the  in- 
tersection of  the  wires,  fig.  683,  with  the  centre  of  the  object- 
glass,  shall  be  parallel  to  the  plane  of  the  circle,  and  in  a  plane 
passing  through  its  centre  and  at  right  angles  to  it. 

At  right  angles  to  the  axis  of  the  telescope  are  two  arms,  m  n, 
which  form  one  piece  with  the  tube,  so  that  when  the  tube  is  turned 
with  the  axis  to  which  it  is  attached,  the  arms  m  n  shall  turn  also, 
always  preserving  their  direction  at  right  angles  to  the  tube.  Marks 
or  indices  are  engraved  upon  the  extremities  m  and  n  of  the  arms 
which  point  to  the  divisions  upon  the  limb  (as  the  diyided  are  is 
called). 

A  clamp  is  provided  on  the  instrument,  by  which  the  telescope, 
being  brought  to  any  desired  position,  can  be  fixed  immoveably  in 
that  position,  while  the  observer  examines  the  points  upon  the  limb 
to  which  the  indices  m  and  n  are  directed. 

Now  let  us  suppose  that  the  visual  angle  under  the  directions  of 
two  distant  objects  within  the  range  of  vision  is  required  to  be 


IIBTDODS  OP  INTKBTIOATIOX. 


101 


The  circle  being  brought  into  tlie  plane  of  the  ohjects, 
and  BxEfJ  ia  it,  the  t«lcscnpe  is  moved  upna  its  axis  until  it  is  di- 
rectei]  to  one  of  the  objects,  aa  that  its  image  stiull  coincide  cxnctlj 
with  the  intenectioa  of  the  wires.  The  telescope  is  then  cJaDiped, 
■od  the  obserrer  examines  the  points  of  tho  divided  limb,  to  which 
ofte  of  (he  indices,  m  fot  esampte,  is  directed.  This  process  is  called 
"reading  off."  The  clamp  being  diseogaged,  the  telescope  is  then 
in  like  manner  directed  to  the  other  object,  and  being  clamped  as 
before,  the  position  of  the  index  is  "  read  off."  The  di^rence  be- 
tween the  Dumben  which  indicate  the  position  of  the  same  index 
in  both  cases,  will  evidentlj  be  the  visual  angle  under  the  ilirec- 
bons  of  the  two  objects. 

As  ft  means  of  further  aocnraey,  both  the  indices  m  and  n  may 
be  "read  off,"  and  if  the  results  differ,  which  they  always  will 
flightly,  owing  to  Tarious  causes  of  error,  a  mean  of  the  two  may 
bt  lafcen. 

It  is  evident  that  the  same  results  would  bo  obtained  if,  iusteail 
of  uabiog  the  telescope  move  upon  tLe  circle,  it  were  immov^ahly 
uticbed  to  it,  aud  that  the  circle  itself  turned  upon  its  centre,  os  a 
wheel  does  upou  its  axle,  carrying  the  telescope  with  it.  In  this 
ca.'e  the  divided  limb  of  the  circle  is  made  to  move  before  a  fixed 
index,  and  the  angle  under  the  dircctiona  of  the  objects  will  bo 
Bieasured  by  the  length  of  the  arc  which  passes  before  the  index. 

Sach  a  combinatioD  is  represented  in  section  in  fy.  689  where 


Fig.Mfl. 
T  is  the  telescope,  p  the  pieces  by  which  it  is  attached  to  the  circle 
4  B  seen  edgewise,  the  axis  of  which  D  works  in  a  solid  block  of 
netal.     The  fixed  index  r  is  directed  to  the  gradaated  limb  which 
mores  before  it 

This  is  the  moet  frequent  method  of  mounting  instruments  used 
in  astroaoniy  for  angalar  measurement. 

2S05.  ErpfdienU  /or  meaiuring  the  fraction  of  a  divirlon. — 
It  will  happen  in  general  that  the  index  will  be  directed,  not  to  any 
enct  divitdon,  bat  to  some  point  mtermcdiute  between  two  divi- 
HM  id  the  limb.    In  thit  case  expedients  are  provided  b;  which 


103 


ASTRONOmr. 


Fig.  690. 


the  fraction  of  a  degree  between  the  index,  and  the  last  dimon 
which  it  has  passed,  may  be  ascertained  with  an  extnordinaiy  de- 
gree of  precision. 

2306.  By  a  Vernier,  —  This  may  be  accomplished  bj  means  of 
a  supplemental  scale  called  a  Yebnieb,  alreadv  described  (1854). 

2307.  By  a  compound  microacopef  and  mi- 
crometric  screw,  —  The  same  object  may,  how* 
ever,  be  attained  with  £u*  greater  accuracy  by 
means  of  a  compound  microscope  mounted 
as  represented  in  Jig,  690,  so  that  the  ob- 
server looks  at  the  index  through  it  A 
system  of  cross  wires  is  placed  in  the  field 
of  view  of  the  microscope,  and  the  whole 
may  bo  so  adjusted  by  the  action  of  a  fine 
screw,  that  the  index  shall  coincide  pre<»9ely 
with  the  intersection  of  the  wires.  The 
screw  is  then  turned  until  the  intersectioa 
of  the  cross  is  brought  to  coincide  with  the 
previous  division  of  the  limb )  and  the  number  of  turns  and  frac- 
tion of  a  turn  of  the  screw  will  give  the  fraction  of  a  degree  be- 
tween the  index  and  the  previous  division  of  the  limb. 

It  is  necessary,  however,  to  ascertain  previously  the  value  of  a 
complete  revolution  of  the  screw.  This  is  easily  done  by  toming 
the  screw  on  which  the  intersection  of  the  cross  is  moved  from  one 
division  to  the  adjacent  one.  Dividing,  then,  one  degree  of  the 
limb  by  the  number  of  turns  and  fraction  of  a  turn,  the  are  which 
corresponds  to  one  complete  turn  will  be  found. 

2308.  Observation  and  measurement  of  minute  angles,  —  When 
the  points  between  which  the  angular  distance  required  to  be  ascer- 
tained arc  so  close  together  as  to  be  seen  at  one  and  the  same  time 
within  the  field  of  view  of  the  telescope,  a  method  of  measurement 
is  applicable,  which  admits  of  even  greater  relative  accuracy  than 
do  the  methods  of  observing  large  angular  distances.  This  arises 
from  the  fact  that  the  distance  between  such  points  may  be  deter- 
mined by  various  forms  of  micrometric  instruments,  in  which  fine 
wires,  or  lines  of  spider's  web,  are  moved  in  a  direction  perpendio- 
ular  to  their  length,  so  as  to  pass  successively  through  the  points 
whose  distance  is  to  be  observed. 

2309.  TJie  parallel  wire  micrometer.  —  One  of  the  forms  of  mi- 
crometric apparatus  used  for  this  purpose  is  represented  in  trans- 
verse section  in  Jig,  691.  This,  which  is  called  the  parallel 
WIRE  MICROMETER,  consIsts  of  two  sliding  frames  across  which  the 

Earallel  wires  or  threads  c  and  D  are  stretched.  These  frames  are 
oth  moved  in  a  direction  perpendicular  to  that  of  the  wires  by 
screws,  constructed  with  very  fine  threads,  and  called  from  their  use 
j^CROMETER  SCREWS.     This  frame  is  placed  in  the  focus  of  the 


METHODS  OF  mVESTIGATION. 


108 


objeck-gbMB  of  the  telescope^  so  that  the  eye  viewing  the  objecta 
mder  oheenration  sees  also  distinctly  the  parallel  and  moveable 


Kg.  691. 

These  wires  are  moved  by  the  screws  until  they  pass  through 
the  points  whose  distance  asunder  is  to  be  measured.  This  being 
aoeomplishedy  one  of  them  is  moved  until  it  coincides  with  the 
other,  and  the  number  of  turns  and  parts  of  a  turn  of  the  screw 
necessary  to  produce  this  motion  gives  the  angular  distance  between 
tbe  points  under  observation. 

In  this,  as  in  the  case  explained  in  (2307),  it  is  necessary  that 
the  angle  corresponding  to  one  complete  revolution  of  the  screw  be 
peviously  ascertained,  and  this  is  done  by  a  process  precisely  sLmi- 
iar  to  that  explained  in  the  former  case.  An  object  of  known 
tnguhur  magnitude,  as,  for  example,  a  footrule  at  the  distance  of  a 
hundred  yirds,  is  observed,  and  the  number  of  turns  necessary 
to  carry  the  wire  from  end  to  end  of  its  image  is  ascertained. 
The  angle  such  a  rule  subtends  at  that  distance  being  divided  by 
the  number  of  turns  and  parts  of  a  turn,  the  quotient  is  the  angle 
corresponding  to  one  complete  revolution  of  the  screw. 

2310.  Measurement  of  the  apparent  diameter  of  an  object.  — 
When  an  object  is  not  too  great  to  be  included  in  the  field  of  view 
of  the  telescope,  its  apparent  diameter  (1117)  can  be  measured  by 
each  an  apparatus.  To  accomplish  this  the  screws  are  turned  until 
the  wires  c  and  D,^^.  691,  are  made  to  touch  opposite  sides  of  the 
disk  of  the  object.  One  of  the  screws  is  then  turned  until  the 
wires  coincide,  and  the  number  of  turns  and  parts  of  a  turn  gives 
the  apparent  magnitude. 


CHAP.  11. 

THK  OXNKRAL  ROTUNDITY  AMD  DIMENSIONS  OF  THE  EARTH 

2311.  The  earth  a  ttatUm  from  which  the  universe  is  observed. 
— The  earth  is,  in  various  points  of  view,  an  interesting  object  of 
adentifie  investigiition.    The  naturalist  regards  it  as  the  habitation 


104  ASTRONOMY. 

of  the  nnmerona  tribes  of  ori^nued  b«tngB  vtiioli  an  tlis  spaod 
subject  of  his  obseiration  aDd  inqniir,  and  eiaminea   enrioaiil 

tbose  properties  and  qualities  of  soil,  olimate,  and  atmosphere,  bj 
which  it  is  fitted  for  their  DtaintenaDce  and  propagatioii,  and  tk 
conditions  trhicb  govern  their  dietribation  over  its  snr&oe.  7w 
geologist  and  mineraloffist  regard  it  ai  the  theatre  of  vast  phjsial 
operations  continued  Ibrongb  perioda  of  time  eztendins  infinite^ 
bcjoud  the  records  of  hnman  history,  tbe  roanlta  of  which  are  seea 
ID  the  state  of  its  crust  The  astronomer,  risii^g  above  these  de- 
tails, regards  it  as  a  whole,  examines  its  form,  ioTestigates  its  oo- 
tioDB,  measures  its  magnitude,  and,  aboye  all,  oonaiderg  it  as  tk> 
BtatioD  from  which  alone  he  can  take  a  survey  of  tbat  nnivoH 
which  fbrms  the  pecaliar  object  of  his  study,  and  as  the  odIt  wk 
dnlus  or  standard  by  which  the  magnitudes  of  all  the  other  bodM 
in  tbe  universe,  and  tbe  distances  which  separate  them  tcm  Ibi 
earth  and  from  each  other,  can  be  measored. 

2812-  Necestarff  to  aacertain  it*  form,  dimentiont,  anrfmetibaa 
—  But  since  the  apparent  magnitudes,  motiona,  and  relatiye  ar- 
nngemcnt  of  snrroundiag  objects  severally  vaiy,  not  only  with 
every  change  in  the  position  of  the  station  of  the  observer,  bil 
even  with  every  change  of  position  of  the  observer  on  that  etatia^ 
it  is  most  oeceasary  to  ascertBia  with  all  Bttaioable  accuraoj  the  di- 
mensions of  tbe  earth,  which  is  the  station  of  the  aatroDOBUiMl 
observer,  its  form,  and  the  changes  of  positioQ  in  relation  to  an- 
rounding  objects  to  which  it  is  subject. 

2313.  Form  ghbular.  —  The  first  impres«on  produced  fay  ibt 
aspect  presented  by  the  surface  of  tbe  earth  b  that  of  a  vast  iadeS 
nite  plane  surface,  broken  only  by  tbe  accidents  of  the  groand  oi 
land,  such  as  bills  and  tnonntaiDs,  and  by  tbe  more  mutable  fonni 
due  to  the  agitation  of  the  fluid  mass  on  the  sea.  Even  this  <1» 
parturo  from  the  appearance  of  an  extensive  plane  surface  ceases  oi 
the  sea  out  of  eight  of  land  in  a  perfect  calm,  and  on  certaia  plana 
of  vast  extent  on  land,  such  as  some  of  the  prairies  of  the  America! 
continents. 

This  first  impression  is  soon  shown  to  be  fallacious;  and  it  ii 
easily  demonstrated  that  the  immediate  indications  of  the  unudet 
sense  of  vision,  each  as  they  are,  are  loosely  and  incorrectly  inter 
pretcd,  and  that,  in  fact,  even  that  small  part  of  the  earth's  sur&a 
which  falls  at  once  within  tbe  range  of  the  eye  in  a  fixed  positioi 
(fofs  not  appear  to  be  a  plane. 

Supposing  that  any  extensive  part  of  the  surface  of  the  eartl 
were  really  a  plane,  let  several  stakes  or  posts,  of  equal  height,  hi 
erected  along  tbe  same  straight  line,  and  at  equal  distance^  say  i 
mile  apart.  Let  these  stakes  be  represented  by  s  a,  s'  J,  a"  i\  So. 
Jig.  692,  and  let  a  stake  of  equal  height  o  o  be  erected  at  the  sta 
tion  of  the  observer.     Now,  if  the  surface  were  a  plane,  it  is  en 


If BTHODS  OF  XNVESTIGATION. 


105 


dsDt  thai  the  points  Sy  tl^  tl\  &c.  most  appear  to  an  eye  placed  at  o 
in  the  same  Yisual  line,  and  would  each  be  visible  through  a  tube 


r 

] 


Kg.  692. 

directed  at  o  parallel  to  the  surface  o  8.  But  such  will  not  be  found 
to  be  the  case.  When  the  tube  is  directed  to  <,  all  the  succeeding 
points  /y  /',  &c.  will  be  htUyu>  its  direction.  If  it  be  directed  to  «% 
tbe  point  s  will  be  abovty  and  %'  and  all  the  eucceediug  points  will 
l)e  htlmo  its  direction.  In  like  manner,  if  it  be  directed  to  fl\  the 
preceding  points  <  and  /  will  be  above,  and  the  succeeding  points 
wow  its  direction.  In  effect  it  will  appear  as  though  each  succeed- 
ing stake  were  a  little  shorter  than  the  preceding  one.  But  as  the 
stiUKS  are  all  precisely  equal,  it  must  be  inferred  that  the  successive 
points  of  the  surfiu^  s,  a',  s",  s"',  &c.  are  relatively  lower  than  the 
Btation  o.  Nor  will  the  effects  be  explained  by  the  supposition  that 
the  snrfisbce  o  8  s'  s",  &c.,  is  a  descending  but  still  a  plane  surface, 
because  in  that  case  the  points  Sj  <',  tf\  &c.  must  still  be  in  the  same 
Tisnal  line  directed  from  o.  It  therefore  follows  that  the  surface  in 
the  direction  o  s'  s"  s'",  &c.  is  not  plane  but  curved^  as  represented 
mfig.  693,  where  the  visual  lines  are  in  obvious  accordance  with 
the  actual  appearances  as  above  explained. 


Fig.  693. 

Now  since  these  effects  are  found  to  prevail  in  every  directioi 
around  the  point  of  observation  o,  it  follows  that  the  curvature  of 
the  surface  prevails  all  around  that  point;  and  since  the  extent  of 
the  cUpresnon  of  the  points  s,  s',  6f\  &c.  at  equal  distances  from  o, 
are  equal  in  every  direction  around  o,  it  follows  that  the  curvature 
is  in  every  direction  sensibly  uniform  around  that  point. 

Bat  by  shifting  the  centre  of  observation  o,  and  making  umilar 


106  ASTRONOMY. 

observations  elsewhere,  and  on  every  part  of  the  earth  where  sach 
a  process  is  practicable,  not  only  are  like  effects  observed,  but  the 
degree  of  degression  corresponding  to  equal  distanoes  firom  the  cen- 
tres of  observation  is  the  same. 

Hence  we  infer  that  the  surface  of  the  earth,  as  ohierved  directly 
hy  the  eycj  is  not  a  plane  surface,  but  one  everywhere  curved,  and 
that  the  curvature  is  everywhere  uniform,  at  least  that  no  departure 
from  perfect  uniformity  in  its  general  curvature  exists  sufficiently 
considerable  to  be  discovered  by  this  method. 

But  the  only  form  of  a  solid  body  which  has  a  surface  of  uniform 
curvature  is  a  sphere  or  globe,  and  it  is  therefore  eatablished  that 
Buch  is  the  form  of  the  earth. 

2314.  This  conclusion  corroborated  by  circumnaviaatum.  — If  a 
vessel  sail,  as  fur  as  it  is  practicable  to  do  so,  constantly  in  the  bum 
direction,  it  will  at  length  return  to  the  port  of  its  departure,  hav- 
ing circumnavigated  the  earth ;  and  during  its  course  it  appears  to 
pass  over  an  uniform  sur&oe.  This  is  obviously  what  must  taki 
place  so  far  as  regards  that  part  of  the  earth  which  b  covered  with 
water,  supposing  it  to  be  a  globe. 

2315.  Corroborated  by  lunar  eclipses,  —  But  the  most  sbikiiic 
and  conclusive  corroboration  of  the  inference  just  made,  and  indeed 
a  phenomenon  which  alone  would  demonstrate  the  form  of  the 
earth,  is  that  which  is  exhibited  in  lunar  eclipses.  These  appear- 
ances, which  are  so  frequently  witnessed,  are  caused  by  the  earth 
coming  between  the  sun  and  the  moon,  so  as  to  cast  its  shadow  upon 
the  latter.  Now  the  form  of  that  shadow  is  always  precisely  that 
which  one  globe  would  project  upon  another.  The  phenomenon 
thus  at  once  establishes  not  only  the  globular  form  of  the  earthy 
but  that  of  the  moon  also. 

2316.  Various  effects  indicating  the  earth* s  rotundity, — Wia 
rotundity  of  the  earth  being  once  admitted,  a  multitude  of  its  oon- 
sequences  and  effects  present  themselves,  which  supply  corrobontm 
evidence  of  that  important  proposition. 

When  a  ship  sails  from  the  observer,  the  first  part  which  should 
cease  to  be  visible,  if  the  earth  was  a  plane,  would  be  the  rod  of 
the  top-mast,  having  the  smallest  dimensions,  and  the  last  the  hull 
and  sails,  being  the  greatest  in  magnitude ;  —  but,  in  fact,  the  very 
reverse  takes  place.  The  hull  first  disappears,  then  the  sails,  and 
in  fine  the  top-mast  alone  is  visible  by  a  telescope,  appearing  like  a 
pole  planted  in  the  water.  This  becomes  gradually  shorteri  ap- 
pearing to  sink  in  the  water  as  the  vessel  recedes  from  the  eye. 

These  appearances  are  the  obvious  consequences  of  the  gradoal 
interposition  of  the  convexity  of  the  part  of  the  earth's  surface  ovw 
which  the  vessel  has  passed,  and  will  be  readily  comprehended  by 
the  fig.  694. 


DIHSKSIONS  Of  THE  BABTH. 


If  the  obwrrer  Uke  a  more  elevated  position,  the  Eame  BDcoession 
if  pbenomeuft  will  be  preaented,  only  greater  distanoes  will  be 


to  produce  the  ume  degree  of  apparent  aiukiDg  of  tlie 

I^iid  ii  Tuible  from  the  top-mast  in  approaching  the  shore,  when 
il  euinot  be  seen  from  the  deck. 

Tb«  top  of  the  peak  of  TeoeriBe  cao  be  seen  from  a  distaooe  when 
tiie  baM  of  the  monDtaiD  is  invisible. 

The  BCD  bUdm  on  the  enmrnits  of  the  Alpa  long  afler  sunset  in 
the  valleja. 

An  aeronant  ascendiog  after  stiDset  baa  witneseed  the  sun  to  re- 
ippeu  with  all  the  eficcts  of  snnriae.  On  descending,  he  witnessed 
asemnd  moaet. 

2317.  jDunenttoni  of  de  tarih.  —  Method  of  menfurinif  a  de- 
gree. —  Having  thne  nacertained  that  the  form  of  the  earth  is  a 
globe,  it  now  remuns  to  discover  its  magnitude,  or  what  is  the  same, 
Ut  diameter. 

For  this  parpoee  it  will  be  ncceasair  first  to  ascertain  the  actual 
length  of  a  degree  npon  ita  sur&ce,  that  is,  the  distance  between 
two  points  on  w  earface,  so  placed  that  the  lines  dmwo  from  them 
to  toe  centre  shall  make  with  each  other  an  angle  of  one  degree. 

Let  p  and  p',  fg.  695,  represent  two  places  upon  the  earth's 
MT&oe,  distant  from  each  other  from  60  to  100  miles,  and  let  c  be  tbo 
eentre  of  the  earth.  Now,  let  ua  suppose  that  two  observers  at  the 
places  p  and  ^  observe  two  stars  s  and  i*,  which  at  the  same  time 
are  verticallj  over  the  two  places,  and  to  which,  therefore,  plumb- 
Unes  Bospcnded  at  the  two  places  would  be  directed.  The  direction 
of  these  plumb-lines,  if  continued  downwards,  would  iDtcrsect  at  c, 
the  centre  of  the  earth. 

The  visoal  angle  under  the  directions  of  these  stars  (  and  i*  at  // 
is  t|/^,  and  at  C  is  soi'.  But,  owing  to  the  insigniGcaot  proportion 
which  the  distances  pji  and  pc,  bear  to  the  di.-ttanccs  of  the  ftars 
(as  will  be  made  evident  hereaficr),  the  visual  angle  of  the  siars, 
whether  seen  from  p  or  C,  will  be  the  same.     If,  then,  thb  visual 


108 


ASTRONOMY. 


angle  at  jA  be  measured,  as  it  may  be  with  the 
greatest  preciiiony  we  may  consider  it  as  the  magni- 
tude of  the  angle  p  c  p'. 

Let  the  actual  distance  D,  between  the  places,  p 
and  p\  be  measured  or  ascertained  by  the  process  of 
surveying,  and  the  number  of  seconds  in  the  observed 
angle  «pV  be  expressed  by  a.  If  d  express  the  dis- 
tance of  two  points  on  the  earth  which  would  subtend 
at  the  centre  c  an  angle  of  1^,  we  shall  then  have — 

a  :  3600  ::D:d  =  j>  X  ^^ 

a 

since  the  number  of  seconds  in  a  degree   is  3600 

(2292). 

2318.  Length  of  a  degree,  —  In  this  way  it  hu 
been  ascertained  that  the  length  of  a  degree  of  the 
earth's  surface  is  a  little  less  than  70  British  statute 
miles,  and  may  be  expressed  in  feet  (in  round  num- 
bers) by  365,000. 

It  will  therefore  be  easy  to  remember  that  the 
length  of  a  degree  is  as  many  thousand  feet  as  there 
are  days  in  the  year. 

2319.  Length  of  a  second  of  the  earth,  —  Since 
a  second  is  the  3600th  part  of  a  degree,  it  follows 
also  that  the  length  of  a  second  is  an  hundred  feet 
very  nearly,  a  measure  also  easily  remembered. 

2320.  Change  of  direction  of  the  plumb-line  in 
passing  over  a  given  direction,  —  From  what  has 
just  been  explained  it  will  be  understood  that  since 
a  plumb-line  always  points  to  the  centre  of  the  earth 
(when  its  direction  is  undisturbed  by  any  local  attrac- 
tion), its  change  of  direction,  in  passing  from  any  one 
place  to  any  other,  may  be  always  found  by  allowing 
1"  for  every  hundred  feet  in  the  direct  line  joining 

the  places,  or  still  more  exactly  by  allowing  365,000  feet  for  ever)' 
degree,  and  a  proportional  part  of  this  length  for  every  fraction  of 
a  degree  between  the  places. 

2321.  To  find  the  earth* s  diameter, —  Nothing  can  be  more  easy, 
after  what  has  been  stated,  than  the  solution  of  the  problem  to  deter- 
mine the  earth's  diameter.  By  what  has  been  explained  (2294), 
if  r  express  the  radius  or  semidiameter  of  the  earth  0/),  a  the  arc 
pp  of  the  earth's  surface  between  the  two  places,  and  a  the  angle 
p  c  p'y  wc  shall  have  — 

206265 
r  =  a  X  T, — . 


Fig.  695. 


DIMBNSIONS  OF  THK  EAHTH.  109 

if  the  distance  a  he  one  degree^  this  will  become  — 

r=:?|^  X  206265  =  20,912,979, 

or  yerj  nearly  21  million  feet,  which  is  eqnal  to  3960  statute  miles. 
8o  that  the  diameter  of  the  earth  would  be  7920  miles,  or  in  round 
irambers  (for  we  are  not  here  pretending  to  extreme  arithmetical 
precision)  8000  miles. 

The  process  of  observation  above  explained  is  not  in  its  details' 
exactly  that  by  which  the  magnitude  of  the  earth  is  ascertained, 
bat  it  is  in  spirit  and  principle  the  method  of  observation  and  cal- 
colation.  It  would  not  be  easy  to  find,  for  example,  any  two  suffi- 
ciently observable  stars  which  at  one  and  the  same  moment  would 
be  vertically  over  the  two  places  p  and  p',  but  any  two  stars  nearly 
over  them  would  equally  answer  the  purpose  by  observiug  the  extent 
of  their  departure  firom  the  vertical  direction.  Neither  is  it  neces- 
nry  that  the  two  observations  should  exactly  coiucide  as  to  time ; 
bat  these  details  do  not  affect  the  principle  of  the  method,  and  will 
be  more  clearly  intelligible  as  the  student  advances. 

2322.  Superficial  inequalities  of  the  earth  relatively  insignijir 
cant,  —  It  is  by  comparison  alone  that  we  can  acquire  any  clear  or 
definite  notions  of  distances  and  magnitudes  which  do  not  como 
under  the  immediate  cognizance  of  the  senses.  If  we  desire  to 
acquire  a  notion  of  a  vast  distance  over  which  we  cannot  pass,  we 
compare  it  with  one  in  which  we  have  immediate  and  actual  ac- 
quaintance, such  as  a  foot,  a  yard,  or  a  mile.  And  since  the  area 
or  superficial  extent  of  smrfaces  and  the  volume  or  bulk  of  solids 
are  respectively  determined  by  the  length  of  their  linear  dimen- 
sions, the  same  expedient  suffices  to  acquire  notions  of  them.  Id 
Astronomy,  having  to  deal  with  magnitudes  exceeding  in  enormous 
proportions  those  of  all  objects,  even  the  most  stupendous,  which 
are  so  approachable  as  to  afford  means  of  direct  sensible  observa- 
tion, we  are  incessantly  obliged  to  have  recourse  to  such  comparisons 
in  order  to  give  some  degree  of  clearness  to  our  ideas,  since  without 
them  oar  knowledge  would  become  a  mere  assemblage  of  words, 
numbers,  and  geometrical  diagrams. 

Let  ns,  then,  consider  the  dimensions  and  form  of  the  earth,  as 
they  have  been  ascertained  in  the  preceding  paragraphs. 

When  it  is  stated  that  the  earth  is  a  globe,  the  first  objection 
which  will  he  raised  by  the  uninformed  student  is  that  the  conti- 
neota,  islands,  and  tracts  of  land  with  which  it  is  covered  are 
marked  by  considerable  inequalities  of  level ;  that  mountains  rise 
into  ridges  and  pedes  of  vast  height;  that  the  seas  and  oceans, 
though  level  at  their  surface  in  a  certain  general  sense,  are  agitated 
by  great  waves,  and  alternately  swelled  and  depressed  by  tides,  and 
that  the  solid  bottom  of  them  is  known  to  be  subject  to  inequalities 

m-  10 


110  ABIBOKOWr. 

analogonB  in  cbaiacter,  and  not  less  in  depth  tiun  Uiaae  whU  jm- 
vail  on  the  Intid.     Since,  then,  it  ie  the  chanotemtio  property  of  ■   ; 

flobe  that  all  points  on  its  sor&oe  are  equally  distant  fitim  iti  eeakt,  s 
ow,  it  may  be  demanded,  can  a  mass  of  matter,  go  tueqnal  mik  p 
surface  as  the  earth  is,  be  a  globe  t  k 

It  may  be  conceded  at  onoe,  in  reply  to  this  olgeotiaB,  tint  Ht  f 

earth  is  not,  in  the  strict  geometiio  sense  of  tba  tem,  s  rioba-  M  I 

let  na  conBidcr  the  extent  of  its  departare  from  the  g^oDulwCii^  I 

-  so  far  as  relates  to  the  anperfidal  inequalities  jnst  ftdTnted  ta  I 

The  moat  lofty  monnlain  peaks  do  not  exceed  fire  miles  in  hd^  I 
Few,  indeed,  approach  that  limit.  Most  of  the  oonndenUe  mooB-  ^ 
tainons  distriots  are  limited  to  less  than  half  that  height.  No  eon- 
uderable  tract  of  land  has  a  general  elevation  even  of  one  mik. 
The  deepest  parts  of  the  sea  bave  not  been  sonnded ;  bnt  it  is  co- 
tain  that  their  depth  does  not  exceed  the  heights  of  the  moat  loftj 
moaulains,  and  the  general  depth  is  incomparably  less.  The  sa|a^ 
ficial  inequalities  of  the  aqneoos  surfitco  produced  by  waves  rad 
tides  are  comparatively  insignificant. 

Now,  let  us  consider  how  these  seven]  soperficial  ioeqaaliliM 
would  be  rcprcBcnted,  observing  a  due  proportion  of  scale,  em 
on  the  most  stupendous  model. 

Construct  a  globe  20  feet  in  diameter,  as  a  model  of  the  eatd. 
Since  20  feet  represents  8000  miles,  l-400th  part  of  a  foot,  v 
3-lOOtb  parts  of  an  inch,  represents  a  mile.  The  height,  therelfan, 
of  the  most  lofty  mountain  peak,  and  the  greatest  depth  of  the  ooeu, 
would  be  represented  by  a  protuberance  or  a  hole  having  no  greater 
elevation  or  depth  than  lf)-100ths,  or  about  the  seventh  part  of  u 
inch.  The  general  elevation  of  a  continent  would  be  fiurly  reprs- 
seotcd  by  a  leaf  of  paper  pasted  upon  the  surface,  having  the  thieknoi 
of  less  than  the  fiftieth  of  an  inch ;  and  a  depression  of  little  greattf 
amonnt  would  express  the  depth  of  the  general  bed  of  the  sea. 

It  will  therefore  be  apparent,  that  the  departure  of  snob  a  modd 
from  the  true  form  of  a  globe  would  be  In  all,  save  a  strictly  geomst- 
rical  sense,  absoluh^ly  iosignificant. 

2323.  lictatioe  dimcmions  of  iJie  almoit}>here.  —  The  sar&ce  of 
the  earth  is  covered  by  an  ocean  of  air,  which  floats  upon  it  as  the 
waters  of  the  seas  rest  upon  their  solid  bed.  The  density  of  this 
fluid  is  greatest  in  the  stratum  which  is  in  immediate  contaot  wiib 
the  surface  of  the  land  and  water  of  the  earth,  and  it  diminishes  in 
a  very  rapid  ratio  in  ascending,  so  that  one  half  of  the  entire  atmc- 

'  ere  is  included  in  the  strata  whoso  height  is  within  3)  miles  of 
surface.  At  an  altitude  of  SO  miles,  or  the  hundredth  part  of 
the  earth's  diameter,  the  rarefaction  must  bo  so  extreme,  that  neither 
aaimal  life  nor  combustion  could  bo  miuntaincd. 

The  atmosphere,  being  then  limited  to  such  a  hdght,  woold  be 


t 


DIMlNSiem  OF  TUB  BARTH.  Ill' 

Mited  €B  tte  model  above  deseribed  bj  a  Btratnm  two  indies 

Intfthiek. 

S4.  jQT  fft«  earA  moffedf  hno  eouid  tig  mcHan  he  perceived  T^ 
ig  tlras  aaoerluiiedy  m  a  loogh  way,  the  fomi  and  Pennons 
)  earth,  let  na  oonnuier  the  qoertion  of  its  rest  or  moUlihr. 
dung  m  mora  rapogmmi  to  the  first  impressions  reoeited  from 
ipael  of'tbe  snrfiwe  of  the  earth,  and  all  npon  it,  than  the  idea 
k  ia  in  motion.  But  if  this  umyersal  impression  be  traced  to 
mn,  and  ri^tlj  interpretedi  it  will  not  be  foand  erroneous, 
Wl  Ibnn  no  exoepdon  to  the  general  maxim  which  indnoes  all 
My  not  eren  exoeptiog  philcNKypherB,  to  regard  wiUkoot  disre^^ 
IS  which  have  obtainea  nniyeisal  popalar  acceptation. 
bat  ia  the  stalnlity  and  repose  asonoed  hj  the  popular  jnd^ent 
leaxth?  Bepose  eertainljabsolate,  so  was  regurdsfiU  objects 
^^  or  popular  oontemph&on.  It  is  maintained,  and  maintained 

thai  eyery  thing  upon  the  earth,  so  frr  as  the  agency  of  ex- 
[  CMises  is  concerned,  is  at  rektire  rest  Hills,  mountains, 
alleys,  oceans,  seas,  and  rivers,  ss  well  as  all  artificial  structures, 
1  raalive  repose;  and  if  our  observation  did  not  extend  to 
ts  exterior  to  the  globe,  the  popular  maxim  would  be  indispu- 
But  the  astronomer  contemplates  oljects  which  either  escape 
ttention  of,  or  are  imperfectly  known  to,  mankind  in  genmi; 
be  phenomena  which  attend  these  render  it  manifest,  that  while 
irth,  in  relation  to  all  objects  upon  it  and  forming  piurt  of  it,  is 
it^  it  is  in  motion  with  relation  to  all  the  otherl)odies  of  the 


e  motion  of  objects  external  to  the  observer  is  perceiyed  by  the 
of  nght  only,  and  is  manifested  by  the  relative  displacement 
idnces  among  the  objects  aftcted  by  it,  vrith  relation  to  objects 
id  them  which  are  not  in  motion,  and  with  relation  to  each 
Motions  in  which  the  person  of  the  observer  participates 
aftet  the  senses  both  of  feeling  and  sight.  The  feeling  is 
led  bytiieasitation  to  which  the  body  of  the  observer  is  exposed. 
(,  in  a  carnage  which  starts  or  stops,  or  suddenly  increases  or 
cens  its  speed,  the  matter  composins  the  person  of  the  observer 
I  tendency  to  retain  the  motion  which  it  had  previous  to  the 
fs,  ami  is  acooidingly  afiected  with  a  certain  force,  as  if  it  were 
nd  or  drawn  from  rest  in  one  direction  or  the  other.  But  once 
>ilile  of  uniform  motion,  the  sense  of  feeling  is  only  afiiected  by 
af^tation  proceeding  from  the  inequalities  of  the  road.  If  these 
aahties  are  totally  removed,  as  they  are  in  a  boat  drawn  at  a 
■m  mte  on  a  canal,  the  sense  of  feeling  no  longer  affords  any 
In^  whateyer  of  the  motion. 

iimuurkable  example  of  the  absence  of  all  consciousness  of 
<i«y  to  fidr  as  mere  fbeling  is  concerned,  is  presented  to  all  who 
^  lioaided  in  a  balloon.    As  the  aerial  vehicle  floats  with  the 


112  ABTROROHT. 

Btntnm  of  the  air  in  which  it  is  eiupended,  the  feeling  of  the  un- 
naot  ig  that  of  the  most  absolute  repose.  The  bmlloon  seema  u  find 
and  immoveable  as  the  solid  globe  itself,  and  nothing  oonld  prodnoa 
in  the  vojager,  blindfolded,  aoy  couscioaBacBg  whatever  of  moluL 
WhoD  however  his  ejea,  anbaadaged,  are  turned  downwarda,  he  mh 
the  raet  diorama  Ixlow  moving  under  him.  Fields  and  wood^  viL 
lagea  and  towDs,  pass  in  aDCoeeuon,  and  the  phenomena  are  socb  m 
to  imprese  on  the  eye,  and  through  the  eje  npon  the  mind,  the  en- 
viction  that  the  halloon  is  stationatj,  and  the  earth  moving  anderiL 
A  ccTlun  effort  of  the  nnderetanding,  alight,  it  i>  troe,  bat  atilln 
.efibrt,  is  required  to  arrive  at  the  inference  that  the  impreanoo  thai 
produced  on  the  souBe  of  vision  is  an  illngion,  that  the  motioa  vilh 
which  the  landscape  seems  to  be  affected  ia  one  which  in  rati^ 
affects  the  balloon  in  which  the  spectator  is  suspended,  and  that  tlui 
motion  is  cqnal  in  speed,  and  contrary  in  direction,  to  that  which 
appears  to  affect  the  subjacent  country. 

Now  it  will  bo  evident,  that  if  the  globe  of  the  earth,  and  lU 
npon  it,  were  floating  in  space,  and  moving  in  any  direction  at  any 
uniform  rate,  no  consciousness  of  snch  motion  could  affect  any  lea- 
utive  being  npon  it.  AH  objects  partaking  in  common  in  snch 
motion,  no  more  derangement  among  them  would  ensue  than  ammg 
the  persons  and  objecte  transported  in  the  car  of  the  balloon,  when 
the  aeronaut,  no  matter  what  be  the  speed  of  the  motion,  can  fill  a 
glass  to  the  brim  as  easily  as  if  he  were  upon  the  solid  gnund. 
Supposing,  then,  that  the  earth  were  affected  by  any  motion  in  which 
all  objects  npon  it,  including  the  waters  of  the  ocean,  the  atmo- 
sphere, and  clouds,  would  all  participate,  wonld  the  existence  of  awdi 
a  motion  be  perccircd  by  a  spectator  placed  npon  the  earth  who 
would  himself  partake  of  it?  It  is  clear  that  he  most  remain  tat 
ever  unconscious  of  it,  unless  he  could  find  within  the  range  of  iui 
vision  aomo  objects  which,  not  partaking  of  the  motion,  would 
appear  to  have  a  motion  contrary  to  that  which  the  observer  has  in 
oommon  with  the  earth. 

But  snch  objects  are  only  to  be  looked  for  in  the  regions  of  spaea 
beyond  the  limits  of  the  atmosphere.  Wc  find  them  in  fine  in  the 
sun,  the  moon,  the  stars,  and  all  the  objects  which  the  firmament 
presents.  Whatever  motion  the  earth  may  have,  will  impart  to  all 
these  distant  objects  the  appearance  of  a  motion  in  the  contmy 
dircolion. 

But  how,  it  may  be  asked,  is  the  apparent  motion  produced  in 
distant  objects  by  a  real  motion  of  the  station  in  which  the  ohserva 
is  placed,  to  be  distinguished  from  Ihe  real  motion  of  the  distant 
objects  themselves,  which  would  give  tbcm  the  same  apparent 
motion  7  Since  the  phenomena  are  absolutely  idendficd,  whether 
the  apparent  motion  observed  is  produced  by  a  real  motion  in  tha 
observer,  or  a  real  motion  in  the  object  observed,  it  is  neceauij  to 


on  of  this  visual  line  ia  changed  with  every  I'bange  of  pojiiiion 
t  obscirer,  such  cliingc  of  position  produces  necessarily  a  Jis- 
aent  in  the  apparent  position  of  the  object. 
a  apparent  displace  in  ent  of  any  object  Eccn  at  &  distance,  due 

change  of  position  of  the  obacrrer,  is  called  parallax. 
oIloTB  that  a  distant  object  seen  by  two  obscrrera  at  different 

OD  tb«  eartb  is  seen  in  different  directions,  so  tbst  its  appa- 
>laca  in  the  firmament  will  be  dilTereut.  It  would  therefore 
,  that  the  aspect  of  the  heBTcns  would  vary  with  every  change 
dtion  of  the  observer  on  the  earth,  just  as  the  relative  position 
iects  on  bod  which  are  Btationary,  changes  when  vicwel  from 
«k  of  a  vessel  which  sails  or  steams  along  the  coast.  Bat  it 
ipens,  as  will  appear  hereafter,  that  even  the  greatest  difference 
lition  which  can  exist  between  observers  on  the  earth's  surface 
imall  compared  even  with  the  nearest  bodies  to  the  earth,  that 
nparent  displaccmeot,  or  paballax,  thus  produced  is  very 
;  while  for  the  most  numerous  of  celestinl  objects,  the  stars, 
baolutcly  inappreciable  by  the  most  refined  tueaus  of  observO' 


all  as  it  is,  however,  so  Ear  as  relates  to  the  nearer  bodies  of  the 
le,  it  is  capable  of  definite  measurement,  and  its  amount  for 
if  them  supplies  one  of  the  data  by  which  their  distanoes  are 
ited. 

16.  Apparent  and  true  p/iicc  of  an  oljjcct.  —  DiuTval  pa- 
:  —  When  an  object  is  within  such  a  limit  of  distance  as 
cense  a  sensible  displacement  to  be  produced  wbon  it  is 
1  from  different  narts  of  the  earth's  surface,  it  ia  convenient. 


114 


A8TR0N01IT. 


to  the  Bor&oe  or  vice  vend,  or,  what  is  the  mne,  the 

between  the  true  and  apparent  plaoes,  is  called  the  diubhak 

PARALLAX. 

In  Jig.  696,  let  o  represent  the  centre  of  the  earth,  p  a  plaoe  of 
observation  on  its  sor&ce,  o  an  object  seen  in  the  lenith  of  P,  o' 


Fig.  696. 

the  same  object  seen  at  the  zenith  distance  o  P  o',  and  o"  the  same 
object  seen  in  the  horizon. 

It  is  evident  that  o  will  appear  in  the  same  direction,  whether  it 
be  viewed  from  p  or  c.  Hence  it  follows  that  in  the  zenith  then 
is  no  diurnal  parallax,  and  that  there  the  apparent  place  of  an  ob» 
ject  is  its  true  place. 

But  if  the  object  be  at  o',  then  the  apparent  direction  is  P  O^y 
while  the  true  direction  is  c  o',  and  the  apparent  place  of  the  object 
will  be  a'y  while  its  true  place  will  be  if ;  and  the  diurnal  parallax 
corresponding  to  the  zenith  distance  o  P  o'  will  be  ^  a',  or  the  angle 
^  o'  a",  which  is  equal  to  r  o'  C. 

As  the  object  is  more  remote  from  the  zenith  the  parallax  b  aiig» 
mented,  because  the  semidiamcter  c  p  of  the  earth,  which  passtl 
through  the  place  of  observation,  is  more  and  more  nearly  at  right 
angles  to  the  directions  c  o'  and  P  o'. 

2327.  Ilorizoutal  parallax.  —  When  the  object  is  in  the  horiioni 
as  at  o",  the  diurnal  parallax  becomes  greatest,  and  is  called  the 


APPABBNT  FORM  OF  THE  FIRMAMENT. 


116 


PARATJ^x.  It  is  the  angle  p  o"  o  which  the  semi- 
of  the  earth  subtends  at  the  object. 
If  z  express  the  zenith  distance,  or  the  angle  p  o  o',  a  line  o  n 
from  o  at  right  angles  to  P  O'  n  will  be  expressed  by  z  xr  x 
■n.  Zy  r  being  the  semidiameter  o  p  of  the  earth.  If  d  express  the 
distance  of  the  object  o',  and  m  the  parallactic  angle  p  o'  O,  which 
18  always  very  snudl^  we  shall  havC;  by  the  principle  explained  in 
(2294): 

i"  =  206265"  X  Bin.  z  X  — ,  « 

ti»  parallax  bein^  expressed  in  seconds. 

If  the  object  be  in  the  horizon  as  at  o'',  we  shall  have  z  =  90^, 
md  therefore 

w"  =  206265"x— . 

2328.    Given  the  horizontal  parallax  and  the  earth's  semidt- 

meter,  to  compute  the  distance  of  the  object, — It  is  evident  that  this 

inportant  problem  can  be  solved  by  the  preceding  formulse ;  for  wo 

kfe  (2297) 

206265 
D= — T-„ —  Xr. 

w 


CHAP.  III. 


APPARENT  FORM   AND   MOTION   OF  THE   FIRMAMENT. 

2329.  Aspect  of  the  Jirmammt — If  we  examine  the  heavens 
tidi  attention  on  clear  starlight  nights,  we  shall  soon  be  struck  with 
4e  fidy  that  the  brilliant  objects  scattered  over  them  in  such  incal- 
fldable  numbers  maintain  constantly  the  same  relative  position  and 
■mgement.  Every  eye  is  familiar  with  certain  groups  of  stars 
ailed  constellations.  These  are  never  observed  to  change  their 
ulative  position.  A  diagram  representing  them  now  would  equally 
Kpment  them  at  any  future  time ;  and  if  a  general  map  be  made, 
ihowing  the  relative  arrangement  of  these  bodies  on  any  night,  the 

mm  map  will  represent  them  with  equal  exactness  and  fidelity  on 
■y  other  night  There  are  a  few,  —  some  thirty  or  forty  or  so,  — 
■MDg  many  thousands,  which  are  exceptions  to  this,  with  which, 
kverer,  for  the  present  we  need  not  concern  ourselves. 

2330.  The  celestial  hemisphere.  —  The  impression  produced  upon 
fte  i^t  by  these  objects  is  that  they  are  at  a  vast  distance,  but  all 


lis  ASTBOHOHT. 

ftt  the  MDue  diiUDce.  THej  seem  u  thoogli  tliej  mn  allMhad  ii 
fixed  and  Dnoltenble  poaitioiu  upon  the  mr&oo  of  ft  TMt  hMk 
sphere,  of  whioh  the  pUoe  of  the  obBerrar  is  the  aeotav.  Bithf 
■aide  the  aocide&tal  incqualitiea'  of  the  eroand,  the  obeenw  smMI 
to  Btand  in  the  centre  of  a  vut  oiicnlAr  puoe,  whioh  is  IIk  biarf 
this  celestial  hemisphere. 

2331.  Horizon  and  zenith.  —  This  plane,  extended  Indrfnihh 
aronnd  the  observer,  meete  the  celestial  henuBphen  in  ft<nTal»wUa 
is  called  the  Horizon,  from  the  Greek  word  tftS-r  (harison),  Is 
terminate  or  bomul,  being  the  boundary  or  limit  of  tiw  ivitik 
heavens. 

The  centre  point  of  the  visible  hemisphere — that  pant  whioh  it 
perpendicularly  above  the  obeervcr,  and  to  which  a  plamb-liM  *» 
pended  at  rest  would  be  diiooted  —  is  called  the  ZxsiTB. 

23.')2.  Apparent  rotation  of  the  Jirmament.  -~  A  few  horns'  s^ 
tentive  contemplation  of  the  firmament  at  night  will  enaUe  is; 
common  obaerrer  to  perceive,  tbst  although  the  stars  are,  relatinlj 
to  each  other,  fixed,  the  hemisphere,  at  a  lohole,  is  in  motiaD. 
Looking  at  the  seniih,  constellation  after  constell^on  will  ^fHS 
to  pasa  across  it,  having  risen  in  an  obliqne  direction  from  the  hov 
son  at  one  side,  and,  after  passing  the  senith,  descending  on  tbt 
other  side  to  the  horixon,  in  a  direction  similarly  oblique.  Still 
more  careful  and  longer  continued  obserration,  and  a  oomparisoD,  ■> 
far  as  can  be  made  by  the  eye,  of  the  different  directions  Bnca» 
nvely  assumed  by  the  same  object,  creates  a  suspicion,  which  evoif 
additional  observation  strengthens,  that  the  celestial  vault  has  s 
motion  of  slow  and  uniform  rotation  round  a  certain  diameter  u  SB 
axis,  carrying  with  it  all  the  objects  visible  upon  it,  without  in  the 
least  deranging  their  relative  positions  oi  disturbing  their  anangs- 
ment. 

Such  an  impressioD,  if  well  founded,  would  involve,  as  a  neees- 
sary  consequence,  that  a  certain  point  in  the  heavens,  placed  at  the 
extremity  of  the  axis  of  its  rotation,  would  be  fixed,  and  that  sH 
other  points  would  appear  to  be  carried  around  it  in  cirolee;  eeeh 
such  point  preserving  therefore,  constantly,  the  same  distance  frdn 
the  point  thus  fixed. 

'  2333.  The  pole  ttar.  —  To  verify  this  inference,  we  most  loci 
for  a  star  which  is  not  affected  by  the  apparent  rotation  of  the 
heavens,  which  affects  more  or  less  every  other  star. 

Such  a  star  is  accordingly  found,  which  is  always  seen  in  ihs 
same  direction,  —  bo  far  at  least  as  the  eye,  unaided  by  mon  aom- 
rate  means  of  observation,  can  determine. 

The  place  of  this  star  is  called  the  Pole,  and  the  star  is  oalled 
the  PoLX  Stas. 


APPABIHT  VORM  OF  THE  FIRMAXENT.  117 

RoUitum  proved  hy  trutrumental  obtervatum.  —  Mere 
fienrfttioD,  however^  can  at  moat  only  supply  srounds  for 
eoDJeetore,  either  as  to  the  rotation  of  the  sphere,  or  tiie 
if  Us  poloy  if  sooh  rotation  take  place.  To  yenfj  this  oon^ 
to  determine  with  certainty  whether  the  motion  of  the 
)  one  of  rotation,  and  if  so,  to  ascertain  with  precision  the 
of  the  axis  roond  which  this  rotation  takes  place,  its  yelo- 
,  in  fine,  whether  it  be  uniform  or  yariable, — are  problems 
ighest  importance,  bat  which  are  altogether  beyond  the 
f  mere  yisoal  observation,  unaided  by  instruments  of  pre- 

ILcact  direction  of  the  axis  and  position  of  the  pole.  -* 
%  telescope  of  low  magnifying  power,  supplied  with  micro- 
xes  (2302),  to  be  directed  to  the  pole  star,  so  that  the  star 
sen  exactly  upon  the  intersection  of  the  middle  wires.  If 
were  precisely  at  the  extremity  of  the  axis  of  the  hemi- 
r  at  the  pole,  it  would  remain  permanently  at  the  interseo- 
be  wires,  notwithstanding  the  rotation  of  the  firmament 
oij  however,  found  to  be  the  case.  The  star  will  appear  to 
it,  if  the  magnifying  power  of  the  telescope  be  low  enough, 
:  leave  the  field  of  view.  It  will  appear  to  move  in  a  small 
3  diameter  of  which  is  about  three  degrees.  The  telescope 
3  adjusted  that  the  star  will  move  in  a  circle  round  the  in- 

of  the  middle  wires  as  a  centre;  and  in  that  case  the 
rked  by  the  intersection  of  the  middle  wires  is  the  true 
f  the  Pole,  round  which  the  pole  star  is  carried  in  a  drcle^ 
tance  of  about  1}^,  by  the  rotation  of  the  sphere. 
Equatorial  instrument, — The  exact  direction  of  the  axis 
lestial  sphere  being  thus  ascertained,  it  is  possible  to  con- 
apparatus  which  shall  be  capable  of  revolving  upon  a  fixed 
direction  of  which  shall  coincide  with  that  of  the  sphere ; 

a  telescope  were  fixed  in  the  direction  of  this  axis,  its  line 
fttion  (2303)  would  exactly  point  to  the  celestial  pole, 
this  axis,  thas  directed  and  fixed,  suppose  a  telescope  to  be 
ed  that  it  may  be  placed  with  its  line  of  collimation  at  any 
igle  with  the  axis,  and  let  a  properly  graduated  arc  be  pro- 

which  the  magnitude  of  this  angle  may  be  measured  with 
sal  precision. 

let  A  a',  fig.  697,  represent  the  direction  of  the  axis  on 
e  instrument  is  made  to  revolve.  The  lino  A  a',  if  con- 
» the  firmament,  would  pass  through  the  pole  p.     Let  0  o 

the  line  of  collimation  of  a  telescope,  so  attached  to  the 
that  it  may  be  placed  at  any  desirea  angle  with  it;  which 
eoomplished  by  placing  a  joint  at  o  on  which  the  telescope 
.  Let  N  o  n'  be  a  graduated  arc,  to  which  the  telescope  if 
at  o,  and  which  turns  with  the  telescope  round  the  azia 


118 


ASTROirOHT. 


▲  A^  When  the  telesoope,  being  fixed  at  anj  piopoeed  tnda  00 A' 
with  the  axis,  is  torned  round  A  a',  the  line  of  eolBmatkm  cwMrilMf 
a  oone  of  which  0  is  the  yerfeex  and  o  a'  the  axis,  and  the  exUwily 
o  deeoribee  an  aro  o  (/  of  a  cirele  at  a  distanoe  from  h'  mo—niod  hj 
the  anffle  o  o  a'. 

If  the  line  of  oollimataon  o  o  or  o  o'  be  imagined  to  be  eoatimied 
to  the  heavens,  it  will  desoribe,  as  the  telescope  revolves,  a  oirde 
o  0^  on  the  firmament  corresponding  to  the  oinle  o  ^^  weA  at  Uie 
same  angular  distanoe  op^  dp  from  the  celestial  pole  j9  as  tbe  end  o 


/P 


or  0^  of  the  line  of  collimation  of  the  telescope  is  from  m'  or  a\  la 
short,  the  angle  o  o  n'  equally  measures  the  two  aroS|  the  oeleatial 
arc  op  and  the  instrumental  arc  on'. 

The  instrument  thus  described  in  its  principle  is  one  of  the  mosl 
extensive  utility  in  observatMies,  and  is  called  an  Equatobxal. 

In  its  practical  construction  it  is  very  variously  mounted,  and  is. 
sometimes  acted  upon  by  clock-work,  which  imparts  to  it  a  motioB 
round  the  axis  A  A ,  corresponding  vrith  the  rotation  of  the  celestial 
qphere« 

One  of  the  many  mechanical  arrangements  by  which  this  vmkj  ba> 


APFABSHT  TORM  OS  TBS  IIBMAMBNJ,  119 

flJbetad  b  npnanitod  in  Jiff,  698,  u  ginn  by  the  AstroDomer 
Bmlf  in  lu  leetaraa  delivered  at  the  Ipnrioh  Htueam. 

lb  iaatoiiment  ia  npported  npon  -^YOtHj-aa  thkt  ila  axis  a'  b' 
ibaQ  aoineide  ezaotlj  with  the  directioD  of  the  oele«tial  *»i«i     The 


t^MCope  O  D  tnrQB  upon  a  joint  at  the  centre,  bo  that  diflureot  di- 
rections, such  as  (/  d',  c"  if,  mar  be  given  to  it.  The  motion  npon 
iu  axis  is  imparted  to  it  by  wneel-vork  k  L  k,  impelled  by  clock- 
work, aa  already  mentioned. 

2337.  Rotation  of  firmametit  proved  bg  egvatorial.  —  Nov,  to 
esUbliah,  by  means  of  this  instrument,  the  &ct  that  the  firmament 
Rally  baa  a  motion  of  apparent  rotation  with  a  velocity  rigorously 
Boiform  ronnd  the  axis,  let  the  telescope  be  first  directed  to  any  star, 
0,  /uf.  697,  for  eianiple,  so  that  it  shall  be  seen  upon  the  interaeotioD 
of  the  middle  wires.  The  line  of  coliimation  will  then  be  directed 
to  the  star,  and  tbe  angle  o  o  n'  or  the  an  o  n'  will  express  the  ap- 
parent distance  of  such  star  from  the  pole  p. 

Let  the  instrument  be  then  torned  npon  its  axis  from  east  to  west 
ftbat  is,  in  the  same  directdon  as  the  rotation  of  the  firmament), 
diroagh  any  propoeed  angle,  say  90°,  and  let  it  be  fixed  in  that  po- 
lition.  The  firmament  will  follow  it,  and  after  a  certain  interval 
the  same  star  will  be  seen  npon  tbe  intersection  of  the  wires ;  and 
io  the  aame  manner,  whatever  be  the  change  of  position  of  the  in- 
Mmment  uptw  its  axia,  provided  the  direction  of  the  telescope  npon 
the  arc  o»',Jig.  697,  be  not  chasKod,  the  star  will  always  arrive, 
after  bd  int^val  more  or  leas,  according  to  the  angle  throngh  which 
ihis  instnime&t  has  been  tamed,  upon  the  intersection  of  the  wires 

It  follows,  therefore,  from  this,  that  the  particnlar  star  here  ob- 
wrved  ia  carried  in  a  circle  ronnd  the  heavens,  always  at  the  same 
£stan«e,  op,  ttam  the  celestial  pole. 

The  same  obacrvatioiu  being  made  with  a  like  result  upon  every 


ISO  ASTBOVOHT. 

star  to  which  the  telescope  is  directed,  it  fbllom  tint  tlie  n 
the  firniHtncnt  ia  such  thkt  all  otijeots  npoii  it  deaoribe  dnlei 
angles  to  its  axis,  each  olgeot  ftlirsTi  remaining  at  thfl  mmu 
from  the  pole. 

This  is  precisely  the  effoct  which  wonld  be  pradnoed  hj  the  n^H 
tion  of  the  heavens  round  an  axis  direoled  to  the  pole  from  tlH  |lMa 
of  the  ohscrvcr.  .   ■ 

But  it  remains  to  asoertiLiD  the  time  of  rotatioii,  aod  wbeUMlfell 
rotation  be  uniform.  " 

If  the  telescope  be  directed  as  before  to  aay  itar,  so  that  it  dM 
he  seen  at  the  intersection  of  the  wires,  let  tlie  inatrameDt  lie  Am 
fixed,  being  detached  from  the  clock-work,  and  let  tha  ezaet  tin 
of  the  star  passing  the  wires  be  noted.  On  the  following  oi^^it 
the  approach  of  the  same  hour,  the  same  star  will  be  m  " 

to  the  same  position,  and  it  will  at  length  arrive  again  i 
wires.  Tlic  lime  being  ngnin  exactly  observed,  it  will  be  fi 
the  interval  which  has  elapsed  between  the  two  suocesnve  [ 
of  the  star  over  the  wires  is 

2ab.  56m.  4.09. 

Such  is,  therefore,  the  time  in  which  the  celestial  sphere  nifai 

one  complete  revolution,  and  this  time  will  he  always  found  to  In 
the  same,  whatever  be  the  star  to  which  the  telescope  is  directed. 

To  prove  that  not  only  every  complete  revolution  is  perfbnnedil 
the  same  time,  but  that  the  rotation  during  the  same  revolntiaB  ii 
uniform,  let  the  instrument,  after  being  directed  to  any  star,  be  tmd 
iu  the  direction  of  the  motion  of  the  sphere  through  any  propOHl 
angle,  00°  for  example.  It  will  be  found  that  the  interval  wluA 
will  elapse  between  the  passage  of  the  star  over  the  wires  in  the  tm 
positions  will,  in  this  ease,  he  the  fourth  part  of  '23^  56^  i-09'-, 
and,  in  general,  whatever  be  tho  angle  through  which  the  iDstrmiMiit 
may  be  turned,  the  interval  between  the  passages  of  the  same  slir 
over  the  wires  in  the  two  positions  will  bear  the  same  proportion  to 
23''-  Se™-  409--,  as  the  angle  hears  to  360". 

It  follows,  therefore,  that  the  apparent  rotation  of  the  beanai  u 
rigorously  uniform. 

It  will  be  observed  that  the  time  of  one  complete  revolutioa  it 
S'"-  dS'OI"'  less  than  twenty-four  hours,  or  a  common  day.  The 
caoso  of  this  dificrcnce  will  be  expluined  hereafter. 

2338.  Sidereal  lime.  —  Tho  time  of  one  complete  revolution  rf 
the  firmament  is  called  a  sidereal  day.  This  interval  isdlvided, 
like  a  eomraon  day,  into  24  hours,  each  hour  into  GO  minutes,  aid 
each  minute  into  tiO  seconds. 

Since  in  2-1  sidereal  hours  the  sphere  turns  through  360%  aad 
since  its  motion  is  rigorously  uniform,  it  turns  15°  in  a  udeical 
hour,  and  through  1°  in  four  sidereal  minutes. 


APPARENT  FORM  OP  THE  FIRMAMENT.  121 

2339.    The  game  apparent  motion  observed  by  day.  — It  may  be 
objected  that  althougu  this  description  of  the  movement  of  the 
beavens  accords  with  the  appearances  daring  the  night,  there  is  no 
evidence  of  the  continuance  of  the  same  rotation  daring  the  day, 
■Boe  in  a  doadless  firmament  no  object  is  visible  except  the  sun, 
vliich  being  alone  cannot  manifest  the  same  community  of  motion 
as  b  exhibited  by  the  multitudinous  objects  which,  being  crowded 
10  thickly  on  the  firmament  at  night,  move  together  without  any 
chance  in  their  apparent  relative  position.     To  this  objection  it 
lay  DC  answered  that  the  moon  is  occasionally  seen  in  the  day- 
time as  well  as  the  sun ;  and,  moreover,  that  before  sunset  and 
BDikrise  the  planets  Jupiter  and  Venus  are  occasionally  seen  under 
fmrnrablc   atmospheric  circumstances.     Besides,  with  tclescopctf 
of  saflicicnt  power  properly  directed,  all  the  brighter  stars  can  bo 
btiiietly  seen  when  not  situated  very  near  the  position  of  the  sun. 
Now,  in  all  these  cases,  the  objects  thus  seen  appear  to  be  carried 
nmnd  by  the  same  motion  of  the  firmament,  which  is  so  much 
more  conspicuously  manifested  in  the  absence  of  the  sun  and  at 
night 

2340.  Certain  fixed  point*  and  circles  ncccssari/  to  expi^ss  the 
position  of  objects  on  the  Jieavens,  —  It  will  greatly  contribute  to 
the  facility  and  clearness  with  which  the  celestial  phenomena  and 
their  causes  shall  bo  understood,  if  the  student  will  impress  upon 
his  memory  the  names  and  positions  of  certain  fixed  points,  lines, 
tod  circles  of  the  celestial  sphere,  by  reference  to  which  the  posi- 
tion of  objects  upon  it  are  expressed.  Without  incumbering  him 
with  a  more  complex  nomenclature  than  is  indispensably  necessary 
for  this  purpose,  we  shall  therefore  explain  sonic  of  the  principtil 
of  these  landmarks  of  tlie  heavens. 

2841.  Vcrtiral  circles^  zenith,  and  nadir. — If  from  the  place 
of  the  observer  a  stnnght  line  be  imagined  to  be  drawn  pcM-pcn- 
(iicular  to  tlic  plane  of  the  horizon,  and  to  be  continued  iudeiinitely 
\»)i]i  upwards  and  downwards,  it  will  meet  the  visible  hemisphere 
:it  its  vertex,  the  Zenitu,  and  the  invisible  hemisphere,  which  is 
under  the  plane  of  the  horizon,  at  a  corresponding  point  called  the 
Nadir. 

If  a  plane  be  supposed  to  pass  through  the  place  of  the  ob- 
server and  the  zenith,  it  will  meet  the  celestial  surface  in  a  series 
of  points,  forming  a  circle  at  right  angles  to  the  horizon.  Such  a 
circle  is  called  a  vertical  circle,  or,  shortly,  a  Vertical. 

If  this  plane  be  supposed  to  be  turned  round  the  line  pas«:ing 
upwards  to  the  zenith,  it  will  assume  successively  every  direction 
round  the  observer,  and  will  meet  the  heavens  in  every  possible 
Tertical  circle. 

The  vertical  circles,  therefore^  all  intersecting  at  the  zenith  as  a 
in.  11 


122  ASTRONOMY. 

oommon  point,  divido  the  horizon  as  the  divisions  of  the  hoim  and 
minutes  divide  the  dial-plate  of  a  clock. 

2342.  The  celestial  meridian  and  prime  vertical,  —  That  Yertioil 
which  passes  though  the  celestial  pole  is  called  the  Meridian. 

The  meridian  is,  therefore,  the  only  circle  of  the  heavens  which 
passes  at  once  through  the  two  principal  fixed  points,  the  pole  and 
the  zenith. 

It  divides  the  visible  hemisphere  into  two  regions  on  the  right 
and  left  of  the  observer ;  as  he  looks  to  the  north,  that  which  is 
on  his  right  being  called  the  Eastern,  and  that  which  is  on  hb 
left  the  Western. 

Another  vertical  at  right  angles  to  the  meridian  is  called  the 
PRIME  vertical.     This  is  comparatively  little  used  for  reference. 

2343.  Cardinal  points,  —  The  meridian  and  prime  vertical  di- 
vide the  horizon  at  four  points,  equally  distant,  and  therefore  sepa- 
rated by  arcs  of  90^.  These  points  are  called  the  cardinal 
POINTS.  Those  formed  by  the  intersection  of  the  meridian  with 
the  horizon  are  called  the  North  and  South  points,  that  which  is 
nearest  to  the  visible  pole  in  the  northern  hemisphere  being  the 
north.  Those  formed  by  the  intersection  of  the  prime  vertical  with 
the  horizon  are  called  the  East  and  West,  that  to  the  right  of  an 
observer  looking  towards  the  north  being  the  east. 

The  cardinal  points  correspond  with  those  marked  on  the  card 
of  a  mariner's  compass,  allowance  being  made  for  the  variation  of 
the  needle. 

2344.  The  azimuth.  — The  direction  of  an  object,  whether  tenei- 
trial  or  celestial,  in  reference  to  the  cardinal  points,  or  to  the  plane 
of  the  meridian,  is  called  its  Azimuth.  Thus  it  is  said  to  have  so 
many  demes  of  azimuth  east  or  west,  according  as  the  vertical  oirole, 
whose  plane  passes  through  it,  forms  that  angle  east  or  west  of  the 
plane  of  the  meridian. 

2345.  Zenith  distance  and  altitude.  —  It  is  always  posnble  to 
conceive  a  vertical  circle  which  shall  pass  through  any  proposed 
object  on  the  heavens.  The  arc  of  such  a  circle  between  the  lenith 
and  the  object  is  called  its  Zenith  distance. 

The  remainder  of  the  quadrant  of  the  vertical  between  the  object 
and  the  horizon  is  called  its  Altitude. 

It  is  evident,  therefore,  that  the  altitude  of  the  zenith  is  90^|  and 
the  zenith  distance  of  every  point  on  the  horizon  is  also  90^. 

The  arc  of  the  meridian  between  the  zenith  and  the  pole  is  the 
zenith  distance  of  the  pole,  and  the  arc  of  the  meridian  between  the 
pole  and  the  horizon  is  the  altitude  of  the  pole. 

2346.  Celestial  equator. — If  a  plane  be  imagined  to  pass  tbroogh 
the  place  of  the  observer  at  right  angles  to  the  axis  of  the  sphere, 
and  to  be  continued  to  the  heavens,  it  will  meet  the  surface  of  the 
celestial  vault  in  a  circle  which  shall  be  90^  from  the  pole,  and 


APPABKNT  FORM  OF  THB  FIRMAMEKT. 


123 


vhieh  win  divide  the  sphere  into  two  hemispheres^  at  the  vertex  of 
ooe  of  which  is  the  visible  or  north  pole,  and  at  the  vertex  of  the 
other  the  invisible  or  soath  pole. 

This  circle  is  called  the  celestial  equator. 

The  several  fixed  points  and  circles  described  above  will  be  more 
dearlj  conceived  by  the  aid  of  the  diagram^  y^.  699^  where  o  is  the 


Fig.  699. 

plaee  of  the  observer,  z  the  zenith,  P  the  pole,  s  z  p  N  the  visible, 
and  spzn  the  invisible  half  of  the  meridian ;  s  e  n  w  is  the  horizon 
Men  by  projection  as  an  oval,  being,  however,  really  a  circle ;  N  and 
8  are  the  north  and  south,  and  s  and  w  the  east  and  west  cardinal 
pointa.  The  points  of  the  several  circles  which  are  below  the  horizon 
ne  &tingai8hed  by  dotted  lines.  The  celestial  eqnator  is  repre- 
sented at  JB  Q|  and  the  prime  vertical  at  z  w  e  z,  both  being  looked 
at  edgewise. 

A  plane  Nn,  drawn  through  the  north  cardinal  point  [and  parallel 
to  the  celestial  eonator],  cnts  off  a  portion  of  the  sphere,  having  the 
visible  pole  P  at  its  centre,  all  of  which  is  above  the  horizon ;  and  a 
oorrespooding  plane,  8  s,  through  the  south  cardinal  point,  cuts  off  a 
ptrt,  leaving  the  invisible  pole  at  its  centre,  all  of  which  is  below 
the 


2347.  Apparent  moHon  of  the  cdetiial  tphere,  —  Now,  if  the 
entire  sphere  be  imagined  to  revolve  on  the  line  pop  through  the 
poles  as  a  fixed  axis,  making  one  complete  revolution,  and  in  such  a 
directioii  that  it  will  pass  over  an  observer  at  o,  looking  towards  N 
from  his  right  to  his  left,  carrying  with  it  all  the  objects  on  the 
irmament,  without  disturbing  their  relative  position  and  arrangement, 
we  shall  Ibnn  an  exact  notion  of  the  apparent  motion  of  the  heavens. 
AQ  oljects  rise  upon  the  eastern  half^  be n,  of  the  honzoni  and  set 


124  ASTRONOMY. 

upon  the  wostern  half,  s  w  N.  The  objcots  which  m  nener  to  the 
visible  pole  P  than  the  circle  n  n  never  set;  and  those  which  an 
nearer  to  the  invisible  pole  p  than  the  circle  s  8  never  rise.  Those 
which  are  between  the  equator  M  Q  and  the  circle  n  N  are  longer 
above  the  horizon  than  below  it;  and  those  which  are  between  the 
equator  M  Q  and  the  circle  8  8  are  longer  below  the  horiioii  than 
above  it.  Objects,  in  fine,  which  are  upon  the  equator  are  equal 
times  above  and  below  the  horizon. 

When  an  object  rises,  it  gradually  increases  its  altitade  antQ  it 
reaches  the  meridian.  It  then  begins  to  descend|  and  continoes  to 
descend  until  it  sets. 


CHAP.  IV. 

DIURNAL  ROTATION  OF  THE  EARTH. 

2348.  Apparent  diurnal  rotation  of  the  heavens — its  pomble 
causes,  —  The  apparent  diurnal  rotation  of  the  celestial  sphere  being 
such  as  has  been  explained,  it  remains  to  determine  what  is  the  leu 
motion  which  produces  it.  Now  it  is  demonstrable  that  it  may  be 
caused  indifferently,  either  by  a  real  motion  of  the  sphere  round  the 
observer,  corresponding  in  direction  and  velocity  with  the  apparent 
motion,  or  by  a  real  motion  of  the  earth  in  the  contrary  directioni 
but  with  the  same  angular  velocity  upon  that  diameter  of  the  globe 
which  coincides  with  the  direction  of  the  axis  of  the  celestial  spherei 
and  that  no  other  conceivable  motion  would  produce  that  apparent 
rotation  of  the  heavens  which  we  witness.  Between  these  two  we 
are  to  decide  which  really  exists. 

2349.  Supposition  of  the  real  motion  of  the  universe  inadmis-' 
sible,  —  The  fixity  and  absolute  repose  of  the  globe  of  the  earth 
being  assumed  by  the  ancients  as  a  physical  maxim  which  did  not 
even  admit  of  being  questioned,  they  perceived  the  inevitable  cha- 
racter of  the  alternative  which  the  apparent  diurnal  rotation  of  the 
heavens  imposed  upon  them,  and  accordingly  embraced  the  hypo- 
thesis, which  now  appears  so  monstrous,  and  which  is  implied  in  the 
term  universe,'*'  which  they  have  bequeathed  to  us. 

It  is  true  that,  owine  to  the  imperfect  knowledge  which  prevailed 
as  to  the  real  magnitudes  and  distances  of  the  b^es  to  which  thifl 
common  motion  was  so  unhesitatingly  ascribed,  the  improbability  of 
the  supposition  would  not  have  seemed  so  gross  as  it  does  to  the 
more  enlightened  enquirers  of  our  age.     Nevertheless,  in  any  view 

*  Unus,  onef  and  versum,  tuminfff  or  rotation,  —  taming  with  one  oooi* 
mon  motion  of  rotation. 


DIUBNAL  ROTATION  OP  THE  EARTH.  125 

of  it,  and  ctcd  with  the  most  imperfect  knowledge,  the  hypothesis 

which  required  the  admission  that  the  myriads  of  bodies  which 

ajypear  apon  the  firmament  should  have,  besides  the  proper  mo- 

tMXtt  of  several  of  them,  suoh  as  the  moon  and  planets,  of  which 

the  andents  were  not  unaware,  motions  of  revolution  with  velocities 

m  piodigioas  and  so  marvellonslv  related,  that  all  should,  in  the  short 

mnal  of  twenty-four  hours,  whirl  round  the  axis  of  the  earth  with 

Ae  unerrinff  harmony  and  regularity  necessary  to  explain  the  appa- 

mt  ^umaf  rotation  of  the  firmament,  ought  to  have  raised  serious 

I      fifieolties  and  doubts. 

Bat  with  the  knowledge  which  has  been  obtained  by  the  labours 
of  modem  astronomers  respecting  the  enormous  magnitudes  of  the 
]dDcipal  bodies  of  the  physical  universe,  magnitudes  compared  with 
which  that  of  the  globe  of  the  earth  dwindles  to  a  mere  point,  and 
their  distances,  under  the  expression  of  which  the  very  power  of 
oamber  itself  almost  fails,  and  recourse  is  had  to  colossal  units  in 
order  to  enable  it  to  express  even  the  smallest  of  them,  the  hypo- 
thesis of  the  immobility  of  the  earth,  and  the  diurnal  rotation  of  the 
oountless  orbs,  of  magnitudes  so  inconceivable  filling  the  immensity 
of  spaoe  once  everv  twenty-four  hours  round  this  grain  of  matter 
eompodng  our  globe,  becomes  so  preposterous  that  it  is  rejected, 
not  as  an  improbability,  but  as  an  absiu*dity  too  gross  to  be  even  for 
a  moment  seriously  entertained  or  discussed. 

2350.  Simplicity  and  intrinsic  probability  of  the  rotation  of  the 
earih.  —  But  if  any  ground  for  hesitation  in  the  rejection  of  this 
hypoUieflis  existed,  all  doubt  would  be  removed  by  the  simplicity 
and  intrinnc  probability  of  the  only  other  physical  cause  which  can 
prodooe  the  phenomena.  The  rotation  of  the  globe  of  the  earth 
apon  an  axis  passing  through  its  poles,  with  an  uniform  motion  from 
f^est  to  east  once  in  twenty-four  hours,  is  a  supposition  against  which 
lot  a  single  reason  can  be  adduced  based  on  improbability.  Such  a 
notion  explains  perfectly  the  apparent  diurnal  rotation  of  the  celes- 
mI  sphere.  Being  uniform  and  free  from  irregularities,  checks,  or 
•oltBy  it  would  not  be  perceivable  by  any  local  derangement  of  bodies 
on  the  surface  of  the  earth,  all  of  which  would  participate  in  it. 
Observers  upon  the  surfiu)e  of  our  globe  would  be  no  more  conscious 
of  it,  than  are  the  voyagers  shut  up  in  the  cabin  of  a  canal-boat,  or 
transported  above  the  clouds  in  the  car  of  a  balloon. 

2361.  Direct  proofk  of  the  earth's  rotation,  —  Irresistible,  never- 
thelesB,  ss  this  logioid  aJtemative  is,  the  universality  and  antiquity 
of  the  belief  in  £e  immobility  of  the  earth,  and  the  vast  physical 
importance  of  the  principle  in  question,  have  prompted  enquirers  to 
search  for  direct  proofe  of  the  actual  motion  of  the  earth  upon  its 
%^ik  Two  phenomena  have  accordingly  been  produced  as  imme- 
diate and  condnaive  proof  of  this  motion. 

11* 


128  ABTRONOMT. 

2852.  Proof  hy  the  descent  of  a  hody  from  a  grtai  heigkL — It 
has  been  already  ?184)  shown  that  a  bodj  descending  from  a  mat 
height  does  not  fall  in  the  true  vertical  line,  which  it  would  if  the 
earUi  were  at  rest,  but  eastward  of  it^  which  it  most^  if  the  earth 
have  a  motion  of  rotation  from  west  to  east. 

2353.  Jf.  Leon  FoucauU's  mode  of  demonstration. — ^An  inniii- 
oas  expedient,  by  which  the  diurnal  rotation  of  the  earth  is  ren£red 
visible,  has  been  conceived  and  reduced  to  experiment  by  M.  Leon 
Foucault  This  contrivance  is  based  upon  the  principle,  that  the 
direction  of  the  plane  of  vibration  of  a  pendulum  is  not  a£Eected  by 
any  motion  of  translation  which  may  be  eiven  to  its  point  of  los- 
pcnsion.  Thus,  if  a  pendulum  suspended  in  a  room  and  put  into 
vibration  in  a  plane  parallel  to  one  of  the  walls  be  carried  round  a 
circular  table,  the  plane  of  its  vibration  will  continually  be  parallel 
to  the  same  wall,  and  will  therefore  vary  constantly  in  the  angle  it 
forms  with  the  radius  of  the  table  which  is  directed  to  it 

Now,  if  a  pendulum,  suspended  any  where  so  near  the  pole  of 
the  earth  that  the  circle  round  the  pole  may  be  considered  a  plane, 
be  put  in  vibration  in  a  plane  passing  through  the  pole,  this  plane, 
continuing  parallel  to  its  original  direction  as  it  is  carried  round  the 
pole  by  the  earth's  rotation,  will  make  a  varying  angle  with  the  line 
drawn  to  the  pole  from  the  position  it  occupies.  After  being  carried 
through  a  quarter  of  a  revolution  it  will  make  an  angle  of  90^  with 
the  line  to  the  pole,  and  so  on.  In  fine,  the  direction  of  the  pole 
will  appear  to  be  carried  round  the  plane  of  vibration  of  the  pen- 
dulum. 

The  same  effects  will  be  produced  at  greater  distances  from  the 
pole,  but  the  rate  of  variation  of  the  angle  under  the  plane  of  vi* 
bration  and  the  plane  of  the  meridian  will  be  different,  owing  to  the 
effects  of  the  curvature  of  the  meridian. 

This  phenomenon,  therefore,  being  a  direct  effect  of  the  rotation 
of  the  earth,  supplies  a  proof  of  the  existence  of  that  motion,  at- 
tainable without  reference  to  objects  beyond  the  limits  of  the 
globe. 

2354.  Analogy  supplies  evidence  of  the  earth's  rotation. — The 
obvious  analogy  of  the  planets  to  the  earth,  which  will  appear  moTB 
fully  hereafter,  would  supply  strong  evidence  in  favour  of  the  earth's 
rotation,  even  if  positive  demonstration  were  wanting.  All  the 
planets  are  globes  like  the  earth,  receiving  light  and  heat  from  the 
same  luminary,  and,  like  the  earth,  revolving  round  it.  Now  all 
the  planets  which  we  have  been  enabled  to  observe  have  motions  of 
rotation  on  axes,  in  times  not  very  different  from  that  of  the  earth. 

2355.  Figure  of  the  earth  supplies  another  proof — Bcsidei 
these,  it  will  be  shown  hereafter  that  another  proof  of  the  rotation 
of  the  earth  is  supplied  by  a  peculiar  departure  firom  the  strictly 
globular  form. 


-  I 


BIURNAL  ROTATION  OP  THE  EARTH.  127 

2356.  Horn  this  rotation  of  the  earth  explains  the  diurnal  phe- 
namena. — We  are  then  to  conclude  that  the  earth,  being  a  globe, 
has  a  motion  of  uniform  rotation  round  a  certain  diameter.  The 
universe  around  it  is  relatiyely  stationary,  and  the  bodies  which 
compose  it  being  at  distances  which  mere  vision  cannot  appreciate, 
appear  as  if  they  were  situate  on  the  surface  of  a  vast  celestial 
sphere  in  the  centre  of  which  the  earth  revolves.  This  rotation  of 
the  earth  ^ves  to  the  sphere  the  appearance  of  revolving  in  the 
contrary  direction,  as  the  progressive  motion  of  a  boat  on  a  river 
gives  to  the  banks  an  appearance  of  retrogressive  motion ;  and  since 
the  apparent  motion  of  the  heavens  is  from  east  to  west,  the  real 
rotation  of  the  earth  which  produces  that  appearance  must  be  from 
vest  to  east 

How  this  motion  of  rotation  explains  the  phenomena  of  the  rising 
and  sotting  of  celestial  objects  is  easily  understood.  An  observer 
placed  at  any  point  upon  the  surface  of  the  earth  is  carried  round 
the  axis  in  a  circle  in  twenty-four  hours,  so  that  every  side  of  the 
celestial  sphere  is  in  succession  exposed  to  his  view.  As  he  is 
carried  upon  the  side  opposite  to  that  in  which  the  sun  is  placed,  he 
sees  the  starry  heavens  visible  in  the  absence  of  the  splendour  of 
that  luminary.  As  he  is  turned  gradually  towards  the  side  where  the 
fan  is  placed,  its  light  begins  to  appear  in  the  firmament,  the  dawn 
of  morning  is  manifested,  and  the  globe  continuing  to  turn,  he  is 
hrooght  into  view  of  the  luminary  itself,  and  all  the  phenomena  of 
dawn,  morning,  and  sunrise  are  exhibited.  While  he  is  directed 
tovaitis  the  side  of  the  firmament  in  which  the  sun  is  placed,  the 
other  bodies  of  inferior  lustre  are  lost  in  the  splendour  of  that  lumi- 
oary,  and  all  the  phenomena  of  day  are  exhibited.  When  by  the 
eoDtinued  rotation  of  the  globe  the  observer  begins  to  be  turned 
avay  from  the  direction  of  the  sun,  that  luminary  declines,  and  at 
jength  disappears,  producing  all  the  phenomena  of  evening  and  sunset 

Such,  in  general,  are  the  effects  which  would  attend  the  motion 
d  a  spectator  placed  upon  the  earth's  surface,  and  carried  round 
with  it  by  its  motion  of  rotation.  He  is  the  spectator  of  a  gorgeous 
diorama  exhibited  on  a  vast  scale,  the  earth  which  forms  his  station 
being  the  revolving  stage  by  which  he  is  carried  round,  so  as  to 
view  in  succession  the  spectacle  which  surrounds  him. 

These  appearances  vary  with  the  position  assumed  by  the  observer 
CD  this  revolving  stage,  or,  in  other  words,  upon  his  situation  on  the 
earth,  as  will  presently  appear. 

2357.  The  earth's  axis, — That  diameter  upon  which  it  is  neces- 
sary to  suppose  the  earth  to  revolve  in  order  to  explain  the  pheno- 
Bttna,  is  that  which  passes  through  the  terrestrial  poles. 

2358.  27ie  terrestrial  equator,  pole*,  and  meridians,  —  If  the 
gbbe  of  the  earth  bo  imagined  to  be  cut  by  a  plane  passing  through 
its  centre  at  right  angles  to  its  axis^  such  a  plane  will  meet  tiio  sur- 


128  ASTRONOMY. 

fkoe  in  a  circle,  which  will  divide  it  into  two  homisphereBy  at  the 
summits  of  which  the  poles  aro  situate.     This  circle  is  called  the 

TERRESTRIAL  EQUATOR. 

That  hemisphere  which  includes  the  oontiDent  of  Europe  is 
called  the  NORTHERN  hemisphere,  and  the  pole  which  it  indudei 
is  called  the  northern  terrestrial  pole;  the  other  hemisphen 
hcing  the  southern  hemisphere,  and  including  the  southeeii 
terrestrial  pole. 

If  the  surface  of  the  earth  he  imagined  to  be  intersected  by  planes 
passing  through  its  axis,  thej  will  meet  the  surface  in  circles  which, 
passing  through  the  polos,  will  be  at  right  angles  to  the  equator. 
These  circles  are  called  terrestrial  meridians^  and  will  be  sees 
delineated  on  any  ordinary  terrestrialelobe. 

2359.  Latitudt  and  longitude. — The  pontioii  of  plMes  upon  the 
surface  of  the  earth  are  expressed  and  indicated  by  ttiUnif  tfadr  dia 
tance  north  or  south  of  the  equator,  measured  upon  a  mendiaii  pass- 
ing through  them,  and  by  the  distance  of  such  nieridiui  tiik  oi 
west  of  some  fixed  mcridiui  arbitrarily  selected,  sooh  aa  1|ji«^ 
dian  passed  through  the  observatory  at  Greenwioh.  Ite 
distance,  expressed  in  degrees,  minutes,  and  aeeondip  fa 
Latitude,  and  the  latter,  similarly  expressed,  the  Low 
the  place. 

2860.  Fixed  meridians  —  those  of  Greenwich  amd  jRariur\ 
no  natural  phenomenon  is  found  by  which  a  fixed  HMfidfaii' 
which  longitude  is  measured  can  be  determined, 
geographers  have  not  agreed  in  the  arbitrary  selection  of  ona. 
meridians  of  the  Greenwich  and  P&ris  observatories  hava 
taken,  the  former  by  English  and  the  latter  by  French  woAoiXifbBf 
as  the  startine-point.  To  reduce  the  longitudes  expresaad  by  ailher 
to  the  other,  it  is  only  necessary  to  add  or  substract  the  angb  imder 
the  meridians  of  the  two  observatories,  which  has  been  aaoertained 
to  be  2""  2(K  22",  the  meridian  of  Paris  being  east  of  that  of  Green- 
wich. 

2361.  How  the  diurnal  phenomena  vary  with  the  latitude,— 
Let  s  iE  N  %Jig'  700,  represent  the  earth  suspended. in  space,  sur- 
rounded at  an  immeasurable  distance  by  the  stellar  universe.  The 
magnitude  of  the  earth  being  absolutely  insi^ificant  compared  with 
the  distances  of  the  stars,  the  aspect  of  these  will  be  the  same 
whether  they  are  viewed  from  any  point  on  its  surface,  or  from  its 
centre.  The  observer  may  therefore,  whatever  be  his  position  on 
the  earth,  be  considered  as  looking  from  the  centre  of  the  celestial 
sphere. 

Let  us  suppose,  in  the  first  place,  the  observer  to  be  at  o,  a  point 
on  its  surface  between  the  equator  M  and  the  north  pole  N,  the  lati- 
tude of  which  will  therefore  be  o  iE,  and  will  be  measured  by  the 
angle  oo  iS.    If  a  line  bo  imagined  to  be  drawn  from  the  centre  G 


DimXAL  BOTAUOH  OF  THI  K&RTH.  189 

ina^  &■  pboe  o  of  the  obnrver,  and  oontinned  npwmnli  to  (he 
haiHeBt,  it  vill  airin  at  the  point  c,  which  ia  the  >enith  of  the 

im If  Ae  temetrial  uia  b  k  be  imBgioed  to  be  oontinned  to 

tie  bmMmnt,  it  vill  anive  at  the  north  eeleetiml  pole  n  and  the 
pole  A  If  the  plane  of  the  teneatrial  equator  x  q 
>  oe  otntuMd  to  the  heaTCW,  it  will  interaoot  the  m- 


ftj£fte« 


wliitial  iflun  at  die  eeleatial  equator  mj. 


Flf.  I0>. 

The  obewver  pUoed  at  o  will  see  the  entiie  hemiiphere  hth'  of 
whiA  hie  Moith  a  i>  the  nunmit;  and  the  other  hemie^faere  kih' 
will  be  iDvinble  to  him,  being  in  &ct  ooncealed  from  hie  view  b; 
tte  earth  oa  which  he  itanda. 

It  b  endent  that  the  iro  of  the  heavena  » n  between  bia  Eenith 
a^  the  nmth  oeleatdal  pole  coDBiatB  of  the  aame  Dumber  of  de|rees 
« (be  an  OH  of  the  terrestrial  meridian  between  his  plaoe  M  ob- 


180  A6TR0N0MT. 

servation  o  and  the  north  terrestrial  polo  N.  The  senith  distance 
therefore  of  the  visible  pole  at  any  plaoe  is  always  equal  to  the 
actual  distance  expre»sed  in  degrees  of  that  place  from  the  terres- 
trial polC)  and  as  this  distance  is  the  complement*  of  the  lati- 
tude, it  follows  that  the  zenith  distance  of  the  yisible  pole  ifl  the 
complement  of  the  latitude,  and  that  the  altitude  of  the  vudUe  pole 
is  equal  to  the  latitude  of  tlie  place. 

2362.  Method  of  finding  the  latitude  of  the  place.  —  The  lati- 
tude of  the  place  of  observation  may  therefore  be  always  deter- 
mined if  the  altitude  of  the  celestial  pole  can  be  observed.  If 
there  were  any  star  situate  precisely  at  the  pole,  it  would  therefora 
be  sufficient  to  observe  its  altitude.  There  is,  however,  no  star 
exactly  at  the  pole,  although,  as  has  been  already  observed,  the 
POLE  STAB  is  very  near  it.  The  altitude  of  the  pole  is  found, 
therefore,  not  by  one,  but  by  two  observations.  The  pole  star,  or 
any  other  star  situate  near  tiie  pole,  is  carried  round  it  in  a  oirde  by 
the  apparent  diurnal  motion  of  the  sphere,  and  it  necessarily  crosses 
the  meridian  twice  in  each  revolution,  once  a&ove,  and  once  hdom 
the  pole.  Its  altitude  in  the  latter  position  is  the  leati^  and  in 
the  rormcr  the  greatest  it  ever  has ;  and  the  pole  itself  is  just  mid- 
way between  these  two  extreme  positions  of  this  oircumpolar  star. 
To  find  the  actual  altitude  of  the  pole,  it  is  only  necessary  then- 
fore  to  take  the  mean,  that  is,  half  the  sum  of  these  two  eztnine 
altitudes.  By  making  the  same  observations  with  several  droum- 
polar  stars,  and  taking  a  mean  of  the  whole,  still  greater  aoounoy 
may  be  attained. 

2363.  Position  of  celestial  equator  and  poles  varies  wiA  the 
latitude.  —  Since  the  altitude  of  the  celestial  pole  is  everywhere 
equal  to  the  latitude  of  the  place,  and  since  the  position  of  the 
celestial  equator  and  its  parallels,  in  which  all  celestial  objects  ap- 
pear to  be  moved  by  the  diurnal  rotation,  varies  with  that  of  the 
pole,  it  is  evident  that  the  celestial  sphere  must  present  a  different 
appearance  to  the  observer  at  every  different  latitude.  In  proceed- 
ing towards  the  terrestrial  pole,  the  celestial  pole  will  gradually  u- 
proach  the  zenith,  until  we  arrive  at  the  terrestrial  pole,  when  it 
will  actually  coincide  with  that  point  ]  and  in  proceeding  towards 
the  terrestrial  equator,  the  celestial  pole  will  gradually  descend 
towards  the  horizon,  and  on  arriving  at  the  Line  it  will  be  actually 
on  the  horizon. 

2364.  Parallel  sphere  seen  at  the  poles,  —  At  the  poles,  therefeie, 
the  celestial  pole  being  in  the  zenith,  the  celestial  equator  will 
coincide  with  the  horizon,  and  by  the  diurnal  motion  all  objects 
will  move  in  circles  parallel  to  the  horizon.     Every  object  wUl 

*  The  complement  of  an  angle  or  arc  is  that  number  of  degrees  by  whieh 
it  differs  from  90<>.    Thus  80^  degrees  is  the  complement  of  60<>. 


DIURNAL  ROTATION  OF  THE  EARTIL  181 

therefore  preserve  daring  twentj-four  hoars  the  same  altitude  and 
the  same  zenith  distance.  No  object  will  either  rise  or  set,  at  least 
so  far  as  the  diurnal  motion  is  conoemed. 

This  aspect  of  the  firmament  is  called  a  parallel  sphere,  the 
motion  being  parallel  to  the  horizon. 

2365.  Right  tphere  $een  cU  the  equator.  —  At  the  terrestrial 
eqaatoFy  the  poles  being  upon  the  horizon,  the  axis  of  the  celestial 
sphere  will  coincide  with  a  line  drawn  upon  the  plane  of  the  horizon 
connecting  the  north  and  south  points.  The  celestial  equator  and 
its  parallels  will  be  at  right  angles  to  the  plane  of  the  horizon ;  aud 
nnce  the  plane  of  the  horizon  passes  through  the  centre  of  all  the 
parallclB,  it  will  divide  them  all  into  equal  Fomicircles. 

It  follow8|  therefore,  that  all  objects  on  the  heavens  will  be  equal 
times  above  and  below  the  horizon,  and  that  thej  will  ri.se  and  set 
in  planes  perpendicular  to  the  horizon. 

This  aspect  of  the  firmament  is  called  a  right  sphere,  the  diurnal 
motioD  bc»ng  at  right  angles  to  the  horizon. 

2366.  Ohtique  gphert  teen  at  intermediate  latit^ides. — At  latitudes 
between  the  equator  and  the  pole,  the  celestial  pole  holds  a  place 
between  the  horizon  and  the  zenith  determined  by  the  latitude.  The 
eelesdal  equator  as  q,  fig.  700,  and  its  parallels,  are  inclined  to  the 
plane  of  the  horizon  at  angles  equal  to  the  distance  of  the  pole  from 
the  zenith,  and  therefore  equal  to  the  complement  of  the  latitude. 
The  centres  of  all  parallels  to  the  celestial  equator  ce  q  which  are 
between  it  and  the  visible  pole  are  above  the  plane  of  the  horizon, 
between  c  and  N,  and  the  centres  of  all  parallels  at  the  other  side 
of  the  equator  below  it  The  parallels,  such  as  Tm'  and  Im,  will 
therefore  be  all  divided  unequally  by  the  plane  of  the  horizon,  the 
visible  part  f  i^  being  greater  than  the  invisible  part  m!  /  for  the 
former,  and  the  invisible  part  m  r  greater  than  the  visible  part  /  r 
for  the  latter. 

It  follows,  therefore,  that  all  objects  between  the  celestial  equator 
mq  and  the  visible  pole  n  will  be  longer  above  than  below  the 
horizon,  and  all  objects  on  the  other  side  of  the  equator  will  be  longer 
below  the  horizon  than  above  it. 

A  parallel  A'  A/  to  the  celestial  equator,  whose  distance  from  the 
Tiyble  pole  is  equal  to  the  latitude,  will  be  entirely  above  the  horizon, 
just  touching  it  at  the  point  under  the  visible  pole ;  and  a  corre- 
iponding  parallel  A  A;,  at  an  equal  distance  from  the  invisible  pole, 
will  be  entirely  below  the  horizon,  just  touching  it  at  the  point  above 
the  inviuble  pole. 

All  parallels  nearer  to  the  visible  pole  than  h'  Jd  will  be  entirely 
above  the  horizon,  and  all  parallels  nearer  to  the  invisible  pole  than 
kk  will  be  entirely  below  it. 

Henoe  it  is  that,  in  European  latitudes,  stars  within  a  certain  lim- 
ited distanco  of  the  north  or  visible  celestial  pole  never  set,  and  stars 


us  ASTBOirOHT. 

mt  t  correx ponding  distance  from  the  Nuth  or  invisible  celestiRl  fob 
never  rise, 

Tlic  observer  can  onlj  see  these  hj  going  to  plues  of  observitiiiB 
having  lower  latitudes. 

TLis  aspect  of  the  firmament  is  called  an  Oblique  bfderx,  lb 
diurnal  motion  bciag  obliijuc  to  the  horizon. 

23C7.  Ohjfcia  in  cekelial  eqxtalur  equal  time*  above  and  belam 
korison.  —  Whether  the  sphere  bo  right  or  obliqae,  the  centre  «f 
tic  celestial  ec|uator  buing  on  the  plane  of  the  horitoo,  one  htlf  it 
that  circle  will  be  bclniv,  uud  the  oifacr  half  above  the  boriuB. 
Every  objei't  upon  it  will  therefore  be  equal  times  above  and  below 
the  horizon,  rising  and  setting  ciacllj  at  the  east  and  west  poieti. 

Tn  the  parallel  sphere,  the  celealiol  equator  coinciding  with  Ik 
horizon,  an  object  upon  it  will  be  carried  ronnd  the  horixon  bj  tb 
diurnal  rotation,  without  cither  rising  or  setting.* 

2368.  Mithoil  of  deierminitig  the  }mirjitud<<.  of  placet.  — Tin 
perfect  uniformity  of  the  earth's  rotation,  inferred  from  the  olMcrnd 
uniformity  of  the  apparent  rotation  of  the  firmament,  is  the  basis  1/ 
all  metboda  of  determining  the  longitude.  The  longitnde  of  a  pliM 
will  be  determined  if  the  angle  under  the  meridian  of  the  place,  sod 
that  of  any  other  piuce  whoso  longitude  is  known,  can  be  fond. 
But  since,  by  the  uniform  rotation  of  the  globe,  (he  meridians  (fill 
places  upon  it  are  brought  in  regular  succeBuon  under  everj  part  rf 
the  firmament,  the  moments  at  which  the  two  meridians  pass  midtt 
the  same  star,  or,  what  is  the  same,  the  momenls  at  which  the  nma 
star  is  seen  to  pass  over  the  two  meridians,  being  observed,  tbg 
interval  will  bear  the  same  ratio  to  the  entire  time  of  the  eaitl^l 
rotation  as  the  diflfurcncc  of  the  longitudes  of  the  two  places  ban 
to  360°. 

To  make  this  more  dear,  let  ns  take  the  case  of  two  places  p  sad 
s'lf:/-  701,  upon  the  equator.  If  c  be  the  centre  of  the  earth,  the 
angle  pop'  will  be  the  difference  between  the  longitudes.  Now, 
let  the  time  be  observed  at  each  place  at  which  any  particular  sin 
s  is  seen  upon  the  meridian.  If  the  motion  of  the  earth  be  id  th( 
direction  of  the  arrow,  the  meridian  of  F  will  come  to  the  star  befim 
the  meridian  of  p'.  This  necessarily  supposes  p  to  be  east  of  if, 
since  the  earth  revolves  from  west  to  east.  Let  the  true  inteml 
of  time  between  the  passage  of  a  over  the  two  meridians  be  (,  let  t 
be  the  time  of  one  complete  revolution  of  the  globe  on  its  axis,  ud 

"The  tencherw]1l  find  it  ndTsnlageous  ta  eiercjae  th a  student  in  tbi 
snliject  of  tlie  precedinf;  pani)>rapliB,  aided  b;  an  nrmillarj  sphere,  or.  if 
that  be  not  nccessiblo,  liy  n  culeslinl  glcdic,  whicb  will  serve  nasrlj  as  well 
Miiiif  questions  will  BuKglOBt  IhemBelves,  arising  out  of  and  deducibU  fMa 
what  bos  been  explained  aboTc,  with  rcsiiect  to  the  various  amtodea  of  lb 
sphere  in  different  latitudes. 


DIUENAL  ROTATION  OP  THE  EARTH. 


183 


VSg.  TOl. 


let  L  be  the  difference  of  the  longitudes,  or 
the  angle  pop';  we  shall  then  have 

< :  T  : :  L  :  360®, 
L=-x360®. 

T 

Bat  in  the  practical  solution  of  this  problem 
a  difficulty  is  presented  which  has  conferred 
historical  celebrity  upon  the  question,  and 
caused  it  to  be  referred  to  as  the  type  of  all 
difficult  enquiries.  It  is  supposed,  in  what 
has  just  been  explained,  that  means  are  pro- 
vided at  the  two  places  p  and  p'  by  which 
the  absolute  moments  of  the  transit  of  the 
star  over  the  respective  meridians  may  be 
ascertained,  so  as  to  give  the  exact  interval 
between  them.  K  these  moments  be  ob- 
served by  any  form  of  chronometer,  it  would 
AeD  be  necessary  that  the  two  chronometers  should  be  in  exact 
aeeofdanoe,  or,  what  is  the  aame,  that  their  exact  difference  may  be 
known.  If  a  chronometer,  set  correctly  by  another  which  is  sta- 
tkmary  at  one  place  P,  be  transported  to  the  other  place  p',  this 
flljed  will  be  attained,  subject,  however,  to  the  error  which  may  be 
iMidenlal  to  the  rate  of  the  chronometer  thus  transported.  If  the 
ih>infifn  between  the  places  be  not  considerable,  the  chronometerd 
Bay  thns  be  brought  into  very  exact  accordance;  but  when  the 
Stiukce  18  great,  and  that  a  long  interval  must  elapse  during  the 
teanaport  of  the  chronometer,  this  expedient  is  subject  to  errors  too 
ttosiderable  to  be  tolerated  in  the  solution  of  a  problem  of  such 
capital  importance. 

It  will  be  apparent  that  the  real  object  to  be  attained  is,  to  find 
phenomenon  sufficiently  instantaneous  in  its  manifestation  to 
with  all  the  necessary  precision,  a  certain  moment  of  time. 
heh  a  phenomenon  would  be,  for  example,  the  sudden  extinction 
d%  eoospicaous  light  seen  at  once  at  both  places.  The  moment  of 
neh  a  phenomenon  being  observed  by  means  of  two  chronometers 
U  the  places,  the  difference  of  the  times  indicated  by  them  would 
be  known,  and  they  would  then  serve  for  the  determination  of  the 
fifference  of  the  longitudes  by  the  method  explained  above.  Several 
^enomena,  both  terrestrial  and  celestial,  have  accordingly  been  used 
ibr  this  purpose.  Among  the  former  may  be  mentioned  the  sudden 
cstmetion  of  the  oxyhydrogen  or  electric  light,  the  explosion  of  a 
mkei,  &c. ;  among  the  latter,  the  extinction  of  a  star  by  the  disc 
if  the  moon  passing  over  it,  and  the  eclipse  of  the  satellites  of  cer- 
tam  planets,  phenomena  which  will  be  more  fully  noticed  hereafter. 

m.  12 


2869.  Lunarnuthod  of  finding  the  bngihide. — The  d 
positioD  of  the  moon  vith  relatioa  to  the  san  and  stara  be 
rapid,  affords  another  phenomeDon  vhich  baa  beeo  found  i  _ 
utility  in  the  determinfttion  of  the  longitude,  eqiedaUj  for  tha~|i 
posee  of  raarinere.  Tables  sre  calenlated  in  wbioh  too  n  * 
parent  distances  tmm  the  aan,  and  manj  of  the  moat  i 
fixed  stars,  are  ffiven  for  short  intervals  cf  time,  and  the 
at  Greenwich  when  the  moon  has  these  distanoea  are  pven.  If  i 
the  msriiier,  obserring  with  proper  instrtunents  the  pontaon  et 
moon  with  relation  to  these  objects,  compares  his  obaerved  diatnap 
with  the  tables  which  are  supplied  to  him  in  the  Nantioal  *'— — ^ 
he  will  find  the  time  at  Greenwich  correspondii]^  tc  tba  wammAm 
his  observation ;  and  being  always,  by  the  ordinaij  metlmdi^  ith 
to  determine  by  observation  the  local  time  at  the  plam  of  hia  cbi^ 
Titioc,  the  difference  gives  him  the  time  required  for  »  atar  to  pat 
from  the  meridian  of  Greenwich  to  the  meridian  of  the  pUce  of  kk 
observation,  or  vice  vertd;  and  this  time  gives  the  long^tndc^  ■ 
already  explained. 

This  last  is  known  as  the  LunAB  method  or  DBTKBUnflRO  ID 

LONOITUDE. 

In  practice,  many  details  are  necessary,  and  varioos  calcnlatiMa 
must  bo  made,  which  cannot  be  explained  here. 

2370.  3fefhod  by  electric  telegraph.  —  When  two  places  are  con- 
nected by  a  line  of  electric  telegraph,  their  difference  of  I 
can  be  easily  and  exactly  determined,  inasmnch  as  instai 
signals  can  be  traoemitted,  by  which  the  local  clocks  can  be  em- 
pared  and  regulated,  and,  if  it  be  so  desired,  kept  in  exact  aoecri' 

2S71.  Paratlfh  of  latitude.  —  A  series  of  points  on  the  ewdi 
which  are  at  equal  distances  from  the  equator,  or  which  hare  tha 
same  latitude,  form  a  circle  parallel  to  the  equator,  called  »  pabaIp 

LEL  OF  LATITUDE. 

Thus  all  places  which  have  the  eame  latitude  are  on  tlie  same  Wt- 
sllel. 

All  places  which  are  on  the  same  meridian  have  tho  same  loDp- 
tnde. 


CHAP.  V. 

BPHEROIDAL  FORM,    MASS,   AND  DENSITY  OF  THE  EARTH. 

2372.  Progreu  of  phj/tical  inveiligalton  approximative.  — It  l 
tlie  condition  of  man,  and  probably  of  all  other  finite  intelliscnoef 
to  arrive  at  the  possession  t^  knowledge  by  the  slow  and  laborioo 


VORM  AND  DSKSmr  OF  THE  EARTH.  186 

of  a  sort  of  flystem  of  trial  and  error.  The  first  oonolonoDS 
by  in  physical  inquiries,  obflervation  conducts  us,  are  never 
lan  very  rough  approximations  to  the  truth.  These  being 
mI  to  subsequent  comparison  with  the  originals,  undergo  a 
ies  of  corrections,  the  more  prominent  and  conspicuous  de- 
irom  conformity  being  removed.  A  second  approximation, 
only  an  approximation,  is  thus  obtained ;  and  another  and 
re  severe  oomparison  with  the  phenomena  under  investigi^ 
made,  and  another  order  of  corrections  is  effected,  and  a 
jprozimation  obtained.  Nor  does  this  progressive  approach 
Bt  exactitude  appear  to  have  any  limit  The  best  results  of 
Ueeioal  labours  are  still  only  close  resemblances  to  truth, 
>faite  perfection  of  which  is  probably  reserved  for  a  higher 
aal  state. 

labours  of  the  physical  inquirer  resemble  those  of  the 
,  whose  first  eflforts  produce  ^m  the  block  of  marble  a 
id  uncouth  resemblance  of  the  human  form,  which  only 
bee  the  grace  and  beauty  of  nature  by  comparing  it  inces- 
nd  indefatigably  with  the  original ;  detaching  from  it  first 
Bser  and  rougher  protuberances,  and  subsequently  reducing 
I  by  the  nicer  and  more  delicate  touches  of  the  chisel  to  near 
ity  with  the  model. 

luld,  however,  be  a  great  mistake  to  depreciate  on  this  ao- 
le  results  of  our  first  efforts  in  the  acquisition  of  a  knowledge 
aws  of  nature.  If  the  first  conclusions  at  which  we  arrive 
meous,  they  are  not  therefore  the  less  necessary  to  the  ulti- 
itainment  of  more  exact  knowledge.  They  prove,  on  the 
r,  not  only  to  be  powerful  agents  in  the  discovery  of  those 
9ns  to  which  they  are  themselves  to  be  submitted,  but  to  be 
dispensable  to  our  progress  in  the  work  of  investigation  and 

3  observations  will  be  illustrated  by  the  process  of  instruction 
$overy  in  every  department  of  physical  science,  but  in  none 
ently  and  so  forcibly  as  in  that  which  now  occupies  us. 
.  Figure  of  the  earth  an  example  of  this,  — The  first  con- 
st which  we  have  arrived  respecting  the  form  of  the  eafth 
t  b  a  globe ;  and  with  respect  to  its  motion  is,  that  it  is  in 
rotation  round  one  of  its  diameters,  making  one  complete 
on  in  twenty-four  hours  sidereal  time,  or  23*»*  56™-  4-09*' 
1  or  civil  time. 

.  Globular  figure  incompatible  with  rotation,  — The  first 
I,  then,  which  presents  itself  is,  whether  this  form  and  rota- 
compatible  ?  It  is  not  di£5cu]t  to  show,  by  the  most  simple 
es  <^  physics,  that  they  are  not ;  that  with  such  a  form  such 
m  could  not  be  maintained,  and  that  with  such  a  rotation 
brm  could  not  permanently  continue.    And  if  this  can  be 


186 


ASTROHOMT. 


oertainly  established,  it  will  bo  neeeoBMy  to  ntneo  our  ttepiy  lo 
sabmit  oar  fonncr  conolosions  to  more  rigorous  oompariaon  with  the 
objects  and  phenomena  ^m  which  thev  were  derived,  and  aarffwiain 
which  of  them  is  inexact,  and  what  is  ue  modifioatioii  and  oomoliaa 
to  which  it  most  be  submitted  in  order  to  bo  bnmj^t  into  hanNOj 
with  the  other. 

2875.  Rotation  cannot  he  modified — t^^ppoeed  Jhrm  WMy.-— 
The  oondnmon  that  the  earth  revolTes  <m  its  ana  with  «  aaote 
oorresponding  to  the  apparent  rotation  of  the  finnamant^  ia  one  whisk 
admits  of  no  modifioatum,  and  must  from  its  natara  be  eilhar  ahsa- 
latelj  admitted  or  absolntely  rejected.  The  f^bolar  Ibrm  iinpnlad 
to  the  earthy  however,  has  be^  infened  ficom  dboervitiona  of  a 
genial  nature,  unattended  by  any  conditions  of  eiaot  inaaamwnMJj 
and  which  would  be  equally  compatible  with  innumeiaUe  ftnaii 
departing  to  a  very  considerable  and  measurable  ezlant  ftm 

that  of  an  ezact  geometrieal  aphM 
or  elobe. 

&76.  How  rotaium  wmtd  <^ 
the  tuperfieial  graviljf  en  a  gkim^^ 
Let  NQ8,>S^.  702,  rqpreaant  aas^ 
tion  of  a  globe  supposed  to  harea 
motion  of  rotation  round  the  diametv 
N  8  as  an  axis.  Every  point  on  its 
surface,  such  as  p  or  ^,  will  rsvohe 
in  a  circle,  the  centre  of  which  oorc/ 
will  be  upon  the  axis,  and  the  radiM 
OP  or  (/]^  will  gradually  deoreaaa  m 
approaching  the  poles  N  and  a,  when 
no  motion  takes  place,  and  inll  gra- 
dually increase  in  approaching  the  equator  Q  0  Q,  where  the  ciroia 
of  rotation  will  be  the  equator  itself. 

A  body  placed  at  any  part  of  the  surface,  such  as  P,  being  thns 
earned  round  in  a  circle,  will  be  affected  by  a  centrifu^  foroOi  the 
intensity  of  which  will  be  expressed  by  (314) 

c  =  1-226  X  E  X  N«  X  w, 

where  B=Po,  the  radius  of  the  circle,  N  the  fraction  of  a  revolntioa 
made  in  one  second,  and  w  the  weight  of  the  body,  and  the  diieo- 
tion  of  which  is  Pc. 

This  centrifugal  force  being  expressed  by  p  e  is  equivalent  (170) 
to  two  forces  expressed  in  intensity  and  direction  by  Pm  ana  pa. 
The  component  p  m  is  directly  opposed  to  the  weight  w  of  the  body, 
which  acts  in  the  line  P  o  directed  to  the  centre,  and  has  the  eflM 
of  diminishing  it.  The  component  P  n  being  directed  towards  die 
equator  q,  has  a  tendency  to  cause  the  body  to  move  towarda  die 
equator;  and  the  body,  if  free,  would  necessarily  so  move. 


Pig.  702. 


YORM  AND  DENSITY  OV  THB  BARTH.  187 

Now  it  will  be  eyident,  bj  the  mere  inspeotion  of  the  diagram, 
that  the  nearer  the  point  P  is  to  the  equator  Q,  the  more  directly 
will  the  ceDtrifiigal  foroe  p  c  be  opposed  to  the  weight,  and  coose- 
qnenil J  the  greater  will  be  that  component  of  it,  p  m,  which  will 
have  the  effect  of  dimini^ng  the  weight. 

Bat  this  diminution  of  the  weight  is  further  augmented  by  the 
increase  <^  the  actual  intensity  of  the  centrifugal  force  itself  in  ap- 
proaching the  equator.  By  the  above  formula,  it  appears  that  the 
mteoaitj  of  the  centrifugal  force  must  increase  in  proportion  as  the 
ladios  B  or  Po  increases.  Now  it  is  apparent  that  Po  increases 
giadaallj  in  going  from  P  to  Q,  since  p'  o'  is  greater,  and  Q  o  greater 
ilill  than  P  o ;  and  that,  on  the  other  hand,  it  decreases  in  going  from 
P  to  M  or  8,  where  it  becomes  nothing. 

Thus  the  effect  of  the  centrifugal  force  in  diminishing  weight 
being  nothing  at  the  pole  n  or  s,  gradually  increases  in  approaching 
the  equator ;  Jir$i,  because  its  absolute  intensity  gradually  increases ; 
and  tecondljfy  because  it  b  more  and  more  directly  opposed  to  gravity 
BntU  we  arrive  at  the  equator  itself,  where  its  intensity  is  greatest, 
and  where  it  is  directly  opposed  to  gravity. 

The  effscts,  therefore,  produced  by  the  rotation  of  a  globe,  such 
as  the  earth  has  been  assumed  to  be,  are  — 1^.  The  decrease  of  the 
veights  of  bodies  upon  its  surface,  in  going  from  the  pole  to  the 
equator;  and  2^.  A  tendency  of  all  such  bodies  as  are  free  to 
Move  from  higher  latitudes  in  either  hemisphere  towards  the  equator. 

2377.  Amount  of  the  diminution  of  weight  produced  at  the 
t^puUor  iy  centrifugal  force,  —  This  quantity  may  be  easily  com- 
puted bj  means  of  the  formula 

C  =  1-226  X  E  X  N*  X  W. 

Taking  the  radius  of  the  equator  in  round  numbers  (which  are  suf- 
feient  for  this  purpose)  at  4000  miles,  and  reducing  it  to  feet,  and 
reducing  the  time  of  rotation  23*"'  56*^'  4  09''  to  seconds,  we  shall 
have 

E  =  21,120,000,         N  =     ^ 


86,164  • 
nhstitating  these  numbers  we  have 

c  =  1,226  X  21,120,000  X       \g^^.X  wj  ^ 

and  executing  the  arithmetical  operations  here  indicated,  we  find 

Be  eentrifugal  force  would  therefore  be  the  287th  part  of  the 
w^ty  and  as  it  is  directly  opposed  to  gravity,  the  weight  would 
this  enture  loes. 

19* 


188  A8TR0K01CT. 

2878.  Lou  of  wight  at  other  ktiUmdei,  —  The  eonlrfftigd  flme 
at  any  latitude  p  would  be  less  than  at  Q  in  the  ratio  of  o  Q  to  or. 
But  the  part  of  this  p  m  which  is  direotlj  oppoeed  to  the  weight  ii 
lees  thui  the  whole  p  c,  in  the  ratio  of  p  e  to  p  m^  oTi  what  m  ihb 
game,  of  PC  or  OQ  to  po.  If  then  (f  fcprese  the  whole  eentai-. 
fugal  foroe  at  p,  and  cf'  that  part  of  it  which  is  Meetly  0|ipoied  to 
gamtjf  we  shall  have 

287      oq'  oq     287      \)<r 

PO 

The  number  which  expresses  —  is  that  which  la  called  in  TA 

gonometry  the  cosine  of  the  arc  PQ,  that  is^  the  cosine  of  the  kit 
tude.    Therefore  we  have 


k 


The  loss  of  weight,  therefore,  which  would  be  sustained  bj 
of  the  centrifu^  force  at  any  proposed  latitude,  would  bo  a  ftae- 
taon  of  the  whole  weight,  found  by  dividing  tiie  square  of  the  eonia 
of  latitude  by  287. 

2379.  Effect  of  centrifugal  force  on  the  geographical  conditum 
of  the  tturface  of  the  globe,  —  In  what  precedes,  we  have  only  con-  ^ 
sidered  the  effect  of  that  one,  p  m,  of  the  two  components  of  the 
centrifugal  force  which  is  opposed  to  the  weight     It  remains  to 
examine  the  effect  of  the  other,  p  n,  which  is  directed  towards  the  -h. 
equator.  -^ 

If  the  surface  of  the  globe  were  composed  altogether  of 
matter,  of  such  coherence  as  to  resist  separation  by  the  agenc 
this  force,  no  other  effect  would  take   place  except  a 
towards  the  equator,  which  would  be  neutralized  by  cohesion, 
if  the  surface  or  any  parts  of  it  were  fluid,  whether  liquid  or 
eons,  such  parts,  in  virtue  of  their  mobility,  would  yield  to 
impulse  of  the  clement  pn  of  the  centrifugal  force,  and 
flow  towards  the  equator.     The  waters  of  the  surface  would 
flow  from  the  higher  latitudes  in  either  hem]$*phere,  and 
lating  round  the  equator,  the  surface  of  the  globe  would  be 
into  two  great  polar  continents,  separated   by  a  vast  eqi 
ocean. 

2880.  Such  effects  not  existing^  the  earth  cannot  he  am  t 
globe,  —  But  such  is  not  the  actual  geographical  condition  of 
surface  of  the  globe.  On  the  contrary,  although  about  two-tl 
of  it  are  covered  with  water,  no  tendency  of  that  fluid  to  acoi 
late  more  about  the  equator  than  elsewhere  is  manifested.  1 
and  water,  if  not  indifferently  distributed  over  the  surfiuML  tie 
tainly  not  apportioned  so  as  to  indicate  any  tendency  suon  ■• 


lOSM  AND  DBHSIT7  OV  THS  SABIH. 


189 


akofe  Jewiihail  U,  tfaerefiirOy  the  rotation  of  the  oftrth  be  adnui- 
ted,  it  Hollows  that  its  figure  must  be  snob  as  to  oonntenot  the  ten- 
doMj  of  flnid  matter  to  flow  towards  any  one  part  of  the  sorfaoe 
nther  than  anj  other.  In  shorty  its  ^ore  must  bo  sndi  that 
flsfifty  itself  shall  oonntenwt  that  element  pn  of  the  eentrifugal 
nrae  whieh  tends  to  move  a  bodyfirom  the  higher  latitudes  of  either 
hemisphere  towards  the  equakMr. 

2881.  TheJIs^  tnmi  tker^bre  he  tome  wort  of  oNate  spheroid, 
— Now  this  oondition  would  be  fnlfilledi  if  the  earth,  instead  of 
bang  an  exact  q[diere,  were  an  oblate  spheroid,  having  a  certain 
dtfinite  ellipticityy — that  is,  a  figure  which  would  be  produced  by 
a  ellipee  rerolTing  round  its  shorter  axis.  Such  a  figure  would  re- 
semble an  orange  or  a  turnip.  It  would  be  more  convex  at  the 
•qoator  than  at  the  poles.  A  globe  composed  of  elastic  materials 
mild  be  reduced  to  such  a  figure  by  pressing  its  poles  tcmther,  so 
as  to  flatten  more  or  less  the  sur&ce  of  these  points,  and  pro£oe  a  pro- 
tuberance around  the  equator.  The  meri- 
dians of  such  a  globe  would  be  ellipses, 
having  its  axis  as  their  lesser  axis,  and 
the  diameters  of  the  equator  as  their 
greater  axes. 

The  form  of  the  meridian  would  be 
such  as  is  represented  in  Jig,  703,  n  s 
being  the  axis  of  rotation,  and  jb  q  the 
^-  ^^'-  equatorial  diameter. 

2882.  lu  eilipHci^  mu$i  depend  on  gravity  and  centrifugal 
forte,  —  The  protuberance  around  the  equator  may  be  more  or  less, 
aaaoirding  to  the  ellipticity  of  the  spheroid ;  but  since  the  distribu- 
9m  of  land  and  water  is  indifferent  on  the  surface,  having  no  preva- 
kss  about  the  equator  rather  than  about  the  poles,  or  ince  versdj 
%m  evident  that  the  degree  of  protuberance  must  be  that  which 

and  no  more  than  counteracts,  the  tendency  of  the 

ia  virtue  of  the  centrifucal  force,  to  flow  towards  the  equator. 

pcotnberance  may  be  considered  as  equivalent  in  its  effects  to 

ssdivity  of  regulated  inclination,  rising  firom  each  pole  towards 

To  arrive  at  the  equator,  we  fluid  must  ascend  this 

',  to  which  ascent  gravity  opposes  itself,  with  a  force  de- 

on  its  steepness,  which  increases  with  the  magnitude  of  the 

or,  wnat  is  the  same,  with  the  ellipticity  of  the  sphe- 

the  ellipticity  be  less  than  is  necessary  to  counteract  the 

of  the  centrifugal  force,  the  fluid  will  still  flow  to  the  equator, 

^  earth  would  consbt,  as  before,  of  a  great  equatorial  ocean 

ting  two  vast  polar  continents.     If  the  ellipticity  were  greater 

s  necessary  to  counteract  the  effect  of  the  centrifusal  force, 

mty  would  prevail  over  the  centrifugal  force,  and  Uie  waters 

down  the  acclivities  of  the  excessive   protuberance 


If 


I 


140  ABTROHOHT. 

towards  the  poloa,  and  tba  earth  would  oonaiat  cf  a  not 
ooDtiDent  wpanting  two  polar  ooeans.  f 

Siooe  the  geographical  oonditioD  of  the  anrfiMM  of  the  mA  k  Ml  '. 
ooDNitent  with  either  of  theae  oonset^aeDoet,  it  b  oridnit  tkttt  M  . 
figure  mnat  be  an  oblate  ipheroid,  haTiog  an  olliptNitf  exMlljrM*-' 
reapondiDg  to  the  Tariation  of  gravity  upoo  ita  nu&ee,  diw  to  At 
oombined  effect  of  the  attraetioD  exerted  faj  ita  eomtitaaot  folt 
npon  bodiea  placed  on  its  anrboe,  and  the  oentrifugal  fbraa  mhf 
finm  ita  diurnal  rotation. 

It  remaina,  therefore,  to  determine  what  this  partumlar  depMtf 
ellipticitj  is,  or,  what  ia  the  lame,  to  determine  oj  what  bwa6tt  rf 
its  whole  lengdi  the  eqnatorial  diameter  MQ  exeeedi  Um  ykt 
axis  N8.  ' 

2883.  ESliptieitji  may  he  axlenikOtd  and  meoanre^  and  Af  i* 
nib  compared. — The  degree  of  ellipticdt;  of  the  terrertnal  ^kinil 
may  be  fonud  bj  theory,  er  ascertained  by  observation  and  meaaan- 
ment,  or  by  both  these  methods,  in  which  oase  the  eccotdaaee  « 
discrepHQcy  of  the  results  will  either  prove  the  validi^  of  Ik 
reasoning  on  which  the  theoretical  calculation  is  foonded,  or  indiiata 
the  conditions  or  data  in  such  reasoning  which  nrnst  be  modified. 

Both  these  methods  have  accordingly  been  adopted,  aad  theit » 
Bnlls  are  found  to  be  in  complete  harmony. 

2384.  EUipticiig  cakidated.  —  The  several  qoantidea  which  in 
involved  in  this  problem  are  : — 

1.  The  time  of  rotation  =  H. 

2.  The  fraction  of  ita  whole  length  by  which  the  eqnatorial  a& 

oeeds  the  polar  diameter  =  e. 
8.  The  fraction  of  its  whole  weight  by  which  the  wdght  of  ■ 
body  at  the  pole  exceeds  the  waght  of  the  same  body  st 
the  equator  =^  lo. 

4.  The  mean  denuty  of  the  earth. 

5.  The  law  according  to  which  the  density  of  the  atrata  toim  ia 

proceeding  tima  the  enrfitce  to  the  centre. 

All  these  qoantitjes  have  sooh  a  mutnal  dependence,  that  lAsa 
some  of  them  are  given  or  known,  the  others  may  be  fonnd. 

In  whatever  way  tbe  solution  of  the  problem  may  be  approndiidf 
it  is  evident  that  the  form  of  the  spheroid  must  ha  tbe  same  aa  it 
would  be  if  the  entire  mass  of  the  earth  were  fluid.  If  thia  win 
not  BO,  the  parts  actually  fluid  would  not  be  found,  as  they  are  ■!• 
ways,  in  local  equilibrinm.  The  state  of  relative  density  of  tbe 
strata  proceeding  from  the  surface  to  tbe  centre  is,  however,  not  so 
evident.  Newton  investigated  tbe  question  by  ascertaining  the  farm 
which  the  earth  would  assume  if  it  consisted  of  fluid  matter  of  niiv 
form  density  from  the  surface  to  the  centre ;  and  the  result  of  his 
analysis  was  that,  in  that  case,  asanmiog  tbe  time  of  rotation  to  bl 
what  it  ia,  the  eqnatorial  diameter  must  exceed  the  poUr  bj  At 


FORM  AlfD  DBN8ITT  OF  THB  BARTH.  141 

230th  purt  of  its  whole  lengih,  and  gravity  at  the  pole  most  exceed 
gravity  at  the  equator  hy  the  same  fraction  of  its  entire  force. 

As  physical  science  progressed,  and  mathematical  analysis  was 
brought  to  m  greater  state  of  perfection,  the  same  problem  was  in- 
Tesdgated  by  Cuuraalt  and  several  other  mathematicians,  under  more 
ngofooB  conditions.  The  uniform  density  of  the  constituents  of 
the  emrth — a  highly  improbable  supposition — was  put  aside,  and  it 
was  assumed  that  the  successive  strata  from  the  centre  to  the  sur£EU)e 
inereaaed  in  density  according  to  some  undetermined  conditions.  It 
WM  aaBomed  that  the  mutual  attraction  of  all  the  constituent  parts 
ipoQ  any  one  part,  and  the  effect  of  the  centrifugal  force  arising 
from  the  rotation,  are  in  equilibrium ;  so  that  every  particle  com- 
poBOff  the  spheroid,  from  its  centre  to  its  surface,  is  in  repose,  and 
would  remain  so  were  it  free  to  move. 

By  a  complicated  and  very  abstruse,  but  perfectly  clear  and  certain 
mathematical  analysis,  it  has  been  proved  that  the  quantities  above 
mentioned  have  Uie  following  relation.  Let  r  express  a  certain 
anmber,  the  amount  of  which  will  vary  with  R.    We  shall  then  have 

Now  it  has  been  shown  that  when  R  =  23^  56°^  4*09%  the  number 
r  will  be  ^j,  so  that  in  effect 

e  +  «?= 

116 

This  result  was  shown  to  be  true,  whatever  may  be  the  law  ac- 
cording to  which  the  density  of  the  strata  varies. 

It  further  results  from  these  theoretical  researches  that  the  mean 
density  of  the  entire  terrestrial  spheroid  is  about  twice  the  mean 
density  of  its  superficial  crust. 

It  follows  from  this  that  the  density  of  its  central  parts  must 
greatly  exceed  twice  the  density  of  its  crust 

It  remains,  therefore,  to  see  how  far  these  results  of  theory  are  in 
locordance  with  those  of  actual  observation  and  measurement. 

2385.  HUvpticihf  of  terreitrial  spheroid  by  observation  and  meor 
nwemenL^u  a  terrestrial  meridian  were  an  exact  circle,  as  it  would 
Deeessarily  be  if  the  earth  were  an  exact  globe,  every  part  of  it 
would  have  the  same  curvature.  But  if  it  were  an  ellipse,  of  which 
the  polar  diameter  is  the  lesser  axis,  it  would  have  a  varying  curva- 
tue,  the  convexity  being  greatest  at  the  equator,  and  least  at  the 
poles.  If,  then,  it  can  be  ascertained  by  observation,  that  the 
csrvatme  of  a  meridian  is  not  uniform,  but  that  on  the  contrary  it 
increases  in  going  towards  the  Line,  and  diminbhes  in  going  towards 
the  poles,  we  sh^  obtain  a  proof  that  its  form  is  that  of  an  oblate 


To  compiehend  the  method  of  asoertaininff  this,  it  must  be  con- 
■dered  that  the  curvature  of  circles  diminishes  as  Uieir  diameters 


149  A8TB0N01IT. 

are  augmented.  It  is  erident  that  a  eirole  <^  one  fixA  in  dtameter 
has  a  less  degree  of  carvature,  and  is  less  convex  than  a  drole  one 
inch  in  diameter.  But  an  arc  of  a  circle  of  a  given  angolar  magni* 
tnde,  such  for  example  as  P,  has  a  length  proportional  to  the  diuM> 
ter.  Thus,  an  arc  of  1^  of  a  circle  a  foot  in  diameter,  is  twelve 
times  the  length  of  an  arc  of  1^  of  a  circle  an  inch  in  diameter. 
The  curvature,  thereforei  increases  as  the  length  of  an  an  of  1^ 
diminishes. 

If,  therefore,  a  degree  of  the  meridian  bo  observed,  and  measutd, 
by  the  process  already  explained  (2817),  at  difierent  latitodes,  and 
it  is  fbnnd  that  its  length  is  not  uniformly  the  same  as  it  wonld  be 
if  Uie  meridian  were  a  circle,  but  that  it  is  less  in  approadiing  tbe 
equator,  and  greater  in  approaching  the  pole,  it  will  follow  that  tki 
convexity  or  curvature  increases  towards  the  equator,  and  diminiahas 
towards  the  poles ;  and  that  consequently  the  meridian  has  the  Ibrai, 
not  of  a  circle,  but  of  an  ellipse,  the  lesser  axis  of  which  is  the  polar 
diameter. 

Such  observations  have  accordingly  been  made,  and  the  lengths 
of  a  degree  in  various  latitudes,  from  the  Line  to  66^  N.  and  to  36^ 
S.,  have  been  measured,  and  found  to  vary  from  863,000  £9et  on  the 
Line  to  867,000  feet  at  lat.  66"". 

From  a  comparison  of  such  measurements,  it  has  been  ascertained 
that  the  equatorial  diameter  of  the  spheroid  exceeds  the  polar  by 
,^0th  of  its  length.     Thus  (2384) 

_  1 

'-300* 

2386.  Variation  of  gravity  hy  observation.  —  The  manner  in 
which  the  variation  of  the  intensity  of  superficial  gravity  at  difierent 
latitudes  is  ascertained  by  means  of  the  pendulum,  has  been  already 
explained  (552).  From  a  comparison  of  these  observations  it  has 
been  inferred  that  the  effective  weight  of  a  body  at  the  pole  exceeds 
its  weight  at  the  equator  by  about  the  j^ijth  *  part  of  the  whole 
weight. 

2387.  Accordance  of  these  results  with  theory.  —  By  comparing 
these  results  with  those  obtuned  by  Newton,  on  the  supposition  u 
the  uniform  density  of  the  earth,  a  discrepancy  will  be  found  suffi 
cient  to  prove  the  falsehood  of  that  supposition.  The  value  of  e 
found  by  Newton  is  -Aj^y  its  actual  value  being  ^^|^,  and  that  of  w 
II Jk,  its  actual  value  oeing  y|iy. 

On  the  other  hand,  the  accordance  of  these  results  of  obeervitioa 
and  measurement  with  the  more  rigorous  conclusions  of  later  re- 
searches is  complete  and  striking. 

*  Different  yalues  are  assigned  to  this  —  Sir  John  Herschel  prefers  jj^t 
the  Astronomer  Royal  yl^ .  We  have  taken  a  mean  between  taeis 
istSmatea. 


FORM  AND  DBNSITT  OF  THE  EABTH.         143 

If  m  the  rektioii  between  e  and  tr,  explained  in  (2384), 

we  sobetitate  for  to  the  value  j^^,  obtained  by  observationi  we  find 

_J 1__J_ 

*    115     187  ""300* 

which  18  the  vilne  of  e  obtained  by  computation  founded  on  mea- 
mrement. 

2388.  Dimtnutum  of  weight  due  to  eUtpticity,  —  It  has  been 
ibeady  ahown  (2377)  that  the  loss  of  weight  at  the  equator  due  to 
tke  oentrifugal  force  is  the  287th  of  the  entire  weight.  From  what 
has  been  stated  (2386),  it  appears  that  the  actual  loss  of  weight  at 
the  eqiutor  is  mater  than  this,  being  the  187th  part  of  the  entire 
wei^L     The  difference  in  these  is 

JL 1__  J_ 

187       287  "  537* 

It  appears,  therefore,  that  while  the  287th  part  of  the  weight  is 
btlanced  by  the  centrifugal  force,  the  actual  attraction  exerted  by 
the  earth  upon  a  body  at  the  equator  is  less  than  at  the  pole  by  the 
537th*  part  of  the  whole  weight.  This  difference  is  due  to  the 
elliptical  form  of  the  meridian,  by  which  the  distance  of  the  body 
from  the  centre  of  the  earth  is  augmented. 

2389.  Actual  linear  dimensions  of  the  terrestriol  spheroid.  —  It 
is  not  enough  to  know  the  proportions  of  the  earth.  It  is  required 
to  determine  the  actual  dimensions  of  the  spheroid.  The  following 
ire  the  lengths  of  the  polar  and  equatorial  diameters,  according  to 
the  oompatations  of  the  most  eminent  and  recent  authorities : — 


Fotor  rtfam^fT.... 

Bowl. 

Airy. 

Mile*. 

7899-114 

7926-fl04 

26-471 

1 

Milra. 
7899-170 
7925-548 
26-478 

1 

JllMQlvt*  dUteWPOB 

Kx0HM  of  UM  equatorial  expretaed  in  a  ftaetion  of) 
ita  entire  lengtli.. j 

299-407 

299-330 

The  close  coincidence  of  these  results  supplies  a  striking  example  of 
the  precision  to  which  such  calculations  have  been  brought. 

The  departure  of  the  terrestrial  spheroid  from  the  form  of  an 
exact  globe  is  so  inconsiderable  that,  if  an  exact  model  of  it  turned 
in  ivory  were  placed  before  us,  we  could  not,  either  by  sight  or 
Umeh,  distinguish  it  from  a  perfect  billiard  ball.     A  figure  of  a  me- 

•  According  to  Herschel,  the  690th  part. 


liiisa  aoonntel;  Atxtm  on  pftper  mnld  onlj  be  d 
ft  circle  by  the  moat  pre^ae  meunranioiit.  If  tfio  mgor  ■ 
Buijt  ta  ellipse  were  eqnal  in  length  to  the  page  now  nodv  t 
of  the  reader,  the  lesser  uis  irooU  fall  short  a  tha  mmi*  lan| 
than  the  fortieth  of  an  inch. 

.  Dimention*  of  Aa  ipheroidal  equatorial  e 
*  »d  to  M  iDBoribed  witUn  the  tn 


'-"« 


CI>^ 


Fig.  T04. 


Ephere  n  ^  s  j  be  ima^ned  b 

rtad  having  the  pdar  axia  ■  ^  j 
704,  fi>r  ito  diameter,  »  iplMfl 
■hell  will  be  inoloded  betn^ 
Bor&oe  and  that  of  tbe  ^hij 
oompoaed  <tf  the  protobMWtt  mN| 
'  having  a  thidknesB  qq  of  18  ■flj 
at  the  ecfuator,  and  beooming  ■■I 
duall;  thinner  in  prooaediog  tol| 
poles,  where  its  thitfaieBS  ™>mM 
This  shell,  which  oonatitutai  m 
equatorial  ezceee  of  the  splunH^ 
and  which,  as  will  hereraw  i^ 
pear,  has  a  density  of  not  more  than  half  the  mean  denmty  fflt  m 
earth,  the  hulk  of  which,  moreover,  would  be  imperceptible  vpMi 
more  ioepcctioo  of  the  spheroid,  is  nevertheless  attended  with  wtt 
important  effects,  and  by  its  gravitation  is  the  origin  nf  moat  B&ilb| 
phenomeoa,  not  only  in  remon  to  the  moon,  out  also  to  the  h 
more  distant  mass  of  the  son. 

2391.  Density  and  mait  of  the  earth  by  cimrvatitm. — Ih 
magnitude  of  the  earth,  being  known  with  great  precision,  the  tt 
termination  of  its  mass  and  that  of  its  mean  density  beoome  ooe  wi 
the  same  problem,  since  the  comparison  of  its  mass  with  its  mpi 
tude  will  eivo  its  wean  density,  and  the  oomparieon  of  lis  MB 
density  witli  its  magnitude  will  give  ita  mass. 

The  methods  of  ascertainins  the  mass  or  actual  quantity  of  mrili 
contained  in  the  earth,  are  all  based  upon  a  comparison  of  tban 
vitating  force  or  attraction  which  the  earth  exerts  upon  aa  otgM 
with  the  attraction  which  some  other  body,  whose  mass  ia  azaW] 
known,  exerts  on  the  same  object.  It  is  assnmed,  as  a  postnlate  a 
axiom  in  physics,  that  two  masses  of  matter  which  at  eqnal  dittaan 
exert  equal  attractions  on  the  same  body,  must  be  eqnal,  Bnt  ■■  i 
is  not  always  possible  to  bring  the  attracting  and  attracted  bodits  I 
equal  distances,  their  attractions  at  unequal  distances  may  be  A 
served,  and  the  attractions  which  they  would  exert  at  equal  diatanei 
may  thence  be  inferred  by  the  general  law  of  gravitation,  by  whid 
the  attraction  exerted  by  the  same  body  increases  as  tbo  aqnan  d 
the  distance  from  it  is  diminished. 
TliuB,  if  sixtbo  mass  of  the  carAi,  II  vVq  »Uxw!i»ni  \h  «inr(a  i 


10EM  AVD  onaof  ov  no  iabxb.  145 


air  uy  odMT  lUitiani  o^^ 

a:a'::i/*:d^j 


ndtheiebn 


If  a  1m  tlie  attnwtion  which  uiy  man  m  of  known  qoMitity  ex- 
«li  at  Uw  distenoe  i/  upaa  the  same  body  npon  whioh  the  etrth 
cntti  the  altnelion  ▲',  we  ehall  have — 

B:M::A':a; 
nddMnfan 

_  A'  A       D^ 

a  a     1^ 

H  tiherafbie^  the  ttaes  w^  Ae  ntio  of  the  attnotionB  A  and  a,  and 
dw  lalio  of  the  disfeanoei  D  and  i/,  be  lespeetivelj  known,  the  mass 
B  of  the  earth  can  be  eompoted. 

2S83.  Dr.  Mukefym^B  mtbaitm  l^  ihe  attraction  of  SehehaUim. 
— This  eelebiated  pioUem  oouuted  in  detennining  the  ratio  of  the 
mean  denai^  of  a  mountain  oidled  Sohehallien;  in  Perihshirey  to  tliat 
of  the  earth|  bj  aaoertaining  the  amount  ii  the  deviation  of  a 

^ lb-line  from  the  direction  of  the  tnie  vertical  produced  by  the 
attraction  of  the  mountain. 
To  render  this  method  practicable^  it  is  Deoessary  that  the  moun- 
tain eeleded  be  a  aoUtaiy  one,  atandins  on  an  extenaiTe  plain,  since 
otherwiae  the  deviation  of  the  plumb-line  would  be  afiected  by 
Beif^boiiring  eminenoea  to  an  extent  which  it  might  not  bo  possible 
to  galimafe  with  the  neceaaaiy  precision.  No  eminence  sufficiently 
eonaideiaUe  eziata  near  enough  to  Sdiehallien  to  produce  such  dia- 


The  mountain  xanginff  east  and  weati  two  stations  were  selected 
on  ita  Dorthen  and  aonthem  aoolivitieSi  so  as  to  be  in  the  same  me- 
ridiaa,  or  very  nearly  so.  A  plumb-line,  attached  to  an  instrument 
called  a  aentth  aactor,  adapted  to  measure  with  extreme  accuracy 
naall  aenith  distancesi  waa  brought  to  each  of  these  stations,  and 
the  diatanee  of  the  aame  atari  aeon  upon  the  meridian  from  the  di* 
raeciona  of  the  ptumb-Une,  were  obaerved  at  boUi  plaoea. 

The  iKffcieiiee  between  thoae  diatamcea  gave  the  ansle  under  the 
two  diiaelbna  of  the  phimb-Une.  ^Hiia  wm  be  more  mearly  under- 
stood fegr  itfcience  to  Jig.  705|  where  p  and  j/  represent  the  pointa 
of  aaapenaioB  of  the  two  plumb-linea.  If  the  mountun  were  re- 
Boved,  they  would  hana  in  the  direction  po  and  p^o  of  the  earth's 
eentfe,  aad  their  diieetma  would  be  inclined  at  the  angle  pop'. 
Bat  the  alliaotioD  exerted  hj  the  inteljacent  mass  producea  on  each 
"1aaa%)htdetaeHoii  ItMida  the  monntaiui  ao  that  Oie  two  dixee- 

nr.  .  18 


IM 


AflXROSOMT. 


ttcNui  of  tfie  plnmb-liM^  iosiead  of  cuurwgliig  to  tka  oeain  of  At 

earth  c,  converge  to  a  point  e  nearer  to  tEe  snrfiMe,  and  form  vM 
each  other  an  angle  pcf  greater  than  POP^  bj  the  som  of  the  two 
defleotiona  opc  and  op^c 


.5"-' 


Fig.  705. 

Now  bj  means  of  the  zenith  eeotor  the  distances  s  z  and  s  S'  of 
the  points  z  and  if  from  any  star  snoh  as  s,  can  be  obserred  with  a 
precision  so  extreme  as  not  to  be  subject  to  a  greater  error  than  a 
small  fraction  of  a  second.    The  diffsrenoe  of  these  distances  will  be^ 

sz' — BZ  =  ZZ'^ 

tiie  apparent  distance  between  the  two  points  z  and  zi'  on  the 
heavens  to  which  the  plumb-line  points  at  the  two  stationa.  This 
distance  expressed  in  seconds  gives  the  magnitude  of  the  angle  Pel' 
formed  bj  the  directions  of  the  plumb-line  at  the  two  atataons, 
which  is  we  sum  of  the  deflection  produced  by  the  local  attraetioD 
of  the  mountain. 

If  the  mountain  were  not  present,  the  an^le  p  c  p^  could  be  aa> 

oertained  by  the  zenith  sector;  but  as  the  indications  of  that  instiii- 

ment  have  reference  to  the  direction  of  the  plumb-linei  it  is  ren* 

dered  inapplicable  in  oonsequenoe  of  the  disturbing  efl^  of  the 

jnoantMia. 


VOBM  AKD  BSHBITT  OW  THB  BABTH.        14T 

To  detannint  the  magDitiide  of  the  ngle  pop^,  therefore,  the 
direct  dktuMe  between  the  statioiiB  p  and  P^  is  uoertained  by 
nuking  m  survey  of  the  moantain,  whioh^  as  will  presently  appear, 
is  also  necessary,  in  order  to  determine  its  exact  volume.  For 
every  hundred  feet  in  the  distance  between  p  and  p^  there  will  be 
1"  in  the  angle  PCP^  (12319).  Binding,  therefore,  the  direct  dis- 
tance between  p  and  P'  in  feet,  and  dividing  it  by  100;  we  shall 
have  the  angle  p  c  p^  in  seconds. 

In  the  case  of  the  experiment  of  Dr.  Maskelyne,  which  was  made 
in  1774,  the  angle  pci/  was  found  to  be  41",  and  the  angle  Pc  p^ 
^^.    The  sum  of  the  two  deflections  was  therefore  12^'. 

The  survey  of  the  mountain  supplied  the  data  necessary  to  deter- 
mine its  actual  volume  in  cubic  miles,  or  fraction  of  a  cubic  mile. 
An  elaborate  examination  of  its  stratification,  by  means  of  sections, 
borings,  and  the  other  usual  methods,  supplied  the  data  necessary 
to  determine  the  weishts  of  its  component  parts,  and  thence  the 
weight  of  its  entire  vouime ;  and  the  comparison  of  this  weight  with 
its  volume  gave  its  mean  dennty. 

If  the  mean  density  of  the  eartli  were  equal  to  that  of  the  moun- 
tiin,  the  entire  weight  of  the  earth  would  be  greater  than  that  of 
the  mountain,  in  exactly  the  same  proportion  as  the  entire  volume 
of  the  earth  exceeds  that  of  the  mountain ;  and  these  volumes  being 
known,  the  weight  s  of  the  earth  on  that  supposition  was  computed, 
and  by  the  formula  given  in  (2391)|  or  others  based  upon  the  same 

principles,  the  ratio  -  of  the  attraction  of  the  earth  to  that  of  the 

mountain  was  computed,  and  thence  the  sum  of  the  deflections  which 
the  mountain  would  produce  was  found,  which  instead  of  12"  was 
about  24".  It  followed,  therefore,  that  the  denaty  of  the  earth  must 
be  double,  or,  more  exactly,  eighteen-tenths  of  that  of  the  moun- 
tain, in  order  to  reduce  the  deflections  to  half  their  computed  amount. 

Tlie  mean  density  of  the  mountain  having  been  ascertained  to  be 
about  2}  times  that  of  water,  it  followed,  therefore,  that  the  mean 
density  of  the  earth  is  about  five  times  that  of  water. 

2393.  Caveiuiuh'i  toluiion.  —  At  a  later  period  Cavendish  made 
the  experiment  which  bears  his  name,  in  which  the  attraction  exerted 
by  the  earth  upon  a  body  on  its  snr&ce  was  compared  with  the  at- 
tractioii  exerted  by  a  larse  metallic  ball  on  the  same  body;  and  this 
experiment  was  repeated  still  more  recently  by  Dr.  Reich,  and  by 
the  late  Mr.  Francis  BaiW,  as  the  active  member  of  a  committee  of 
the  Boyal  Astronomical  Societv  of  London.  All  these  several  ex- 
peiimenters  proceeded  by  methods  which  differed  only  in  some  of 
their  practicid  details,  and  in  the  conditions  and  precautions  adopted 
to  obtain  more  accurate  results. 

In  the  appumtUB  used  by  Mr.  Baily,  the  latest  of  them,  the  at- 
Inetiiig  bodies  with  whidi  the  globo  of  the  earth  was  oom^and 


14t 


iunnoHoicT. 


mre  two  bdls  of  btd,  «idi  a  IboI  in  dinMler.  Hm  hQ&m  wfoa 
wfaidb  tkeir  tttnetkm  «w  inanifeitod  wan  small  hJik,  abool  two 
iimImb  in  diameter.  The  former  wen  snppoited  on  the  enda  of  an 
oUmig  horiiOQtal  atage^  eapaUe  of  being  tnmed  round  n  Tovtioal 
azia  aopporting  the  stoge  at  a  point  midway  between  them.  Latjfy. 
TOdrepnaentaphmof  theafiparatiia.   The  large metalliebaUa  Band 


Fig.  7M. 

if  are  anpported  upon  a  rectangular  stage  represented  bj  the  dotlal 
lines,  and  so  moonted  as  to  be  capable  of  beioff  tamed  round  ill 
aentve  o  in  its  own  plane.  Two  small  balls  a,  a,  about  two  inehss 
in  diametsr,  are  atlnohed  to  the  ends  of  a  rod^  ao  thai  the  diatanap 


FORM  AND  DSN8ITY  OF  THE  BARTH.  149 

between  thttreentres  shall  be  nearly  equal  to  b  b'.  Thit  rod  is  snp- 
ported  at  c  by  two  fine  wires  at  a  very  small  distance  asunder,  so 
that  the  balls  will  be  in  repose  when  the  rod  a  a'  is  directed  in  the 
plane  of  the  wires,  and  can  only  be  turned  from  that  plane  by  the 
aetioo  of  a  small  aud  definite  foroe,  the  intensity  of  whicn  can  always 
be  aaoertained  by  the  an|[le  of  defleetkm  of  the  rod  a  a'.  The  exact 
direction  d  the  rod  a  o^  is  observed,  without  approaching  the  appa- 
ritos,  by  means  of  two  small  telescopes  t  and  t',  and  the  extent  of 
its  departora  from  its  positimi  of  equilibrium  may  be  measured  with 
great  precision  by  micrometers. 

In  the  performance  of  the  experiment  a  multitude  of  precautions 
were  taken  to  remove  or  obviate  various  causes  of  disturbance,  such 
as  currents  of  air,  which  miffht  arise  from  unequal  changes  of  tem- 
peratnre  which  need  not  be  described  here. 

The  large  balls  being  first  placed  at  a  distance  from  the  small 
ones,  the  Erection  of  the  rod  in  its  position  of  equilibrium  was  ob- 
served with  the  telescopes  ti^.  The  stage  supporting  the  large 
balls  was  then  turned  until  they  were  brought  near  the  small  ones, 
at  represented  at  b  b'.  It  was  then  observed  that  the  small  balls 
were  attracted  by  the  large  ones,  and  the  amount  of  the  deflection 
of  the  rod  a  a'  was  observed. 

The  frame  supporting  the  lai^  balls  was  then  turned  until  b  was 
brought  to  bf  and  b'  to  ^,  so  as  to  attract  the  small  balls  on  the 
other  side,  and  the  deflection  of  a  a'  was  again  observed.  In  each 
case  the  amount  of  the  deflection  being  exactly  ascertained,  the  in- 
tensity of  the  deflecting  force,  ^d  its  ratio  to  the  weight  of  the 
balls,  became  known. 

The  properties  of  the  pendulum  supplied  a  very  nmple  and  exact- 
means  of  comparing  the  attraction  of  the  balk  b  and  b'  with  the 
attraction  of  the  earth.  The  balb  a  a'  were  made  to  vibrate  through 
a  small  are  on  each  side  of  the  position  which  the  attraction  gave 
them,  and  the  rate  of  their  vibration  was  observed  and  compeared 
with  the  rate  of  vibration  of  a  common  pendulum.  The  relative  in- 
tensity of  the  two  attractions  was  computed  from  a  comparison  of 
these  rates  by  the  principles  established  in  (542).  The  precision  of 
which  this  process  of  observation  is  susceptible  may  be  inferred 
from  the  fiu:t  that  the  whole  attraction  of  the  balls  b  b'  upon  a  a' 
did  not  amount  to  the  20-millionth  part  of  the  weight  of  the  balls 
a  a',  and  that  the  possible  error  of  the  result  did  not  exceed  2  per 
cent  of  its  whole  amount 

The  attraction  which  the  balls  b  b'  would  exert  on  a  a',  on  the 
supposition  that  the  mean  density  of  the  earth  is  equal  to  that  of 
the  metallic  balls  B  b',  was  then  computed  on  the  principles  ex- 
plained in  (2381),  and  found  to  be  less  than  the  actual  attraction 
obsared,  and  it  was  inferred  that  the  density  of  the  earth  was  less 
thaft  thai  of  the  balls  b  b'  in  the  same  ratio. 

13* 


160  AffntovoMr. 

Is  fine,  it  mulled  thai  tbe  men  denrflf  of  tlie  Mrth  ii  647 
times  the  denrity  of  water. 

The  Mooidanee  of  this  reealt  with  thoee  of  the  SehehaDiMi  ez- 
perimenty  and  the  ealoalatioiis  npoii  the  igare  of  the  laiieeUiil 
w^hmmd,  eapply  a  itrikittg  proof  of  the  troth  of  the  thoeiy  ef 
mvitalMm  on  wUch  all  theee  three  ind^endeftt  iBYeatigBlioM  we 
oaeedy  and  of  the  validity  of  the  reaiODi&g  mpcm  wUeh  they  hoe 
been  oondiioted. 

S894.  Vdume  tmd  wtighi  pf  Ae  earlik  — Havhig  ■eiilwiml 
the  finear  dimensiona  and  the  mean  deneity  of  the  earth,  il  ia  n 
qoeelion  of  mere  arithmetiflal  Ubonr  to  oomnate  its  lokhiM  and  ili 
wdghi  TiJdng  the  dimenaiona  of  the  globe  as  abendy  alaled^  ili 
irdonie  eontaina 

259^800  milliona  of  oabie  miles. 
882,425y(K)0;000  Ullions  of  eaUo  fbei 

The  average  weUht  of  each  oobio  fbot  of  the  earQi  being  6-C7 
times  the  weight  ofia  oabic  foot  of  wateri  is  854*876  lbs.,  or  0'16S7 
of  a  ton.    It  followBy  thereforoi  that  the  total  weight  ef  the  earth  ii 

6,069,094,272  billions  of  tons. 


CHAP.  VL 

THE  0B8ERVAT0RT. 


2895.  Knowledge  of  the  vMtrumenU  of  observation  neeeuaiy.  — 
Haying  explained  the  dimensions,  rotation,  weight,  and  density  of 
the  earth,  and  described  generally  the  aspect  of  the  firmament  and 
fixed  lines  and  points  npon  it,  by  which  the  relatiye  position  and 
motions  of  celestial  objects  are  defined,  it  will  be  necessary,  befeie 
proceeding  to  a  further  exposition  of  the  astronomical  phenomena, 
to  explain  the  principal  instruments  with  which  an  observatory  b 
ftimished,  and  to  show  the  manner  in  which  they  are  applied,  ao  as 
to  obtain  those  accnrate  data  which  supply  the  basis  of  tnose  calcn- 
lations  from  which  has  resulted  our  knowledge  of  the  great  laws  of 
the  universe.  We  shall  therefore  here  explun  the  form  and  use  d 
soch  of  the  instruments  of  an  observatoir  as  are  indispensably  ne- 
cessary for  the  observations  by  which  such  data  are  supplied. 

2896.  The  catronomical  dock,  —  Since  the  immediate  objects  of 
all  astronomical  observation  are  motions  and  magnitudes,  and  since 
motions  are  measured  by  the  comparison  of  space  and  time,  one  of 
the  most  important  instruments  of  observation  is  the  time-pieoe  or 
chronometer,  which  is  constructed  in  various  forms,  according  to  tte 
oirenmstances  under  which  it  is  used  and  the  degree  of  accnraej 


THE  OB8BBTAT0BT. 


161 


n»wry  to  be  cMdiwd.    Ii  ■  statioiur;  obaemiory,  a  pandnlnm 
eloek  IB  the  form  wlopted. 

The  nie  of  the  Mdvnomioil  olock  is  so  reffnlated  thst,  if  any  of 
the  itan  be  olaemd  which  are  npoD  the  oelmtiKl  meridiui  at  the 
■omeot  at  which  the  handi  pout  to  0^  0^  0*',  they  will  igun  point 
to  0^  0**  0^  wh«  the  Mine  atan  an  nest  seeo  on  the  meridian. 
The  iotaml,  whii&  is  called  a  ndereal  daj,  is  divided  into  tweoty- 
Ijar  eqnal  |Hrta,  called  bisirxal  houhs.  The  honi^band  moves 
erer  one  pnadftl  dtriiioD  of  ita  dial  in  tbii  ioterral.  In  like  man- 
Mr  Ibo  UUnJTM  asd  aiooxD-HAMDH  move  on  divided  droleg,  each 
Boring  over  the  anooessive  divisionB  in  the  iDtervals  of  a  minate 
ad  a  aeeood  mpeetively. 

The  pendnlnm  » the  orieioal  and  only  real  measnre  of  tine  in 
this  iutrvment.  The  haoda,  the  dials  on  which  they  play,  and  the 
nechaniam  which  ragnlatea  and  proportion!  their  movements,  are 
only  expedieiita  tor  registering  the  nomber  of  vibrationfl  which  the 
pendolom  haa  made  in  the  interval  which  elapses  between  any  two 
phenomena.  Apart  from  this  conTenienoe,  a  mere  pendnlnm  an- 
connected  with  wheel-work  or  any  other  mechanism,  the  ribrations 
of  which  woold  be  counted  and  recorded  by  an  observer  stationed 
near  it,  wonid  eqoally  serve  as  a  measare  of  time. 

And  this,  in  &ct,  is  the  method  actually  used  in  all  exact  astro- 
nomical obeervatiODa.  The  f^e  of  the  observer  b  occupied  in 
watching  the  progress  of  the  object  moving  over  the  wires  (2302) 
in  the  field  lA  view  of  the  telescope.  His  ear  is  occupied  in  noting, 
and  his  mind  in  counting  tbe  successive  beats  of  tbe  pendulam, 
which  in  all  astronomical  docks  is  so  constructed  as  to  produce  a 
■officiently  lond  and  distinct  sound,  marking  the  close  of  each  soc- 
cessive  second.  The  piactised  observer  is  enabled  with  considerable 
pcclaioa  in  this  »ay  to  subdivide  a  second,  and  determine  tbe  mo- 
ment of  the  occnrrence  of  a  phenomenon  within  a  smalt  fraction  of 
that  iDtervaL  A  star,  for  example,  is  seen  to  tbe  left  of  tbe  wire 
m  m!  at  tifjig.  707,  at  one  beat  of  tbe  pendu- 
lum, and  to  the  right  of  it  at  J  with  the  next. 
The  observer  estimates  with  great  precision  (be 
proportion  in  which  the  wire  divides  the  dis- 
taace  between  tbe  points  i  and  ^,  and  can 
therefore  determine  the  fraction  of  a  second 
after  being  at  »,  at  which  it  wss  upon  tbe 
wire  mm'. 

Altbongb  the   art  of  constructing  cbrono- 
nc.  IIT.  meters  has  attained  a  surprising  degree  of  per- 

fection, it  is  not  perfect,  and  the  Eate  of  even 
the  beat  of  aach  instruments  is  not  absolutely  uniform.  It  istbere- 
foce  ntvtmrf  from  time  to  time  to  check  the  indirations  of  the 
clock  by  t^owring  its  rate.     If  the  clock  were  absolutely  perfect, 


AsnumoMT. 


nm  would  furbam  nM&ijSA  X  60  X  MbSMWh^ 

the  iDteiTal  between  two  BooeoHrn  ntniM  of  tM  wmam 


Now  ft  good  utroi 


Ml  doAw 


mke  M  man;  u  86,401  aor  to  few  u  8d,8M  vOintion  ia  Aa  ^ 
tamL  In  m  om  eue  ita  nte  woold  ba  too  bit,  lad  ia  lh«  «ttv 
too  iltnr  by  1  in  86.400.  Svan  with  tooli  u  amnaiMi  nto  Hm 
«nr  thrown  npoa  an  obaamtion  of  one  Wxa  woold  not  «aaaad  ttt 
ai(h  put  of  a  aoooad.  H;  howew,  tba  nta  ba  obMmd,  ana 
Ak  etnir  mar  be  alhnrad  fbr,  and  no  other  will  Hndn  am*  Aa 
xamota  poanbjlitjy  of  a  obaoge  of  nte  naoe  th«  nta  wia  hat  ■«» 
t^ned. 

2897.   TJu  muuU  i»ttmmaU.^ 
Bomieal  obenntiana  an  made  at  t 


upon  tho  oaleatial  meridian,  and  in  a  \  _, 

daas  of  anob  oDaemtioiia  the  lole  pnipoae  of  the  ofaaamr  ii  te 
determine  with  preoaion  the  time  when  the  olgeot  ia  fanojtht  to  flii 
xwridian  b;  the  aj^iannt  diornal  motion  of  the  Hamamat. 


Tbia  phenomenon  of  passing  the  meridian  is  called  the  iSARSn; 
and  an  inetmment  monnted  lo  snob  a  manner  aa  to  enable  an  ob' 


THB  OBSBBVATORT.  158 

Mner,  mxpg&dd  with  a  dook,  to  aaoertun  (he  ezaot  time  of  the 
TBANBiTy  is  cmlled  a  transit  instrument. 

Such  an  instrame&t  consists  of  a  telescope  so  mounted  that  the 
line  ci  cdlimation  will  be  succeasivelj  directed  to  every  point  of 
the  celestial  meridian  when  the  telescope  is  moyed  upon  its  axis 
Uuooph  180^ 

This  is  accomplished  by  attaching  the  telescope  to  an  axis  at  right 
angles  to  its  line  of  collimation^  and  placing  the  extremities  of  such 
axis  OQ  two  hcriiontal  supports,  which  are  exactly  at  the  same  level, 
and  in  a  line  directed  east  and  west  The  line  of  collimation  when 
horizontal  will  therefore  be  directed  north  and  south ;  and  if  the 
teksoope  be  tomed  on  its  axis  through  180^,  its  line  of  collimation 
will  move  in  the  plane  of  the  mendian,  and  will  be  successively 
directed  to  all  points  on  the  celestial  meridian  from  the  north  to  the 
pde,  thence  to  the  zenith,  and  thence  to  the  south. 

The  instroment  thus  mounted  is  represented  in  Jig,  708.  Two 
stone  piers  are  erected  on  a  solid  foundation  standing  east  and  west. 
In  the  top  of  each  of  them  is  inserted  a  metallic  support  in  the 
form  of  a  T  to  receive  the  cylindrical  extremities  of  the  transverse 
arms  A B  of  the  instrument  The  tube  of  the  telescope  CD  con- 
EJsts  of  two  eoual  parts  inserted  in  a  central  globe,  forming  part  of 
the  transversal  axis  a  b.  Thus  mounted,  the  telescope  can  oe  made 
to  revolve  like  a  wheel  upon  the  axis  A  b,  and  while  it  thus  revolves 
its  line  of  collimation  would  be  directed  successively  to  all  the 
points  ci  a  vertieal  circle,  the  plane  of  which  is  at  right  angles  to 
the  axis  A  B.  If  the  axis  be  exactly  directed  east  and  west,  this 
vertical  must  be  the  meridian. 

2398.  Its  adjustments. — ^Thb,  however,  supposes  three  conditions 
to  be  fulfilled  with  absolute  precision : 

1^.  The  axis  A  B  must  be  level. 

2^.  The  line  of  collimation  must  be  perpendicular  to  it 

3^.  It  must  be  directed  due  east  and  west. 

In  the  original  construction  and  mounting  of  the  instrument  these 
three  conditions  are  kept  in  view,  and  are  nearly,  but  cannot  be 
exactly,  fulfilled  in  the  first  instance.  Id  all  astronomical  instru- 
ments the  conditions  which  they  are  required  to  fulfil  are  only  ap- 
proximated to  in  the  making  and  mounting ;  but  a  class  of  expedi- 
ents caUed  adjustmbnts  are  in  all  cases  provided,  by  which  each 
of  the  requisite  conditions,  only  nectrii/  attained  at  first,  are  fulfilled 
with  infinitely  greater  precision. 

In  all  such  adjustments  two  provisions  are  necessary :  Jirstf  a 
method  of  detecting  and  measuring  the  deviation  from  the  exact 
fulfilment  of  the  requisite  condition ;  and  seco^ly,  an  expedient  by 
which  such  deviation  can  be  corrected. 

2399.  To  make  the  axis  level.— li  the  axis  AB  be  not  trulv 


154 

level,  its  Jevi; 

r-^tj'ii!.;:  m„,„ 

This  ..„,„i, 

Ji'liiiil,.  ii,,|,.,.ii.- 

all  Vi,L-iJitJ-,  (1; 

ti  i-iit-Iaiiou. 


and  wlien  it  is  i- 
/>"/-/-/..■  .fiprmli 
sition,  and  then 
tnjTRnnl  on  or  a 
of  its  luDgtlj.  ' 
moiinted  m  to  Ik 
anil  is  so  adjastc. 
iiue  joining  the 
bubble  will  rest . 
a  anj  J. 

To  ascertain  v 
poinia,  Lo  level, 
F"dod  from  ibr 
and  /.,  tliejr  arc  1 
atcs  IB  ibc  more  . 
The  optTalion  m- 
twein  the  ccDtn' 
A  level  is  pro 
suf=pi;nsion  com- 

cylinders.  If  it 
thus  ui>on  the  , 
the  otJier,  it  wi" 
luore  remote,  or 
Tn  accompli, 
A  of  the  axis  re 
cpacc  vertiitalh 
tbc-ref..r,.  Riiseci 
Jfvel  rc-si.s  bed 
ukJ  be  susj^ii 


TH>  0B9XBTAT0KT.  167 

ibie  disk,  U  abmmi,  tbe  time  of  the  tniuft  ia  the  in- 
wbioli  the  centra  of  tbe  diik  ia  upon  the  middle  win.  This 
wd  bj  obeervin^  the  instuitB  whwh  the  westeni  and  iiiitmu 
flf  the  disk  loDch  CKdi  of  the  wim.    Th«  noddle  of  theae 
re  the  momeMli  et  wbieh  the  emtn  of  the  &k  m  npoa 
nsftec^Teiy.     Tiking  >  mean  of  the  eontnt  of  tko 
edges,  the  conlMt  of  the  weatem  edge  with  the  mUdU 
^    'wiU  lie  obtsiued ;  lad,  in  Hka  manner,  m  mma  at  the  oontMti 
>>«  eftHttini  edge  wiU  dn  the  eootaet  of  that  edge  iritfa  tiit 
We  wu«,  and  x  meafl  of  theee  two  will  ^Te  the  momeot  of  the 
-at  of  tbo  MQtre  of  the  £ek,  or  a  neu  of    "  "  -      - 

•  dff^  will  ^ye  the  Bme  nnlt. 


At  ni^t  ibny  are  rendered  nriUe 
^  Winp.  by  trhicb  the  Ud  of  view  ia  &iiiuy  illmimated. 
-40S.  Apparent  moHom  of  tHjeOt  U^fidd  of  vie». — 8ii>ee  Oe 
pe  rcTcrees  the  diijeeto  obeemd,  the  motiOB  in  the  field  will 
to  be  &om  west  to  flHt,  while  that  of  the  firmament  ia  tram 
to  wwt  An  objeet  «iQ  Aerafim  ento-  the  field  of  new  oo 
«ut  ride,  and,  having  enaaed  it,  wiQ  learn  it  on  the  eaat  ride. 
"^Dee  the  sphere  re*anw  at  tfaa  rats  of  16'  per  hour,  15  per 
^^l^^ote,  or  15"  per  seoond  of  ttma,  an  ohjeet  will  be  seen  to  pam 
^^^^  tiu  field  of  Tiew  nth  >  motien  ahaohitelT  nnifbrm,  the  space 
^^^^d  oror  between  tm  aoeoeaaiTe  beata  at  Uie  pendnltun  boiu; 
■SMhljr  15  -. 

^  *■  Tibs,  if  the  tnoon  or  mm  he  in  or  near  the  eqoator,  the  disk  will 

"^leerTed  to  poM  acroaa  the  field  with  a  viable  motion,  the  inters 

lel<r«eD  the  momenta  of  oootact  of  the  weatern  and  eaatsn 

-'«M  vilb  the  middle  trire  being  2^  8*-,  when  the  apparent  diame- 

ii  32*.     Thus,  the  'liak  appears  to  move  over  a  apaee  eqoal  to 

''VjiUown<iiamotcriiil--4^. 

^i(H.    l'ir,/fi  .if  .i./iinatian,  or  hour  eireta. — Cirelea  of  the 

1^  V  aj^  BphL-re  w  h  ic  !i  pais  Aroagfa  the  polee  are  at  right  an^ea  to 

r*^tel««tial  eqnal'T,  aud  are  on  tlw  heavew  exaotlj  w^  mendiana 

^^^  ^on  the  terrestrial  ^obe.     They  divide  the  cdealial  equator 

.^^lo  arcs  which  nteusure  the  anglea  whieh  and)  oidea  fiwm  with 

h  other.    Thus,  tiro  nioh  didea  whieh  are  at  right  angieeinclnde 

an  of  90'*  of  the  celestial  ecnutor,  and  two  wtuch  fimn  with 

b  other  an  angle  of  1"  indnde  between  them  an  are  of  1°  (^ 

1  eqiutor.    These  oiBOLBa  or  DKCuirATioif,  or  nova. 

they  are  called,  are  carried  ronnd  bj  the  dinrnal  motioD 

J  the  heavens,  and  are  hnNwht  in  enoeeaaion  to  eoinride  with  dw 

leatial  meridian,  the  intervau  between  the  momenta  of  their  ooin- 

ith  the  meridian  bring  alwaja  proporticDal  to  the  anrie 

bnn  with  each  other,  or,  what  is  the  mme,  to  the  an  of  ^ 

equator  iacladad  between  them.     Thns,  i£  tWO  «Mm  « 

14 


^ ^  ...  .  the  instmment  in  AhH 

•not  nMiidiui  of  the  obsemtorr.  Jt,  «n  dirMtiag  the  telescope  ||iB 
it,  it  b  imh  on  the  obb  ud»  or  Um  otb«r  of  the  middle  wire  (Alel 
oaght  to  oMDoida  with  tho  meridiio),  the  tfrwtioii  of  the  szu  ji  l, 
Jig.  710,  will  daviate  to  the  MDt  estonC  Ann  tbe  true  eut  im 
vert,  (BDoe  it  bM  been  alnadj,  hjr  the  pnrvimis  a<)juEtmentg,  n» 
dmd  perpendioakr  to  the  line  of  eolUnetuo.  Tke  entiro  iastnuwtf 
awt  IhenAM*  be  shifted  Kond,  until  tte  nnridiaa  mark  coiaridV 
with  the  middle  wire.  Thii  ie  Moomptiahad  bj  a  proTisirm  luiik 
in  the  rapprat  on  whieh  the  eztrenotjr  at  the  nis  b,  J!g,  70S,  nM^ 
by  which  it  hu  a  oertain  play  in  the  horiiODte]  direction  urged  W 
a  fine  kkw.  In  this  way  the  axii  ab  ii  bnni|;ht  into  the  troeAi 
nation  east  and  wee^  and  thenfbra  the  line  of  coUimaUon  into  ibt 


It  will  be  obeerred  that,  in  explaining  tin  Kcond  adjastment,^ 
has  been  aesnmed  that  the  deriationi  are  not  to  great  as  i^  Ibror 
the  objeot  B  out  of  the  field  of  view  after  tlie  instTument  is  rev«iwd. 
This  condiiiiMi  in  ptaetiee  is  always  folfiUed,  the  extent  of  demlM 
left  to  be  oorreoted  by  the  adjnatments  being  always  very  small. 

2402.  Micrometer  toiret — -meAod  of  obtervAtij  transit.  — In  tb 
foons  of  the  eye-piece  of  the  transit  instrnment.)  the  system  of  si- 
OTometer  wires  (2802),  already  mentioned,  is  placed.  Ihia  oonnh 
commonly  of  5  or  7  equidistant  wins,  [daoed  Tertically  at  equal  &■ 
tanoes,  and  interseoted  at  their  middle  points  by  a  horizontal  wii% 
as  represented  in  Jiff.  707.  When  the  instrament  haa  been  adjoHedi 
the  middle  wire  m  m'  will  be  in  the  plane  of  the  meridian,  and  wban 
an  objeot  is  seen  upon  it,  such  object  will  be  ob  the  celestial  n 
dian,  and  the  wire  itself  may  be  regarded  as  a  small  arc  of 
meridian  rendered  risible. 

The  fixed  stars,  is  will  be  explained  more  ^ly  hDreafter,  sppot 
in  the  telescope,  no  matter  how  high  ita  magnifyiag  power  be,  ■ 
mete  Inoid  points,  having  no  seoaible  magnitniie.  Hy  tbc  diore^ 
motion  of  the  firmament,  the  star  passes  enocessivelj  over  all  Oa 
wires,  a  short  interval  being  interposed  between  its  passages.  Tb* 
obsetrer,  just  before  the  star  approaching  the  meridian  enters  tb 
field  of  view,  notes  and  writes  down  the  houn  and  ntinuits  indicated 
by  the  clock,  and  he  proceeds  to  count  the  lecox'/a  by  hi.s  ear.  lie 
observes,  in  the  manner  already  explained,  to  a  fructioo  of  a  a^eoni, 
the  instant  at  which  the  star  creeses  each  of  the  wires ;  and  taking 
a  mean  of  all  these  times,  he  obtains,  with  a  great  degree  of  prrci- 
■ion,  the  instant  at  which  the  star  passed  the  middle  wire,  which  ii 
the  time  of  the  tranut 

By  thb  expedient  the  result  baa  the  advantage  of  as  manj  iod^ 
pendent  observations  as  there  are  parallel  wires.  The  emn  tf 
vhMrntiim  being  distributed,  are  proportionally  diminialied. 

What  the  >an,  moon,  or  a  planet,  or,\n  pn«n\,ia^  'SiifttL^MA 


raS  0B8IRVAT0R7.  167 

ku  m  aettiUe  disk,  ii  oherved,  the  tiiiie  of  the  transit  is  the  in- 
ilnt  mi  which  the  oentre  of  the  disk  is  upon  the  middle  mre.  This 
ii  obtained  hj  oheemns  the  instants  which  the  western  and  eastern 
•dgoi  of  Ihfl  disk  touch  each  of  the  wires.  The  middle  of  these 
■rtvvahi  are  the  momenta  at  which  the  centre  of  the  disk  is  upon 
dM  wina  napeotitely.  Taking  a  mean  of  the  contact  of  the 
iMtein  cdgesL  the  contact  of  the  western  edge  with  the  middle 
wn  will  be  obtained ;  and^  in  like  manner,  a  mean  of  the  contacts 
k  tba  eastern  edge  will  give  the  contact  of  that  edge  with  the 
■iddle  wize^  and  a  mean  of  these  two  will  give  the  moment  of  the 
tnnat  of  the  centre  of  the  disk,  or  a  mean  of  all  the  contacts  of 
both  edges  will  ^e  the  same  lesnlt 

Bj  day  the  wires  are  visiblei  as  fine  black  Hnes  intersecting  and 
spaemg  oat  the  field  of  view.  At  night  they  are  rendered  visible 
1^  a  lamp,  by  which  the  field  of  view  is  fiunUy  illnminat^. 

2408.  Afparmi  mdurn  of  nbfedi  infield  of  view.  —  Since  the 
tehaeope  reveraea  the  objects  observed,  the  motion  in  the  field  will 
appear  to  be  from  west  to  east,  while  that  of  the  firmament  is  fh>m 
east  to  weat  An  object  will  therefore  enter  the  field  of  view  on 
the  weat  aide,  and,  having  crossed  it,  will  leave  it  on  the  east  side. 

Since  the  sphere  revolves  at  the  rate  of  15^  per  hour,  15  per 
minute,  or  15^  per  second  of  time,  an  object  will  be  seen  to  pass 
aeroaa  the  field  of  view  with  a  motion  absolutely  uniform,  the  space 
paaaed  over  between  two  successive  beats  of  the  pendulum  being 
mvariably  15". 

Thna,  if  the  moon  or  sun  be  in  or  near  the  equator,  the  disk  will 
be  observed  to  pass  across  the  field  with  a  visible  motion,  the  inter- 
vd  between  the  moments  of  contact  of  the  western  and  eastern 
edges  with  the  middle  wire  being  2"^  8%  when  the  apparent  diame- 
ter is  Z2f.  Thus,  the  disk  appears  to  move  over  a  space  equal  to 
half  its  own  diameter  in  1^  4"-. 

2404.  CirclcM  of  declinationy  or  hour  circles.  —  Circles  of  the 
eelestial  sphere  which  pass  through  the  poles  are  at  right  angles  to 
the  celestial  equator,  and  are  on  the  heavens  exactly  what  meridians 
ire  npon  the  terrestrial  globe.  They  divide  the  celestial  equator 
into  area  which  measure  the  angles  which  such  circles  fonn  with 
each  other.  Thus,  two  such  circles  which  are  at  right  angles  include 
an  are  of  90^  of  the  celestial  equator,  and  two  which  form  with 
each  other  an  angle  of  1^  include  between  them  an  arc  of  1^  of 
tbe  eekstial  equator.  These  cirolcs  of  declination,  or  hour 
cilCLis  as  they  are  called,  are  carried  round  by  the  diurnal  motion 
ci  the  heavens,  and  are  brought  in  succession  to  coincide  with  the 
eelestial  meridian,  Uie  intervals  between  the  moments  of  their  coin- 
cidenee  with  the  meridian  being  always  proportional  to  the  ande 
tbey  form  with  each  other,  or,  what  is  the  same,  to  Uie  arc  of  the 
celestial  equator  included  between  them.    Thus^  if  two  drcles  of 

III.  14 


U8  ASTBOKOMT. 

deolumtioQ  fomi  with  each  other  in  angle  of  80^,  the  Intenral  be- 
tween the  moments  of  their  coincidence  with  the  meridiui  will  be 
two  mdereal  hoars. 

The  relative  position  of  the  droles  of  declination  wiUi  respeot  to 
each  other  and  to  the  meridian,  and  die  gnooesaive  posltienB  aarained 
by  any  one  such  circle  daring  a  complete  revelation  of  the  -toherei 
will  be  perceived  and  nnderstood  without  difficulty  by  the  ud  of  a 
celestial  globe,  without  which  it  is  ecaicely  possible  to  oblain  ny 
clear,  or  definite  notion  of  the  apparent  motions  of  celestial  objeelk 

2405.  Right  ascension. — The  arc  of  the  celestial  equator  be* 
tween  any  circle  of  declination  and  a  certain  point  on  the  equator 
called  the  first  point  of  Aries  (which  will  he  defined  harodla)^ 
is  esMed  the  right  asoension  of  all  objects  through  wbieh  die 
circle  of  declination  passes.  This  arc  is  always  understood  to  be 
measured  from  the  point  where  the  circle  of  deelination  meets  tlie 
celestial  equator  westward,  that  is,  in  the  direction  of  ihe  af^Mureiit 
diurnal  motion  of  the  heavens,  and  it  may  extend,  therefbre,  OfV 
any  part  whatever  of  the  equator  from  0^  to  860^. 

K^ht  ascension  is  expressed  sometimes  according  to  mngukr 
magnitude,  in  degrees,  minutes,  and  seconds;  but  since,  aoomiag 
to  what  has  been  explained,  these  magnitudes  are  proportional  to 
the  time  they  take  to  pass  over  the  meridian,  ri^t  ascension  is  also 
often  expressed  immediately  by  this  time.  Thus,  if  the  right 
ascension  of  an  object  is  15^  15'  15",  it  will  be  expressed  also  by 

In  general,  right  ascension  expressed  in  degrees,  minutes,  and 
seconds  may  be  reduced  to  time  by  dividing  it  by  15 ;  and  if  it  be 
expressed  in  time,  it  may  be  reduced  to  angular  language  by  multi- 
plying it  by  15. 

The  difference  of  right  ascensions  of  any  two  objects  may  be  as- 
certained by  the  transit  instrument  and  clock,  by  observing  the  in- 
terval which  elapses  between  their  transits  over  the  meridian.  This 
interval,  whether  expressed  in  time  or  reduced  to  degrees,  is  their 
difference  of  right  ascension. 

Hence,  if  the  ri^ht  ascension  of  any  one  object  be  known,  the 
right  ascension  of  all  others  can  be  found. 

2406.  Sidereal  clock  indicates  right  ascension,  —  If  the  hands 
of  the  sidereal  clock  be  set  to  0*^  0"*  0**  when  the  first  point  of 
Aries  b  on  the  meridian,  they  will  at  all  times  (supposing  the  rate 
of  the  clock  to  be  correct)  indicate  the  right  ascension  of  such 
objects  as  are  on  the  meridian.  For  the  motion  of  the  hands  in 
that  case  corresponds  exactly  with  the  apparent  motion  of  the  me- 
ridian on  the  celestial  equator  produced  by  the  diurnal  motion  of 
the  heavens.  While  15^  of  the  equator  pass  the  meridian  the 
hands  move  through  1^-,  and  other  motions  are  made  in  the  same 
proportion 


THl  OBAnTAHST. 


U» 


■nrol  cireU.  — Hie  faurit  instrament  uid  aideml 
neana  of  detennining  with  extreme  precisicm  the  id- 
I  an  object  puses  the  meridian ;  bot  the  instrnmeot 
L  with  an;  tooonte  meaiu  of  indicating  the  point  Kt 
nt  is  leeQ  on  the  meridian.  A  drole  is  sometimea,  it 
id  to  the  tavinl^  by  which  the  position  of  this  point 
1;  obflerred ;  bnt  to  ascertain  it  with  a  precision  pro- 
hat  which  the  transit  instmment  detenoiDee  the  neht 
[oirM  an  iDSfanimeat  ooostmoted  and  monnted  for  tnis 
;  in  a  manner,  and  noder  oonditioDS,  altoasther  differ- 
I  Ij  which  the  tnnut  uutntmflnt  is  r^DUted.  The 
atent  adopted  ia  the  most  effinentl;  fiuDiahed  obeer- 
is  pmrpoee  is  the  itnui.  oibolx. 
nest  IS  a  gndasted  cirole,  rimilar  in  form  and  prin- 
itniment  aescribed  in  (2304).  It  is  centred  upon  an 
id  in  the  &oe  irf  a  stone  pier  or  wail  (henoe  the  name), 
)  plane  of  the  meridian.  The  axis,  like  th^t  of  a 
nmt,  is  truly  bcriiontal,  and  directed  dne  east  and 
by  the  conditions  on  which  it  is  fiiat  consbnoted  and 
I  ttearly  in  this  position,  it  is  reodered  exactly  so  by 
Dte,  one  of  which  moves  the  axis  vertically,  snd  the 
tally,  by  means  of  sorewB,  through  spaces  which, 
are  still  large  enoogh  to  en^le  the  obeerrer  to  oonect 
the  alight  errors  of  position  inct 
dental  to  the  workmanship  and 
mounting. 

The  instrument,  as  mounted  and 
ac^iisted,  is  represented  in  pac> 
speotive  inj^.  711,  where  A  is  tho 
stone  wall  to  which  the  instalment 
is  attsobed,  d  the  central  axis  on 
which  it  tarns  J  and  ro  the  tele- 
'  scope,  which  does  not  move  upon 
the  cirole,  bnt  is  immoveably  at- 
tached to  it,  so  that  the  entire 
instniment,  indoding  the  telescope, 
turns  in  the  plane  u  the  moidian 
npon  the  axis  D. 

A  front  view  of  the  oirole  in  the 
plane  of  the  instmment  is  ^tch  in 
M  712. 

ition  is  nsnally  made  on  the  edge,  and  not  on  the  tmaa 
oop  of  metal  thus  engraved  forms,  therefore,  what  may 
tire  of  the  wheel. 

ctmtaining  mercory,  are  placed  on  the  floor  in  cottre- 
la  in  the  plane  of  the  instrument,  in  the  sar&ee  of 


ic.ni. 


IM 


JT 


X* 


«i»'>*^  - 


Fig.ni. 

wliioii  are  wem^  by  lefleotion,  the  objects  u  the^  jmuh  over  die  me* 
ridiaii.  The  obsOTver  is  thus  enabled  to  asoertain  the  directioiiS|  as 
wdl  <^  the  images  of  the  objeots  lefleoted  in  the  meroarj,  as  of  ths 
dl^eots  themselTss,  the  advantage  of  which  will  presentlv  i^pear. 

Oonvenient  ladders,  chairs,  and  oonchesi  capable  of  being  ad- 
justed by  racks  and  oUier  mechanical  arrangements,  ai  any  desired 
indinations,  enable  the  observer,  with  the  ntmoet  ease  and  oomfix^ 
to  applv  his  eye  to  the  telescope,  no  matter  what  be  its  direction. 

In  the  more  important  national  observatories  the  moral  oiieks 
are  eight  feet  in  diameter,  and  conseqnenUy  801*5  inches  in  drmm- 
ference.  Each  degree  upon  the  circamference  measuring,  therefim, 
above  eight-tenths  of  an  inch,  admits  of  extremely  minute  sob- 
division. 

The  divisions  on  the  graduated  edge  of  the  instmment  are  nnm- 
bered  as  usoal  firom  0®  to  860^  roond  tiie  entire  drole.  The  posi- 
tion which  the  direction  of  the  line  of  collimation  of  the  telescope 
has  with  relation  to  the  0^  of  the  limb  is  indiffsrent  Nothing  is 
necessary  except  that  this  line,  in  moving  round  the  ans  D  of  the 
instrument,  shall  remain  constantly  in  the  plane  of  the  meridiaa. 
This  condition  being  fulfilled,  it  is  evident  that,  as  the  circle  revdlvesy 
the  line  of  coUimation  will  be  successively  directed  to  every  point 
of  the  meridian  when  presented  upwards,  and  to  every  point  of  its 
reflected  image  in  the  mercury  when  presented  downwaros. 

2408.  J^u)d  of  observing  withiL — The  position  of  the  instru- 
ment when  directed  successively  to  two  oljects  on  the  meridian,  or 


THB  0B8SBVAT0RT.  161 

to  UuSr  imagefl  lefleoted  in  the  mereary,  being  obseryed,  tbe  angular 
diBtancey  or  tbe  arc  of  the  meridian  between  them,  will  be  foand  by 
•scertaining  the  arc  of  the  graduated  limb  of  the  instrument,  which 
paasee  before  any  fixed  point  or  index,  when  the  telescope  is  turned 
from  the  direction  of  the  one  object  to  the  direction  of  the  other. 

2409.  Compound  micro9Cope$^^  their  number  and  tue. — This 
tro  18  obserred  by  a  compound  microecope  (2307)|  attached  to  the 
wall  or  pier,  and  directed  towaxda  the  i^aduated  Hmb.  The  man- 
ner in  which  the  fraction  of  a  division  of  the  limb  is  observed  by 
this  expedient  has  been  already  explained.  But  to  give  greater 
prednon  to  the  observation,  as  well  as  to  efikce  the  errors  which 
night  ariae,  either  from  defective  centreing,  or  from  the  small  de- 
ruigement  of  figure  that  might  arise  from  the  flexure  produced  by 
the  weight  of  the  instrument,  several  compound  microscopes  — 
generally  nx — are  provided  at  nearly  equal  distances  around  the 
umb,  so  that  the  observer  is  enabled  to  note  the  position  of  six  in- 
dices. The  six  arcs  of  the  limb  which  pass  under  them  being  ob- 
served, are  equivalent  to  six  independent  observations,  the  mean  of 
which  beins  taken,  the  errors  incidental  to  them  are  reduced  in  pro- 
portion to  weir  number. 

2410.  Circle  primarily  a  differential  imtrument,  —  The  obser- 
vatioDSy  however,  thus  taken  are,  strictly  speaking,  only  differential. 
The  arc  of  the  meridian  between  the  two  objects  is  determined,  and 
this  arc  is  the  difference  of  their  meridional  distances  from  the 
senith  or  from  the  horiaon ;  but  unless  the  positions  which  tbe  six 
indexea  have,  when  the  line  of  collimation  is  directed  to  the  zenith 
or  horiaon,  be  known,  no  positive  result  arises  from  the  observa- 
tiooa;  mx  can  the  absolute  distance  of  any  object,  either  from  the 
horiioD  or  the  zenith,  be  ascertained. 

2411.  Method  of  oMcertaining  the  horizontal  point. — ^The  ''read- 
ing," aa  it  is  technically  called,  at  each  of  the  microscopes,  in  any 
propoaed  position  of  ihe  instrument,  is  the  distance  of  that  micro- 
ioope  bom  the  lero  point  of  the  limb.  Now  it  is  easy  to  show  that 
half  the  som  of  the  two  readings  at  any  microscope,  when  the  tele- 

.  scope  is  successively  directed  to  an  ob- 

^^^^  "*"-s^  ject  and  its  image  in  the  mercury,  will 

j^  ^?         be  the  reading  at  the  same  microscope 

when  the  line  of  collimation  is  horizontal. 

Let  a  circle  be  imagined  to  be  drawn 

upon  the  stone  pier  around  the  instru- 

the 

Let 

when 

the 

position  of  the  zero  of  the  limb.     Let 

Vlf.  711.  c  I  be  the  position  of  the  telescope  wher 

14* 


4  C  }h 


16B  AflTROVOMT. 

dirsoled  to  the  imtge  of  the  sraie  ol^jeet  in  Ae  meroniy.  If  siPca 
oi|  1^  will  then  be  the  place  of  the  wro,  becMue  the  wuo  vSl  he 
mored  with  the  instrament  throoffh  the  same  epeee  ae  that  Hmngfet 
whieh  the  teleeoope  is  moved.  Sinoe  the  direction  ox  ia  as  miSh 
below  the  horiion  as  oo  is  above  it,  the  dheetion  of  die  boriioB 
mnat  be  that  of  die  point  h  which  biaeeta  the  am  oi.  The  tela* 
aeopei  when  horisontaly  will  have  therafiNw  the  JBieotioD  OB^  an! 
when  it  has  this  position  die  leio  will  evidendy  be  at  af,  the  poini 
which  bisects  the  are  ss^. 

The  ''readingi"  of  the  wimmoape  M,  when  the  tdeaocm  ia  dt 
looted  to  0  and  i|  are  Ms  and  ms^'.  The  ^reaffing"  of  the  aaaa 
BiicrDsoope  when  the  teleeoope  is  boriiontal  woaU  JEe  m/.  Now  ft 
ia  evident,  from  what  has  been  stated  above,  that 

Mi^  —  Ms  =  u$r  —  Mi^; 
and|  thereforei 

Mi^  =  |(Ms  X  MiO; 

thai  isy  the  reading  fixr  the  boriiontal  diroction  of  the  teleaoopt 
woold  be  half  the  sum  of  the  leadinffB  for  an  object  and  its  inum 

2412.  Method  ofobservinff  aUUuaei  amd  tmiA  duimiem.  —-lis 
roadingB  of  all  the  microscopes,  when  the  telescope  is  directed  to  the 
horiKNiy  being  thus  determined,  are  preserved  as  necessary  data  ia 
all  observations  on  the  altitudes  or  zenith  distances  of  objects,  lb 
determine  the  altitude  of  an  object  o,  let  the  telescope  be  diredej 
to  it,  so  that  it, shall  be  seen  at  the  intersection  of  the  wires;  and 
let  the  readings  of  the  six  microscopes  be  On  o^  0^  O41  o^  and  <^ 
and  let  their  six  horiaontal  readines  be  Rn  B«,  H^,  H«,  H^  and  B^ 
We  shall  have  six  values  for  the  altitudes : 

Ai  =  H,  —  o„ 

Aa  =  Hg  —  Oj, 
A«  =  H,  —  C^ 
A4  =  H4  —  O4, 
A»  =  H»  —  O4, 
Af  =  H,  —  0„ 

These  will  be  nearly,  but  not  precisely,  equal,  because  they  will 
dil^  by  the  small  errors  of  observation,  centreing,  and  form.  A 
mean  of  the  six  being  taken  by  adding  them  and  dividing  their  sob 
by  6,  these  differences  will  be  equalis^  and  the  errors  nearly  eflboei, 
so  that  we  shall  have  the  nearest  approximation  to  the  true  al- 
titude-— 

A  =  H^i  +  ^1  +  ^t  +  ^  +  ^i  +  ^-l- 

The  altitude  of  an  object  being  known,  its  senith  distance  may  be 
found  bv  subtracting  the  altitude  from  90° :  thus,  if  z  express  the 
lenith  distance,  we  shall  have 

«  =  90«  — A. 


THB  0B8SRVAT0RT.  163 

2418.  MeAod  of  deierminxmg  the  potiHon  of  the  pole  and  equator. 
— The  miml  drole  may  be  regarded  as  the  celestial  meri<uan  re- 
daeed  in  scale,  and  broagfat  immediately  under  the  hands  of  the 
obeenreTi  so  tluU  all  distances  upon  it  may  be  submitted  to  exact 
enminatioQ  and  measurement  Besides  the  lenith  and  horizon,  the 
poatioiis  of  whioh|  in  relation  to  the  miorosoopes,  have  just  been 
sseertained,  there  are  two  other  points  of  equal  importance,  the 
pole  and  tlM  equatOTi  whioh  should  also  be  established. 

The  stars  which  arc  so  near  the  celestial  pole  that  they  never  set, 
are  carried  by  the  diurnal  motion  of  the  heavens  round  the  pole  in 
SDull  cirdes,  crossing  the  visible  meridian  twice,  once  above  and 
OBce  below  the  pole.  Of  all  these  circumpolar  stars,  the  most  im- 
portant and  the  most  useful  to  the  observer  is  the  pole  star,  both 
because  of  its  dose  proximity  to  the  pole,  from  which  its  distance  is 
only  11%  and  because  its  magnitude  is  si^ciently  great  to  be  visible 
with  the  telesoope  in  the  day.  This  star,  then,  crosses  the  meridian 
above  the  pole  and  below  it,  at  intervals  of  twelve  hours  sidereal 
tiBM,  and  the  true  position  of  the  pole  is  exactly  midway  between 
the  two  points  where  the  star  thus  crosses  the  meridian. 

I^  therefore,  the  readings  of  the  six  microscopes  be  taken  when 
the  pole  star  OAkes  its  transit  above  and  below  the  pole,  their  read- 
mgi  for  the  pole  itself  will  be  half  the  sum  of  the  former  for  each 


The  readings  for  the  pole  bdng  determined,  those  which  cor- 
respond to  the  point  where  the  celestial  equator  crosses  the  meridian 
Bu^be  found  by  subtracting  the  former  from  90^. 

when  die  positions  of  the  microscopes  in  relation  to  the  pole  and 
equator  are  determined,  the  latitude  of  the  observatorv  will  be 
known,  since  it  is  equal  to  the  altitude  of  the  celestial  pole  (2362). 

2414.  AU  circles  of  declination  represented  hy  the  circle,  —  SiDC4 
the  drcles  of  declination,  which  are  imaginod  to  surround  th« 
heavens,  are  brought  by  (he  diurnal  motion  in  succession  to  coin 
cide  with  the  celestial  meridian  (2404),  since  that  meridian  is  itseU 
represented  by  the  mural  circle,  that  circle  may  be  considered  a. 
presenting  successively  a  model  of  every  circle  of  declination ;  anr 
the  position  of  any  object  upon  the  circle  of  declination  is  repre- 
sented on  the  miual  circle  by  the  position  of  the  telescope  when 
directed  to  the  point  of  the  meridian  at  which  the  object  crosses  it. 

If  the  object  have  a  fixed  position  on  the  firmament,  it  is  evident 
that  it  will  always  pass  the  meridian  at  the  same  point ;  and  if  the 
telescope  be  directed  to  that  point  and  maintained  there,  the  object 
will  be  seen  at  the  intersection  of  the  wires  regularly  after  intervals 
of  twenty-four  hours  sidereal  time. 

2415.  Declination  and  polar  distance  of  an  object,  —  The  dis- 
tance of  an  object  from  the  celestial  equator,  measured  upon  the 
circle  of  dedniation  which  passes  through  it,  is  called  its  declina- 


TfQJift  and  18  HOBTiixor  bouth,  aoixwdiiig  to  Hn  ridSiOf  ttMicqiite 
at  whiob  the  object  ig  placed. 

The  decUoatioD  of  an  olneot  ia  aaoertained  with  tbamiinl  cirak 
In  the  same  maimer  and  by  the  same  obaenratioii  aa  that  whidi 
n^ea  ha  altituder  The  leadii^n  <^  the  miovoaeopea  te  the  o^eot 
Ceing  compaied  with  thur  rea$i\gi  Cur  the  poU  (MIS)^  glf«  tfif 
pdar  diatuice  of  the  object;  aod  the  diffMrenoe  belwieeii  tfaa  polv 
mateticeB  and  90^  mea  the  declination. 

Thus  the  pohr  diatvuse  and  declination  of  an  objeai  an  to  the 
0|aatQr  exactly  what  ita  altitode  and  cenith  dirtma  an  to  te 
horiion.  Bnt  since  the  egoatcy  maintaina  alwaya  the  aamn.poMtipn 
doiiog  the  dinmal  motioa  of  the  heavenai  the  declinatiwi  .aat  poJMr 
dutanoe  of  an  oUect  aie  not  affiwted  by  thatmotioDi  and  remain  the 
aaiftc,  white  th^Jtitode  and  aenithdiatoccB  an  oonatanll^ 

fHU.  Flmium  qf  on  o^  de/mad  h^  ii$  dedmatiom  amdr^ 
^^Kmrntm- — The  poeitioii  of  an  object  on  the  finnament  iadalHw 
mined  by  ita  dedma^cn  and  ri^t  asoenaion.  Itc  dacKnatioii  edbi 
uewa  ite  diBtance  north  or  soath  <^  the  oeleilial  equator^  aaA  ill 
nghi  aacennon  exfoc^am  the  distanoe.of  the  ciidb  of  daottntiQii 
iqpon  which  it  ia  placed  fiom  a  oertaandcAned. point  npoo  tha  eelaaliil 
eqoator. 

It  ia  evident^  thereforei  that  declination  and.  right  aacenaion  difna 
the  position  of  celestial  objects  in  exactly  the  same  manner  aa  ktv 
tode  and  lonffitnde  define  the  position  of  pUoea  on  the  earth.  A 
place  upon  the  globe  may  be  regarded  as  being  prqjeoted  on  the 
neavens  into  the  point  which  forms  its  senith ;  and  henoe  it  iqipesni 
that  the  latitode  of  the  place  is  identical  with  the  declinatioD  of  •  its 
a^th. 

CHAP.  vn. 

ATMOSPHSaiO  RSniACTIOM. 

I  2417.  Apparent  po$itum  of  cdatial  objects  affected  by  reJraeiiotL 
—  It  has  been  shown  that  the  ocean  of  air  which  sorrounds,  reats 
npon,  and  extends  to  a  certain  limited  height  above  the  Bnr&oe  of 
the  solid  and  liquid  matter  compoeing  the  globe,  decreases  gradnally 
in  density  in  rising  from  the  sarfewe  (719) ;  that  when  a  ray  of 
light  passes  from  a  rarer  to  a  denser  transparent  medium^  it  ia  de- 
flected towards  the  perpendicular  to  their  common  surface ;  and  that 
the  amount  of  such  deflection  increases  with  the  diffisrence  of  den- 
sities and  the  angle  of  incidence  (978  et  seq,).  These  propertieSi 
which  air  nas  in  common  with  all  transparent  media,  prodnce  in^ 
portent  effects  on  the  apparent  positions  of  celestial  objects. 


ATMOSPHIBIO  BBFEACTIOK. 


166 


Let  8  a,  Jig,  714,  be  a  ny  of  light 
ooming  from  any  distant  object  s,  and 
fidliog  on  the  surface  of  a  series  of  layers 
of  transparent  matter,  increasing  in 
density  downwards.  The  ray  s  a,  pass- 
ing into  the  first  layeri  will  be  d^ected 
in  the  direction  aa^  towards  the  per- 
pendioolar;  passing  thence  into  the 
nezty  it  will  be  agam  deflected  in  the 
dueotion  a^  a^,  more  towards  the  per- 
pendicular;  and^  in  fine,  passing  through 
the  lowest  layer,  it  wUl  be  rail  more 
deflected,  and  will  enter  the  eye  at  e, 
in  the  direction  a^e:  and  since  every 
object  is  seen  in  the  direction  from 
which  the  visual  ray  enters  the  eye, 
the  objeet  8  will  be  seen  in  the  direction  e  s',  instead  of  its  true 
direotm  aa.  The  effwt^  therefore,  is  to  make  the  object  appear 
to  b6  neaier  lo  the  aenithal  direction  than  it  really  is. 

And  this  is  what  actually  occurs  with  respect  to  all  celestial  ob- 
jects seen,  as  such  objects  always  must  be,  through  the  atmosphere. 
The  visual  ray  SD^Jig.  715,  passing  through  a  succession  of  strata 
of  ttr,  gradually  and  oontinually  increasing  in  density,  its  path  will 
be  a  oorve  bending  from  d  towards  A,  and  convex  towards  the 


i 


Ilf.7U. 


■ffuOiAl  line  A  %.    The  direotion  in  wbibh  dit  olifeaiira  k 
being  tbat  in  which  the  Tisoal  ny  enters  the  eye,  will  be  the 

St  A«  to  the  curve  atA.    The  objeetwill  therefore  be  eeen  im  the 
lOtion  A  « instead  of  D  eu 

It  has  been  shown  that  the  defleotion  prodneed  byntfcnelian  is 
inpreased  with  the  increase  of  the  wgle  of  incidenee.  Nowyisilhe 
nreeent  ease,  the  ang}e  of  ineidenoe  is  the  anj^  mider  the  tens 
Sieotaon  of  the  objeot  and  the  lenithal  line,  oTi  what  is  the  asss^ 
Oie.  «enith  distanoe  of  the  olgect  The  ezten^  tbsnfaii^  to  wUoh 
aqy  oeleatial  oljeet  is  distarbed.finom  its  tme  plaee  hj  the  wfawisi 
of  tfie  aUnoanherei  inereases  with  its  lenith  distanea.  TIm  ssAmt 
Am  iS|  there&re,  nothing  in  the.  seoithy  and  greatest  iatk»ks» 
rison. 

2418.  Law  of  aimotphine  re/mdjpM. — The  extent*  ts  wUdi  a. 
celestial  object  is  displaoed  by  refiraotiony  therefev^  dsneiida  ^oi 
and  increases  with  its  distance  from  the  senith :  ana  it  mm  be 
shown  to  be  a  conseqoenoe  of  the  ganend  prinoiples.of  aptie%  thsif 
when  otiier  things  are  the  samCi  the  at^taal.  (jianlity.ef 'tlda'  di^ 
placement  (excent  at  very  low  altUndoa)  vaiiea  in  the  pKOfmAm  ef < 
th#  tangent  of  the  lenith  distance. 
Thns.  if  AZ,  Jig.  716;  be  the  senithal  diieotioB,  and-  AO^  A9fi 

AO",  Ac,  be  the  directions  of  eelsaM 
objectsi  their  senith  distanoea  being. 
ZAOy  ZA(/y  ZAO^,  Ac,  the  qnaittitiia 
of  refiraction  by  which  they  will  be 
severallY  affected,  Qr,  what  is  the  sanML 
the  differences  between  their  true  and 
apparent  directions,  will  be  in  the  latis 
of  the  tangents  zt,  zi^,  zif,  fte.|Of 
Fig.  716.  the  senith  distances.* 

*  This  law  may  be  demonstrated  as  foUows : — The  an^e  of  IneidMiM 
of  the  visaal  ray  is  equal  to  the  lenith  distanoe  s  of  ^  dl|)eet.  If  r 
express  the  refraotioD,  the  angle  of  refraotion  will  be  s — r.  Let  As 
index  of  refraction  (980)  be  m.  By  the  general  law  of  refraotion  we  hafSb 
thecefore, 

sin.  s  —  m  X  sin.  (i — r)  —  m  X  sin.  a  cos.  r  —  m  X  cos.  t  dn.  r. 

But  since  r  is  a  yery  small  angle,  if  it  be  expressed  in  seoMids^  we  MBL 
have 

COS.  f  >■  1.  sin.  r  ■■ • 

'  206266* 

and,  consequently, 

«* 
sin.  f  »  m  X  sin.  i  —  m  x  cos. «  X 


206266' • 
and,  therefore, 

r-  206266>'^X  5^^  X  ^?1?- 206266'^ X  '5^  X  tan.  i. 

m         Gos.jr  m 


ATM08PHXRIC  RBlTRACTION.  167 

This  law  prevails  with  eonndenble  exaotitode,  except  at  very 
low  altitodeSy  where  the  refraotions  depart  from  it^  and  become  an- 
certain. 

2419.  Quanii^  of  re/raeHon, — When  the  latitade  of  the  ob- 
servatory is  known,  the  aotoal  quantity  of  refraction  at  a  ^ven 
altitude  may  be  ascertained  by  observing  the  altitudes  of  a  circum- 
polar  star,  when  it  pssBce  the  meridian  above  and  below  the  pole. 
The  sum  of  these  altitudes  would  be  exactly  equal  to  twice  the 
ktitude  (2862)  if  the  refraction  did  not  exist,  but  since  by  its 
ciiBctB  the  star  is  seen  at  greater  than  its  true  altitudes,  the  sum  of 
the  altitudes  will  be  JP^ter  than  twice  the  latitude  by  the  sum  of 
the  two  refractions.  This  sum  will  therefore  be  known,  and  beine 
divided  between  the  two  altitudes  in  the  ratio  of  the  tangents  of 
the  senith  distances^  the  quantity  of  refraction  due  to  each  altitude 
will  be  known. 

The  pole  star  answers  best  for  this  observation,  especially  in  these 
aad  higher  latitudes,  where  it  passes  the  meridian  within  the  limits 
of  the  more  regular  influence  of  refraction ;  and  the  diflerence  of 
its  altitudes  bemg  only  8^,  no  considerable  error  can  arise  in  ap- 
portioning the  total  refraction  between  the  two  altitudes. 

2420.  Tabki  of  re/radian,  —  To  determine  with  great  exacti- 
tude the  average  quantity  of  refraction  due  to  different  altitudes, 
and  the  various  physical  conditions  under  which  the  actual  refrac- 
tion departs  frt>m  such  average,  is  an  extremely  difficult  physical 
problem.  These  conditions  are  connected  with  phenomena  subject 
to  uncertain  and  imperfectly  known  laws.  Thus,  the  quantity  of 
refiaction  at  a  given  altitude  depends,  not  only  on  the  density,  but 
also  CO  the  temperature  of  the  successive  strata  of  air  through 
which  the  visual  ray  has  passed.  Although,  as  a  general  faiot,  it  is 
apparent  that  the  temperature  of  the  air  falls  as  we  rise  in  the 
atmosphere  (2185),  yet  the  exact  law  according  to  which  it  de- 
creases is  not  fully  ascertained.  But  even  though  it  were,  the 
refraction  is  also  influenced  by  other  agencies,  among  which  the 
hymmetric  condition  of  the  air  holds  an  important  place. 

From  these  causes,  some  uncertainty  necessarily  attends  astro- 
nomical observations,  and  some  embarrassment  arises  in  cases  where 
the  quantities  to  be  detected  by  the  observations  are  extremely 
minute.  Nevertheless,  it  must  he  remembered,  that  since  the  total 
amount  of  refraction  is  never  considerable,  and  in  most  cases  it  is 
extremely  minute,  and  since,  small  as  it  is,  it  can  be  very  nearly 
estimated  and  allowed  for,  and  in  some  cases  wholly  effaced,  no 
serious  obstacle  is  offered  by  it  to  the  general  progress  of  astro- 
nomy. 

Tables  of  refraction  have  been  constructed  and  calculated,  partly 
from  observation  and  partly  from  theory,  by  which  the  observer 
Okay  at  once  obtain  the  average  quantity  of  refraction  at  each  aLii« 


168  ASTBOBroinr. 


tilde;  and  mles  are  given  by  whioh  this  atenge  wflraelien  wtaj  be 
eoRceted  aooording  to  the  peonliar  atate  of  the  baionieler,  ttav^ 
mometefi  and  other  indioatora  of  the  phyrieal  atate  of  the  dr. 

2421.  Average  quantU^  at  mean  aUUmkt. — Whik  the  ntm^ 
tion  IB  nothing  in  the  ienith|  and  aomewhat  nealer  tfc«i  As  i^ 
parent  diameter  of  the  son  or  moon  in  the  noriioBi  ii  doaa  Ml 
amount  to  ao  much  as  1',  or  the  thirtieth  part  of  thia  diaawitari  ai 
the  mean  altitude  of  46^. 

2422.  Effisd  OH  riiing  and  teUinff.  — Ita  mean  qoantitjr  bi  Aa 
horiion  ia  83',  which  being  a  litdo'  more  than  the  mean  appaml 
dbmietera  of  the  ann  and  moon,  it  fbUowa  that  theae  oUeoli^  at  tta 
moment  of  rising  and  aettinji;,  are  viaiUe  abofe  the  horiioB,  tta 
lower  edge  of  their  diaka  jnaC  tooohing  it,  when  in  lealitj  ttiqr  M 
below  it,  the  upper  edge  of  the  diak  juat  touohing  it 

The  moments  of  rising  of  all  objeeta  are  therefore 
and  thoee  of  aetting  retuded|  by  refiraetionr    The  ann  and 
a^apear  to  rise  hefi^  they  have  really  riaeui  and  to  aet  q/ler  ik^ 
wre  really  aet;  and  the  aame  ia  true  of  all  other  dbgeeta. 

2428.  General  effect  of  Ae  barometer  on  re/raeiunu  Bm 
the  barometer  rises  with  the  inereaaed  weight  and  denai^  of  lb 
air,  its  rise  ia  attended  by  an  augmentation,  and  ita  nil  by  a 
decrease,  of  refraotion.  It  may  be  assumed  that  the  refraotioo  aft 
any  proposed  altitude  is  increased  or  diminished  by  l-800th  part  of 
ita  mean  quantity  for  every  10th  of  an  inch  by  which  the  barometer 
exceeds  or  falls  short  of  Uie  height  of  80  inches. 

2424.  Effect  of  thermometer, — As  the  increase  of  temperature 
causes  a  decrease  of  density,  the  effect  of  refraction  is  diminished 
by  the  elevation  of  the  thermometer,  the  state  of  the  barometer 
being  the  same.  It  may  be  assumed,  that  the  refraction  at  in 
proposed  altitude  is  diminished  or  increased  by  the  420th  part  el 
its  mean  amount  for  each  degree  by  which  Fahrenheit's  thermomelar 
exceeds  or  &lls  short  of  the  mean  temperature  of  55^. 

2425.  Twilight  cawed  5y  the  reflection  of  ike  atmo$phere»'^ 
The  sun  continues  to  illuminate  the  clouds  and  the  supenor  stnii 
of  the  air  after  it  has  set,  in  the  same  manner  as  it  shines  on  thi 
summits  of  lofty  mountain  peaks  long  after  it  has  descended  fkeai 
the  view  of  the  inhabitants  of  the  adjacent  plains.  The  air  ni 
clouds  thus  illuminated,  reflect  light  to  the  surfiuw  below  thsBi 
and  thus,  after  sunset  and  before  sunrise,  produce  that  liffht^  melt 
or  less  feeble  according  to  the  depression  of  the  sun,  <»Sed  rwi* 
LIGHT.  Immediately  after  sunset  the  entire  visible  atmoepheMb 
and  all  the  clouds  which  float  in  it,  are  flooded  with  sunlight,  aat 
produce,  by  reflection,  an  illumination  little  less  intense  than  befbn 
the  sun  had  disappeared.  According  as  the  sun  sinks  lower  aad 
lower,  less  and  less  of  the  visible  atmosphere  receives  his  light,  aad 
less  and  less  of  it  is  transmitted  by  reflection  to  the  vaxhce,  wbA 


ANNITAL  MOnON  OP  THE  EABTH.  169 

bj  dow  degrees,  all  reflection  oeasea,  and  night 


of  phenomena  are  developed  in  an  opposite  order 
lonrise  in  the  morning,  commenoing  with  the  first  feeble  light 
n,  and  ending  with  the  full  blase  of  day  when  the  disk  of  the 
xmies  nsible. 

general  efieet  of  the  air,  elondS|  and  vapours  in  diffusing 
jid  rendering  more  eff9ctual  the  general  illumiDation  pro- 
ij  the  son,  £m  been  already  explained  in  (923,  924). 
I.  Ovai  /arm  of  diski  of  sun  and  moon  explained.  —  One 
most  ourioos  effects  of  atmospheric  refraction  is  the  oval  form 
disks  of  the  sun  and  moon,  when  near  the  horizon.  This 
^mn  the  unequal  refraction  of  the  upper  and  lower  limbs, 
ler  being  nearer  the  horizon  is  more  ^ected  by  refraction, 
irefore  raised  in  a  greater  degree  than  the  upper  limb,  the 
f  which  is  to  bring  the  two  limbs  apparently  closer  together, 
difference  between  the  two  refractions.  The  form  of  the 
therefore  affected  as  if  it  were  pressed  between  two  forces, 
rag  above,  and  the  other  below,  tending  to  compress  its  ver- 
uneter,  and  to  give  it  the  form  of  an  ellipse,  the  lesser  axis 
*h  is  vertical,  and  the  greater  horizontal.* 

CHAP.  vm. 

ANNUAL  MOTION   OF  THE  EARTH. 

.  Apparent  motion  of  the  sun  in  the  heavens,  —  Indcpen- 
of  the  motion  which  the  sun  has  in  commoQ  with  the  entire 
mt,  and  in  virtue  of  which  it  rises,  ascends  to  the  meridian, 
B,  it  is  observed  to  change  its  position  from  day  to  day  with 
I  to  the  other  celestial  objects  among  which  it  is  placed.  In 
ipect,  therefore,  it  differs  essentially  from  the  stars,  which 
n  their  relative  positions  for  months,  years,  and  ages,  unal- 

16  exact  position  of  the  sun  be  observed  from  day  to  day  and 
onth  to  month,  through  the  year,  with  reference  to  the  stars, 
be  found  that  it  has  an  apparent  motion  among  them  in  a 
ixcle  of  the  celestial  sphere,  the  plane  of  which  forms  an 
f  23®  28'  with  the  plane  of  the  celestial  equator. 
L  Ascertained  hy  the  transit  instrument  and  mural  circle,  — 
pparcnt  motion  of  the  sun  was  ascertained  with  considerable 

aa  explanation  of  the  great  apparent  magnitiide  of  the  lolar  and  lunar 
lAa^g  aad  mtltiag,  gee  (1170). 

15 


170  iUST&ONOMT. 

preoiaon  before  the  inyentioD  of  the  teleeoope  ftnd  tlie  snbfeqi 
and  consequent  improvement  of  the  instnimente  of  obeemtkn. 
majy  however,  be  made  more  dearly  maniftat  by  the  tnoiiit  ioi 
ment  and  mnral  circle. 

If  the  transit  of  the  snn  be  obeerred  daily  (2402)|  and  ili  i 
ascension  be  ascertained  (2405),  it  will  be  rooiid  tlu^  from  da 
day  the  right  ascension  continnallY  inoreaaeB,  bo  that  the  eirak 
declination  (2404)  passing  throogh  the  centre  of  the  aon  if  eai 
with  the  son  round  the  heavensi  making  a  complete  refoliitioii  : 
year,  and  moving  constantly  from  west  to  east,  or  in  a  divectua 
trary  to  the  apparent  diurnal  motion  of  the  firmament 

If  the  point  at  which  the  sun's  centre  crosses  the  meridiaii  i 
be  observed  with  the  mural  circle  (2408),  it  will  be  fimnd  toeb 
from  day  to  day.  Let  its  distance  from  the  celestial  ecniatori  m 
declination,  be  observed  ^2415)  daily  at  noon.  It  will  oe  loan 
be  nothing  on  the  21st  ca  March  and  21st  of  September,  on  wl 
days  the  polar  distance  of  the  sun's  centre  will  be  therefion  \ 
The  sun's  centre  is,  then,  on  these  days,  in  the  cdeslial  eqn 
After  the  2l8t  March  the  sun's  centre  will  be  north  of  the  eqvi 
and  its  declination  will  continually  increase,  until  it  beoomoa 
28'  on  the  2l8t  June.  It  will  then  begin  slowly  to  decrease, 
will  continue  to  decrease  until  2l8t  September,  when  the  centn 
the  sun  will  again  be  in  the  equator.  After  that  it  will  pass 
meridian  south  of  the  equator,  and  will  consequently  have  m 
declination.  This  will  increase  until  it  becomes  23^  28'  on  the ! 
December ;  after  which  it  will  decrease  until  the  centre  of  the 
returns  to  the  equator  on  the  2l8t  March. 

By  ascertaining  the  position  of  the  centre  of  the  sun's  disk  1 
day  to  day,  by  means  of  its  right  ascension  and  declination  (24 
and  tracing  its  course  upon  the  surfiice  of  a  celestial  globe,  its  ] 
is  proved  to  be  a  great  circle  of  the  heavens,  inclined  to  the  equ 
at  an  angle  of  23""  28'. 

2429.  The  ecliptic,  —  This  great  circle  in  which  the  centre  o( 
disk  of  the  sun  thus  appears  to  move,  completing  its  revolution 
in  a  year,  is  called  the  ecliptic,  because,  for  reasons  which  will 
explained  hereafiter,  solar  and  lunar  eclipses  can  never  take  p 
except  when  the  moon  is  in  or  very  near  it. 

2430.  The  equinoctial  poinU, —  The  ecliptic  intersects  the  ei 
tial  equator  at  two  points  diametrically  opposite  to  each  other 
vidiog  the  equator,  and  being  divided  by  it  into  equal  parts.  Tl 
are  called  the  equinoctial  points,  because  when  the  centre  of 
solar  disk  arrives  at  them,  being  then  in  the  celestial  equator, 
sun  will  be  equal  times  above  and  below  the  horizon  (2867), 
the  days  and  nights  will  be  equal. 

2431.  The  vernal  and  atUumnal  c^tnoxet.  — The  equinoc 
jM)int  at  which  the  sun  passes  from  the  south  to  the  north  of 


ANNUAL  MOTION  OF  THE  EARTH.  171 

oeleatial  equator  is  called  the  vernal,  and  that  at  which  it  passes 
from  the  north  to  the  south  is  called  the  autumnal,  equinoctial 
point.  The  times  at  which  the  centre  of  the  sun  is  found  at  these 
poiots  are  called,  respectively,  the  vernal  and  autumnal  equi- 
noxes. 

The  vernal  equinox,  therefore,  takes  place  on  the  2l8t  March, 
and  the  autumnal  on  the  2l8t  September. 

2432.  The  tecuons.  —  That  semicircle  of  the  ecliptic  through 
which  the  sun  moves  from  the  vernal  to  the  autumnal  equinox  is 
north  of  the  celestial  equator ;  and  during  that  interval  the  sun  will 
therefoie  (2351)  be  longer  above  than  below  the  horizon,  and  will 
p—  the  meridian  above  the  equator  in  places  having  north  latitude. 
The  daji^  therefore^  daring  that  half-year,  will  be  longer  than  tho 
nishts. 

Thai  semieircle  through  which  the  centre  of  the  sun  moves  from 
the  autumnal  to  the  vernal  equinox  being  south  of  the  celestial 
cqnatOT,  the  sun,  for  like  reasons,  will  during  that  half-year  be 
iooger  bebw  than  above  the  horizon,  and  the  days  will  be  shorter 
than  the  nightSi  the  sun  rising  to  a  point  of  the  meridian  below  tho 
equator. 

The  three  months  which  succeed  the  vernal  equinox  are  called 
SEPEINO,  and  those  which  precede  it  winter;  the  three  months 
which  precede  the  autumnal  equinox  are  called  summer,  and  those 
which  suooeed  it  winter. 

2433.  The  $oltticei.  — Those  points  of  the  ecliptic  which  are 
midway  between  the  equinoctial  points  are  the  most  distant  from  the 
celestial  equator.  The  arcs  of  the  ecliptic  between  these  points  and 
the  equinoctial  pmnts  are  therefore  90^.  These  are  called  the  sol- 
stitial points,  and  the  times  at  which  the  centre  of  the  solar  disk 

throu|di  them  are  called  the  solstices. 

The  summer  solstice,  therefore,  takes  place  on  the  21st  June,  and 
the  winter  polstioe  on  the  21st  December. 

This  distance  of  the  summer  solstitial  point  north,  and  of  the 
winter  solstitial  point  south  of  the  celestial  equator  is  28^  28'. 

The  more  distant  the  centre  of  the  sun  is  from  the  celestial 
equator,  the  more  unequal  will  be  the  days  and  nights  (2356),  and 
oooseqaently  the  longest  day  will  be  the  day  of  the  summer,  and 
the  shortest  the  day  of  the  winter,  solstice. 

It  will  be  evident  that  the  seasons  must  be  reversed  in  southern 
latitudes,  since  there  the  visible  celestial  pole  will  be  the  south  pole. 
The  summer  solstice  and  the  vernal  equinox  of  the  northern,  are  the 
winter  solstice  and  autumnal  equinox  of  the  southern  hemisphere. 
Nevertheless,  as  the  most  densely  inhabited  and  civilized  parts  of 
the  globe  arc  in  the  northern  hemisphere,  the  names  in  reference  to 
the  loeal  phenomena  are  usually  preserved. 

2434.  Toi  Zodiac. — It  will  be  shown  hereafter  that  the  ap- 


172 


ABTBOHOmr. 


ptreni  motions  of  the  planets  are  indiided  wiliUn  m  qnoa  of  tta 
eelestial  sphere  extending  a  ftw  degrees  north  and  sondi  ef  dbo 
ecliptic.  The  zone  of  the  hearens  indaded  within  these  limils  is 
called  ihe  zodiao. 

2435.  The  signs  of  the  zodiac— The  cirole  of  the  ndiae  is  A- 
lided  into  twelve  eqoal  parts,  called  bign8|  each  of  whidi  tlierafae 
measures  80^.  The^  are  named  firom  principal  wmstdkiioBS^  er 
mops  of  8tarS|  which  are  placed  in  or  near  them.  B^pmung 
Srom  Ae  yemal  eqninozial  pomt^  ihej  are  as  foDowB  ^— 


7.  Libra  (the  balance}  .m....^-  a 

8.  Scorpio  (the  tooriiioQ)  ....m.  H^ 

9.  8agittariii8(diearehar)«..-  f 

10.  Gaprioomns  (the  goat)  ...•-  1^ 

11.  Aquarios  (the  waterman)  M.  IK 

12.  Piaees  (the  fiahea)  .......m...  X 


1.  Aif  es  (the  ram) op 

2.  Taimu  (the  biul) ^  \s 

5.  Gemini  (the  twina)  ...• n 

4.  Cancer  (the  crab) ss 

6.  Leo  (the  lion) ....- 1^ 

6.  '^go(theTirgin) Tlj 

Thus  the  pomtion  of  the  yenial  equinoctial  point  ia  the  msr 
FOINT  OF  ARIES,  and  that  of  the  autumnal  the  riBsr  Mim  Of 
UBBA.  The  summer  solstitial  point  is  at  the  nsar  pom  ^Oi 
GANOXBy  and  the  winter  at  the  fikst  point  or  OAPftioo&ir. 

2486.  The  trojncs.  — The  points  of  the  ecliptao  at  which  Am 
centre  of  the  sun  is  most  distant  from  the  celestiat  equator  are  abo 
called  the  tropios,— the  northern  being  the  tbopio  ov  qanoiBi 
and  the  southern  the  tropio  op  oaprioorn. 

This  term  tropio  is  also  applied  in  geo^phy  to  those  parte  of 
the  earth  whose  distances  from  the  terrestrial  eauator  are  equal  to 
the  greatest  distance  of  the  centre  of  the  solar  disk  from  the  cdes- 
tial  equator.  The  northern  tropio  is,  thereforei  a  paralld  of 
latitude  23^  28'  north,  and  the  southern  tropio  a  paraUd  of 
latitude  28^  28'  south  of  the  terrestrial  equator. 

2487.  Celestial  latitude  and  longitude. — The  terms  latitude  and 
longitude,  as  applied  to  objecto  on  tho  heavens,  have  a  signifioatina 
different  from  that  given  to  them  when  applied  to  places  upon  the 
earth.  The  latitude  of  an  object  on  the  heavens  means  ite  nistainii 
from  the  ecliptic,  measured  in  a  direction  perpendicular  to  the 
ecliptic ;  and  ite  longitude  is  the  are  of  the  ecliptic,  between  the 
first  point  of  Aries  and  the  circle  which  measures  ite  latitiidi^ 
taken,  like  the  right  ascension,  according  to  the  order  of  the  djgns. 

Thus,  since  the  centre  of  the  sun  is  always  on  the  ecliptic^  ill 
latitude  is  always  0^.  At  the  vernal  equinox  ite  longitude  is  (P.  at 
the  summer  solstice  it  is  90^,  at  the  autumnal  equinox  180^,  ana  li 
tho  winter  solstice  270^. 

2488.  Annual  motion  of  the  earth.  —  The  apparent  ansoal  flU 
tion  of  the  sun,  described  above,  is  a  phenomenon  which  can  bnl 
proceed  from  one  or  other  of  two  causes.  It  may  arise  from  a  w 
annual  revolution  of  the  sun  round  the  earth  at  rest^  or  from  a  lei 


I- 

]| 

h 
I 


I 


ANNUAL  MOTION  OF  TUE  EARTH.  173 

reTolatioii  of  the  earth  round  the  son  at  rest.  Either  of  these 
causes  would  ezpLun,  in  an  equally  satisfactory  manner,  all  the  cir- 
enmstances  attending  the  apparent  annual  motion  of  the  sun  around 
Uie  firmament  There  is  nothing  in  the  appearance  of  the  sun 
itself  which  could  give  a  greater  probahilitj  to  either  of  these  hy- 
potheses than  to  the  other.  If,  therefore,  we  are  to  choose  between 
them,  we  must  seek  the  grounds  of  choice  in  some  other  circum- 
stanoes. 

It  was  sot  until  the  reviTal  of  letters  that  the  annual  motion  of 
the  earth  was  admitted.  Its  apparent  stability  and  repose  were 
until  then  universally  maintained.  An  opinion  so  long  and  so 
deeply  rooted  must  have  had  some  natural  and  intelligible  grounds. 
These  grounds,  undoubtedly,  are  to  be  found  only  in  the  general  im- 
pression, that  tf  the  globe  moved,  and  especially  if  its  motion  had 
so  enormous  a  velocity  as  must  be  imputed  to  it,  on  the  supposition 
that  it  moves  annually  round  the  sun,  we  must  in  some  way  or 
other  be  sensible  of  such  movement 

All  the  reasons,  however,  why  we  are  unconscious  of  the  real  ro- 
tation of  the  earth  upon  its  axis  (2350)  are  equally  applicable  to 
show  why  we  must  be  unconscious  of  the  progressive  motion  of  the 
earth  in  its  annual  course  round  the  sun.  The  motion  of  the  globe 
through  space  being  perfectly  smooth  and  uniform,  we  can  have  no 
sensible  means  of  knowing  it,  except  those  which  we  possess  in  the 
case  of  a  boat  moving  smoothly  alon^  a  river :  that  is,  by  looking 
abroad  at  some  external  objects  which  do  not  participate  in  the  mo- 
tion imputed  to  the  earth.  Now,  when  we  look  abroad  at  such 
objects,  we  find  that  they  appear  to  move  exactly  as  stationary  ob- 
jects would  appear  to  move,  seen  from  a  moveable  station.  It  is 
plain,  then,  if  it  be  true  that  the  earth  really  has  the  annual  motion 
round  the  sun  which  is  contended  for,  that  we  cannot  expect  to  be 
conscious  of  this  motion  from  anything  which  can  be  observed  on 
our  own  bodies  or  those  which  surround  us  on  the  surface  of  the 
earth  :  we  must  look  for  it  elsewhere. 

But  it  will  be  contended  that  the  apparent  motion  of  the  sun, 
even  upon  the  argument  just  stated,  may  equally  be  explained  by 
the  motion  of  the  earth  round  the  sun,  or  the  motion  of  the  sun 
round  the  earth ;  and  that,  therefore,  this  appearance  can  still  prove 
nothing  positively  on  this  question.  We  have,  however,  other 
proofs,  of  a  very  decisive  character. 

Newton  showed  that  it  was  a  general  law  of  nature,  and  part,  in 
fact,  of  the  principle  of  gravitation,  that  any  two  globes  placed  at  a 
distance  from  each  other,  if  they  are  in  the  first  instance  quiescent 
and  free,  must  move  with  an  accelerated  motion  to  their  common 
eentre  of  gravity,  where  they  will  meet  and  coalesce ;  but  if  they 
be  projected  in  a  direction  not  passing  through  this  centre  of  gravity, 
they  will  both  of  them  revolve  in  orbits  around  that  point  periodically 

15* 


I 


174  ASTRONOIIT. 

Now  it  will  appear  hereafter  that  the  oomiiioii  eentn  ef  gnmfef 
of  the  earth  and  sun,  owiDg  to  the  immenee  prepondennoe  of  tfie 
mass  of  the  sun  (309),  is  plaoed  at  a  pcnnt  yerr  near  the  oentre  of 
the  son.  Bound  that  point,  therefore,  the  earth  maa^  aeoodUng  to 
this  prindplei  revolve. 

24^9.  MMm  of  light  provet  the  cmnual  moticm  of  Ae  earA, — 
Sinoe  the  principle  of  gravitation  itself  mig^t  be  oonndered  as  more 
or  less  h^theticad,  it  has  been  oonsiderod  desirable  to  find  oAer 
independent  and  more  direct  proob  of  a  phenomenoni  bo  Audamen- 
tally  important,  and  so  oontruy  to  the  fint  impresrions  of  mankind, 
as  the  revdution  of  the  earth  and  the  qniteoenoe  of  the  son.    A 
remarkable  evidence  of  this  motion  has  been  acoordinglv  diseovered 
in  a  vast  body  of  apparently  complicated  phenomena  whibh  are  th«  | 
immediate  effects  of  snch  a  motion,  whicn  could  not  be  explained 
if  the  earth  were  at  rest  and  the  sun  in  motion,  and  which,  m  finej 
would  be  inexplicable  on  any  other  suppodtion  save  the  revolntion 
of  the  earth  round  the  sun. 

It  has  been  ascertained,  as  has  been  already  ezplained.  that  li^l 
is  propagated  through  space  with  a  certain  great  but  definite  veloatj 
of  about  192,000  miles  per  second.  That  light  has  this  vdodtf  ia 
proved  by  the  body  of  optical  phenomena  which  cannot  be  expbonec 
without  imputing  to  it  such  a  motion,  and  which  are  perfectly  ex* 
plicable  if  such  a  motion  be  admitted.  Independently  of  this, 
another  demonstration  that  light  moves  with  this  velocity  is  supplied 
by  an  astronomical  phenomenon  which  will  be  noticed  in  a  subse- 
quent part  of  this  volume. 

2440.  Aberration  of  lighL  —  Assuming,  then,  the  velocity  of 
light,  and  that  the  earth  is  in  motion  in  an  orbit  round  the  Bun  with 
a  velocity  of  about  19  miles  per  second,  which  must  be  its  epeed  if 
it  move  at  all,  as  will  hereafter  appear,  an  effect  would  be  pxT)dneed 
upon  the  apparent  places  of  all  celestial  objects  by  the  oombinalion 
of  these  two  motions,  which  we  shall  now  explain. 

It  has  been  stated  that  the  apparent  direction  of  a  visible  oUeet 
is  the  direction  from  which  the  visual  rav  enters  the  eye.  Now 
this  direction  will  depend  on  the  actual  direction  of  the  ray  if  the 
eye  which  receives  it  be  quiescent;  but  if  the  eye  be  in  motion,  the 
same  effect  is  produced  upon  the  organ  of  sense  as  if  the  ray,  be- 
sides the  motion  which  is  proper  to  it,  had  another  motion  equal 
and  contrary  to  that  of  the  eye.  Thus,  if  lieht  moving  firom  the 
north  to  the  south  with  a  velocity  of  192,000  miles  per  aeeond  be 
struck  by  an  eye  moving  from  west  to  east  with  the  same  velocity, 
the  efiect  produced  by  the  light  upon  the  organ  will  be  the  same  as 
if  the  eye,  being  at  rest,  were  struck  by  the  light  havine  a  modoo 
compounded 'of  two  equal  motions,  one  from  north  to  souui,  and  the 
other  from  east  to  west.  The  direction  of  this  compound  e£foct 
would|  by  the  principles  of  the  composition  of  motion  (176)^  be 


ANNUAL  MOTION  OF  THE  EARTH. 


176 


equfaknfc  lo  a  molioii  from  the  direction  of  the  north-east  The 
object  from  which  the  lieht  comes  woold,  therefore,  be  apparently 

diapboedy  and  would  be  seen  at  a  point  beyond 
that  which  it  really  occupies  in  the  direction 
in  which  the  eye  of  the  observer  is  moved. 
This  displacement  is  called  accordingly  the 

ABKBRATION  0¥  LIGHT. 

This  may  be  made  still  more  evident  by  the 
Allowing  mode  of  illustration.  Let  o.  Jig,  717, 
be  the  object  from  which  light  comes  in  the 
direction  o  o  ^'.  Let  e  be  the  place  of  the  eye 
of  the  observer  when  the  light  is  at  o,  and  let 
the  eye  be  supposed  to  move  from  e  to  e^'  in 
the  same  time  that  the  light  moves  from  o  to 
^\  Let  a  straight  tube  be  imagined  to  be  di- 
rected from  the  eye  at  e  to  the  light  at  o,  so 
that  the  lieht  shall  be  in  the  centre  of  its 
opening,  while  the  tube  moves  with  the  eye 
from  oe  to  (/'  ef',  maintaining  constantly  the 
same  direction,  and  remaining  parallel  to  itself: 
the  light  in  moving  from  o  to  e^',  will  pass 
along  its  axis,  and  will  arrive  at  ef'  when  the 
eye  arrives  at  that  point.  Now  it  is  evident 
that  in  this  case  the  direction  in  which  the 
object  would  be  visible,  would  be  the  direction 
of  the  axis  of  the  tube,  so  that,  instead  of 
rig.  717.  appeariog  in   the  direction  oo,  which  is  its 

true  direction,  it  would  appear  in  the  direction  o  o'  advanced  from 
o  in  the  direction  of  the  motion  e  d'  with  which  the  observer  is 
affected. 

The  motion  of  lisht  being  at  the  rate  of  192,000  miles  per 
second,  and  that  of  the  earth  fif  it  move  at  all)  at  the  rate  of  19 
miles  per  second  (both  these  velocities  will  be  established  hereafter), 
it  follows,  Uiat  the  proportion  of  oe!^'  to  ee"  must  be  192,000  to 
19,  or  10,000,  to  1. 

The  ANGLE  OF  ABERRATION  ooo'  will  Vary  with  the  obliquity 
of  the  direction  e  e"  of  the  observer's  motion  to  that  of  the  visual 
my  oe".  In  all  cases  the  ratio  of  oc"  to  ee"  will  be  10,100  to  1. 
If  the  direction  of  the  esurth's  motion  be  at  right  andes  to  the 
directiim  oe**  of  the  object  o,  we  shall  have  (2294)  the  aberration. 

'      206,265^  20"-42 

If  the  angle  o^e  be  oblique,  it  will  be  necessary  to  reduce  ec" 
to  its  component  at  right  angles  to  o  d\  which  is  done  by  multiply- 
bg  it  by  the  trigonometrical  sine  of  the  obliquity  od'eoi  the  di- 


•  • 


176  ASTRONOMY. 

notioii  of  the  object  to  that  of  the  earth's  motum.  If  thk  obli- 
qnity  be  expressed  by  o,  w e  shall  have  for  the  abenations  in  general 

a  =  20^42x  sin.  o. 

Aoeording  to  this,  the  aberration  would  be  greatest  when  the  direo- 
tion  of  the  earth's  motion  is  at  right  angles  to  that  of  the  objeot^ 
and  woold  decrease  as  the  angle  o  decreases,  being  nothing  when 
the  object  is  seen  in  the  direction  in  which  the  eaith  is  moruij^  or 
in  exactly  the  contrary  direction. 

The  phenomena  may  also  be  imagined  by  conndering  that  thi 
earth|  in  rerolying  round  the  snn,  constantly  changes  the  direotioi 
of  its  motion ;  that  direction  making  a  complete  rerolntion  with  tbi 
earthy  it  follows  that  the  effect  produced  upon  the  apparent  plao 
of  a  distant  object  would  be  the  same  as  if  that  object  really  re- 
Tolyed  once  in  a  year  round  its  true  place,  in  a  circle  whose  phuM 
would  be  parallel  to  that  of  the  eailh's  orbit,  and  whose  ndin 
would  subtend  at  the  earth  an  ande  of  20^*42,  and  the  objea 
would  be  always  seen  in  such  a  drcle  90^  in  advance  of  the  eaith'i 
place  in  its  orbit 

These  circles  would  be  reduced  by  projection  to  ellipses  of  in- 
finitely various  excentricities,  accoraing  to  the  position  of  the 
object  with  relation  to  the  plane  of  the  earth's  orbit.  At  a  poia 
perpendicularly  above  that  plane,  the  object  would  appear  to  movi 
annually  in  an  exact  circle.  At  points  nearer  to  the  ecliptic,  ik 
apparent  path  would  be  an  ellipse,  the  exccntricity  of  which  weak 
increase  as  the  distance  from  the  ecliptic  would  diminish,  socordiD^ 
to  definite  conditions. 

Now,  all  these  apparent  motions  are  actually  observed  to  afiea 
all  the  bodies  visible  on  the  heavens,  and  to  affect  them  in  precisel} 
the  degree  and  direction  which  vroM  be  produced  by  the  annual 
motion  of  the  earth  round  the  sun. 

As  the  supposed  motion  of  the  earth  round  the  sun  completely 
and  satisfactorily  explains  this  complicated  body  of  phenomena 
called  aberration,  while  the  motion  of  the  sun  round  the  earth 
would  altogetiier  fiiil  to  explain  them,  they  afford  another  striking 
evidence  of  the  annual  motion  of  the  earth. 

2441.  Argument  from  analo^^.  —  In  fine,  another  argument  in 
favour  of  the  earth's  annual  motion  round  the  sun  is  ti^en  from 
its  analogy  to  the  planets,  to  all  of  which,  like  the  earth,  the  sun 
is  a  source  of  light  and  heat^  and  all  of  which  revolve  round  the 
sun  as  a  centre,  having  days,  nights,  and  seasons  in  all  respects 
similar  to  those  which  prevail  upon  the  earth.  It  seems,  therefore, 
contrary  to  all  probability,  that  the  earth  alone,  being  one  of  the 
planets,  and  by  no  means  the  greatest  in  magnitude  or  physical  im- 
portance, should  be  a  centre  round  which  not  only  the  sun,  but  all 
the  other  planets,  should  revolve. 


AnruAL  KoiioK  or  ram  iakth. 


177 


— K  tht  MsflL  le  ■dmitted  to  nors  an- 
■  in  t  dide  whoao 
)  mUlknii  of  mil«8, 
;  dietant  olgeett  from 
'm  other  H  «« (qtpo- 
ftoiicle,  snutseoes- 
■rilf ,  M  ai^  Im  igyed,  Me  thase  objeota  in  -nrj  ^Benat 


To  uuipwhid  tha  afleet  wluoh  ought  be  expected  to  be  pn^ 
iUbmiI  i^ob  the  qpHant  plaeeof  adistant  objeot bj  nioh  a  motum, 
let  Mlill'ir,fig.  718,  v^trewnt  t&e  euth'i 
.  ^  ■nniul  oonm  lomd  dw  hd  aa  leen  in  per- 

i^eotiTe,  ud  let  o  be  anr  distant  objeot 
Tuifale  from  tbe  earth.  The  eztremi^'^x 
ef  the  lioe  lo,  which  ia  the  Tiatud  direction 
of  the  ohjeot,  being  curied  with  the  earth 
round  tiie  dirde  z^^i^,  will  annnaU; 
Jwnribe  a  eooo  of  which  the  baae  is  the 
path  cf  the  earth,  and  the  vertex  ia  the 
place  of  the  objeot  O.  While  the  earth 
iDOree  round  the  circle  ii",  the  line  of 
Timal  direetion  would  therefine  have  a  oor- 
nK^foaSiaB  motion,  and  the  af^arent  plaoa 
of  (he  ol^et  would  be  rocoeanrelj  changed 
with  Ae  change  of  direction  of  thia  line. 
If  the  oltfaot  be  imagioed  to  be  prajeoted 
bj  the  eje  npon  the  firmament,  it  wonld 
tnoe  npon  it  a  path  o  e/  o"  </",  whioh  wonld 
ba  eironlar  ta  elliptioal,  aoocnding  to  the 
direction  of  the  oDJeot  When  ue  earth 
ia  at  ■,  the  object  would  be  seoi  at  o ;  and 
when  the  earth  ia  at  ^,  it  wonld  be  aeen 
at  ^.  The  extent  of  thia  apparent  dio- 
nlaoensDt  of  the  object  wonld  be  meaannd 
n  the  angle  10^,  which  the  diameter  ix" 
«  the  earth'a  path  or  orbit  woold  anbtend 
at  the  elgect  o. 

It  baa  been  atated  that,  in  general,  the 
nparent  dinlaoement  of  a  distant  rinble 
ugect  pndnced  l^  an;  change  in  the  ata- 
tion  fronwbioh  it  15  Tiewedia  called  FABAii- 
ii&x.  That  whieh  ia  prodiuiod  by  the 
ohange  of  pontion  dne  to  the  dinmal  motion 
of  the  earth  being  called  muBMAi.  fabai^ 
diqiheement  dne  to  the  annnal  motion  of 


aMRWBCB 

hkMlbd 


Ike  ABinFAL  PABALLAX. 


178  ASTBOVOMT* 

The  matest  amount,  tiiereforey  of  the  nmiBl  imdhx  fir  my 
propoeed  object  ia  the  angle  which  the  aemidiameier  of  the  earth^ 
orbit  anbtenda  at  such  object,  aa  the  ffreateat  amoant  of  the  dinnal 
parallax  ia  the  angle  which  the  aemiiuameter  of  the  earth  ilaalf  anb-    ] 
tendfr  at  the  object 

Now,  as  the  most  satiafaotory  evidenoe  of  the  amnud  BuHm  of    \ 
the  earth  would  be  the  discovery  of  thia  disphMeneiit^  and  aae*/  '; 
oesaive  changes  of  apparent  position  of  all  objeeta  on  the  fiiBaaianU  ' 
conaeauent  on  auch  motion,  the  absence  of  aw  audi  phenoManoni 
mnat  DO  admitted  to  oonstitnte,  jm'ma/octe,  a  rarmidaUa  wgiuaattlt 
againat  the  earth's  motion. 

2448.  ifa  effecii  Mpon  the  bodies  of  the  eolar  lysfeM  appormt  ^ 
The  effirata  of  annual  parallax  are  observable,  and  inoMd  ana  ol 
oonaklerable  amount,  in  the  case  of  all  the  bodiea  oompoaiiig  ihit 
solar  system.  The  apparent  annual  motion  of  the  son  ia  altogethei 
due  to  parallax.  The  apparent  motiona  of  the  planets  aad  othei 
bodiea  composing  the  solar  aystem  are  the  effecta  of  parallax,  com- 
bined with  the  real  motions  of  these  varions  bodiea. 

2444.  Bwl  erroneondy  explained  by  the  ancietUe—^jnoUmaii. 
lyifem.  —  Until  the  annual  motion  of  the  earth  was  admitted,  these 
effiscta  of  annual  parallax  on  the  apparent  motions  of  the  aolar  sja- 
tem  were  ascribed  to  a  very  complicated  system  of  real  motions  of 
these  bodies,  of  which  the  earth  was  assumed  to  be  the  stationary 
centre,  the  sun  revolving  around  it,  while  at  the  same  time  the 
pknets  severally  revolved  round  the  sun  as  a  moveable  centre. 
This  hypothesis,  proposed  originally  by  Apollonius  of  Perga,  a 
Grecian  astronomer,  some  centuries  before  the  birth  of  Christ,  re- 
ceived the  name  of  the  PTOLXBfAio  Ststem,  having  been  devel- 
oped and  exphuned  by  Ptolemy,  an  Egyptian  astronomer  who 
flourished  in  Uie  second  century,  and  whose  work,  entitled  *'  Syntax,'' 
obtained  great  celebrity,  and  for  many  centuries  continued  to  be 
received  as  the  standard  of  astronomical  science. 

Although  Pythagoras  had  thrown  out  the  ide%,  that  the  annual 
motion  of  the  sun  was  merely  apparent,  and  that  it  arose  from  a 
real  motion  of  the  earth,  the  natural  repugnancy  of  the  human 
mind  to  admit  a  supposition  so  contrary  to  received  notiona  pre 
vented  this  happy  anticipation  of  future  and  remote  discovery  from 
receiving  the  attention  it  merited;  and  Aristotle,  less  sanoiona  than 
Pythagoras,  lent  the  great  weight  of  his  authority  to  uie  contnuy 
hypothesis,  which  was  accordingly  adopted  univen»lly  by  the  leaned 
world,  and  continued  to  prevail,  until  it  was  overturned  in  the  middle 
of  the  sixteenth  century,  by  the  celebrated  Copernicus,  who  revived 
the  Pythagorean  hypothesis  of  the  stability  of  the  sun  and  the 
motion  of  the  earth. 

2446.  Oopemican  syUem, — The  hypothesis  propoeed  by  him 
in  a  work  entitled  "  De  Revolutionibus  Orbium  Ccolestium,    pob- 


AmrUAL  MOTION  OF  THE  EARTH.  179 

in  1548|  at  Uie  moment  of  bis  death,  is  that  since  known  as 
>FKRiaoAN  System,  and,  being  now  established  upon  eyi- 
soflkientlj  demonstrative  to  ^vest  it  of  its  hjpotheti(»d 
fter,  18  admitted  as  the  exposition  of  the  actual  movements  by 
that  part  of  the  nniyerse  called  the  solar  system  is  affected. 
6.  EffwU  of  annual  parallax  of  the  stars.  —  The  greatest 
itj  against  which  the  Gopemican  system  has  had  to  straggle, 
imong  the  most  enlightened  of  its  opponents,  has  been  the 
»  of  all  apparent  effects  of  parallax  among  the  fixed  stars, 
objects  which  are  scattered  in  snch  countless  numbers  over 
part  of  the  firmament.  From  what  has  been  explained,  it 
e  peroeiyed  that,  supposing  these  bodies  to  be,  as  they  evi- 
must  be,  placed  at  vast  distances  outside  the  limits  of  the 
ystem  and  in  every  imaginable  direction  around  it,  the  effects 
lual  parallax  would  be  to  give  to  each  of  them  an  apparent 
I  motion  in  a  circle  or  ellipse,  accordiuff  to  their  direction  in 
n  to  the  position  of  the  earth  in  its  orbit,  the  ellipse  varying 
eccentricity  with  tlus  position,  and  the  diameter  of  the  circle 
]or  axis  of  the  ellipse  being  determined  by  the  angle  which 
iameter  s  i^'  (Jig,  718)  of  the  earth's  orbit  subtends  at  the 
>eing  less  the  greater  the  distance  of  the  star,  and  vice  versA, 
pparent  position  of  the  star  in  this  circle  or  ellipse  would  be 
lUy  always  in  the  plane  passing  through  the  star  and  the  line 
[g  the  sun  and  earth. 

t7.  Close  resemblance  of  these  to  aberration,  —  Now,  it  will  be 
Bnt,  that  such  phenomena  bear  a  very  close  resemblance  to 
of  aberration  already  described  (2440).  In  both  the  stars 
r  to  move  annually  in  small  circles  when  situate  90^  from  the 
ie;  in  both  they  appear  to  move  in  small  ellipses  between  that 
3n  and  the  ecliptic;  in  both  the  eccentricities  of  the  ellipses 
se  in  approaching  the  ecliptic ;  and  in  both  the  ellipses  flatten 
heir  transverse  axis  when  the  object  is  actually  in  the  ecliptic. 
18.  Yet  aberration  cannot  arise  from  parallax.  —  Notwith- 
ng  this  close  correspondence,  the  phenomena  of  aberration  are 
y  incompatible  with  the  effects  of  annual  parallax.  The  ap- 
t  displacement  produced  by  aberration  is  always  in  the  direo 
f  the  earth's  motion,  that  is  to  say,  in  the  direction  of  the 
Dt  to  the  earth's  orbit  at  the  point  where  the  earth  happens  to 
iced.  The  apparent  displacement  due  to  parallax  would,  on  th^ 
iry,  be  in  the  direction  of  the  line  joining  the  earth  and  sun. 
ipparent  axis  of  the  ellipse  or  diameter  of  the  circle  of  aberra- 
s  exactly  the  same,  that  is  20"42,  for  all  the  stars ;  while  the 
ent  axis  of  the  ellipse  or  diameter  of  the  circle  due  to  annual 
ax  would  be  different  for  stars  at  different  distances,  and  would 
in  fact)  in  the  inverse  ratio  of  the  distance  of  the  star,  and 
not  therefinre  be  the  same  for  all  stars  whatever,  except  on  the 


180  A8XB0V01CT. 

■nppontioQ  that  all  stars  are  at  tbe  SMiie  distanoe  from  tiw  solar 
^jsteiDy  a  soppositicm  that  cannot  be  entertained. 

2449.  Oenavl  €hufnct  of  T^art^^ 
—  Since,  then,  with  two  or  throe  ezcepfcionsy  wfaidi  wSl  be  notieed 
hereafter,  no  traces  of  the  efieots  of  annnal  jpacallaz  hare  been  dis- 
ooYered  among  the  innumerable  fixed  stan  bj  which  the  sdar  sys- 
tem is  suiToondedi  and  sincCi  nererthdesSy  the  annnal  motion  of  tin 
earth  in  its  orbit  rests  upon  a  body  of  eridenee  and  is  saroorted  b? 
arguments  which  must  be  regarded  as  condnsiTe,  the  absence  of 
parallax  can  only  be  ascribed  to  the  &ot  that  the  stars  generallj  an 
placed  at  distances  from  the  soUr  system  compared  with  which  tbi 
orbit  of  the  earth  shrinks  into  a  pdnt^  and  therefbre  that  the  mo> 
tion  of  an  observer  round  this  orlnt,  vast  as  it  may  seem  oompsrol 
with  all  our  familiar  standards  of  magnitude,  prodnoes  no  mors  ai 
parent  displacement  of  a  fixed  star  than  the  motion  of  an  antnuMi 
round  a  grain  of  mustard  seed  would  produce  upon  the  sppaie4 
direction  of  the  moon  or  sun.  ' 

We  shall  return  to  the  subject  of  the  annual  parallaz  of  the  stek 
in  a  subsequent  chapter. 

2460.  Thit  diviriol  omd  omwiud  jphmo^^ 
moltbfM  of  the  earth.  —  Considering,  then,  the  annual  roTdntion  d 
the  earth,  as  well  as  its  diurnal  rotation,  established,  it  remains  to 
show  how  these  two  motions  will  explain  the  Tarious  phenomeoi 
manifested  in  the  succession  of  seasons. 

While  the  earth  reyolyes  annually  round  the  sun,  it  has  a  motion 
of  rotation  at  the  same  time  upon  a  certain  diameter  as  an  axis, 
which  is  inclined  from  the  perpendicular  to  its  orbit  at  an  angle  of 
28°  28'.  During  the  annual  motion  of  the  earth  this  diameter 
keeps  continually  parallel  to  the  same  direction,  and  the  eardi  eom» 
pletes  its  reyolation  upon  it  in  twenty-three  hours  and  llllj^t^ 
minutes.  In  consequence  of  the  combination  of  this  moticii  of  ro- 
tation of  the  earth  upon  its  axis  with  its  annual  motion  loond  the 
sun,  we  are  supplied  with  the  alternations  of  day  and  night,  and 
the  succession  of  seasons. 

When  the  globe  of  the  earth  is  in  such  a  pontion  that  it8  north 
pole  leans  to\wd  the  sun,  the  greater  portion  of  its  northern  hemi- 
sphere is  enlightened,  and  the  greater  portion  of  the  southern  hemi- 
sphere is  dark.  This  position  is  represented  in  fig.  719,  where  N 
is  the  north  pole,  and  s  the  south  pole.  The  days  are  therefore 
longer  than  the  nights  in  the  northern  hemisphere.  The  reverse 
is  the  case  with  the  southern  hemisphere,  for  there  the  greater  seg- 
ments of  the  parallels  are  dark,  and  the  lesser  segments  enlightened; 
the  days  are  therefore  shorter  than  the  nights.  Upon  the  equator, 
howcTer,  at  iB,  the  circle  of  the  earth  is  equally  divided,  and  the 
days  and  nights  are  equal.  When  the  south  pole  leans  towards  tho 
sun,  which  it  does  exactly  at  the  opposite  point  of  the  earth's  an* 


ARKCAL  KOnOir  OT  Tns  EARTH.  181 

iml  dibit,  QuvuiutUnceB  m  reversed :  then  the  ityt  are  longer 
than  the  nightB  in  the  Btmthem  hemisphere,  and  the  nights  aro 


Jlg.n9. 


Fig.  T». 


Inger  thtm  th«  Aajs  in  tba  northern  hemisphere.  At  the  intermc- 
4hte  pcinto  of  the  ear&'a  annual  path,  when  the  axis  assnmes  a 
fnititn  pemndieular  to  the  direction  of  the  snn,  fiff.  720,  then 
ll«  eirde  of  lig^t  and  darkness  passes  through  the  poles:  all  paral- 
Us  in  emj  part  of  the  earth  are  eqnally  divided,  and  there  is  eon- 
Bcnientl;  equl  &a,y  and  ni^ht  all  over  the  globe. 

In  the  annesed  perspeebve  diagram,  ^cf.72i,  these  fonr  potations 
d  the  earth  are  exhibited  in  sooh  s  manner  aa  to  be  clearlv  intel- 
lipbls. 


Hf.T!I. 

Od  tbe  day  of  tin  Slst  of  Jnne,  the  north  pole  is  turned  in  the 
fcection  of  the  snn ;  on  the  2Ist  of  December,  the  soatb  pole  is 
tnncd  in  that  direction.  On  tbe  dajs  of  tbe  equinoxes,  the  axis 
of  the  evtb  is  at  right  angles  to  the  direction  of  tne  sun,  and  it  is 
eqnal  day  and  night  everywhere  on  the  earth. 

The  annval  variation  of  tbe  position  of  the  snn  with  rofbrence  to 
r,  or  the  changes  of  its  declination,  arc  cspluncd  by  these 
n^  BOmmer  solstice  —  the  time  when  the  BIu'b  ^a\&iiQ« 
16 


us  ABTR0H0X7. 

from  the  eq|iiAtor  it  the  grealert — takes  plaoe  wImb  Hie  noedi  pole 
heiui  towards  the  sun ;  and  the  winter  solstiee — or  the  time  when 
the  sun's  distance  south  of  the  equator  is  greatest-— takes  phuss 
when  the  south  pole  leans  toward  the  sun. 

In  yirtne  of  tnese  motionS|  it  follows  that  the  son  is  twiee  a  jetr 
vertioal  at  all  plaoes  between  the  tnqpks;  and  at  the  trapios  theiN 
selves  it  is  vertical  once  a  year.  In  all  hi^^wr  latitodes  tiie  poial 
at  which  the  sun  passes  the  meridian  daUr  alternately  approaehes  ti 
and  recedes  from  the  zenith.  From  the  Slst  of  Beoember  mitQ  ths 
2l8t  of  June,  the  point  continuallj  approaches  the  Mmth.  1 
oomes  nearest  to  the  lenith  on  the  2l8t  of  June;  and  from  thatdw 
until  the  2l8t  of  December,  it  contmuallj  reoedes  from  the  Mnittl^ 
and  attains  its  lowest  position  on  the  latter  dsy.  The  diflhmnsl 
therefore,  between  the  meridional  altitudes  of  the  sni  on  the  dsji 
of  the  summer  and  winter  solstioes  at  all  plaoes  wfll  be  tm^l 
twentv-three  decrees  and  twenty-eight  minutesy  or  ibrlj-six  degnA 
and  fifty-six  mmutes.  In  all  plMos  beyond  the  tropics  in  db 
northern  hemisphere,  therefore,  the  sun  rises  at  noon  on  the  im 
of  June,  forty-six  degrees  and  fifty-six  minutes  hMier  than  it  iM 
on  the  21st  of  December.  These  are  the  limits  of  meridioBal  all^ 
tttde  which  determine  the  infiuence  of  the  sun  in  difierent  places. 

2451.  Mean  solar  or  civil  time,  —  It  has  been  explained  that  As 
rotation  of  the  earth  upon  its  axis  is  rigorously  uniform^  and  is  the 
only  absolutely  uniform  motion  among  the  many  and  complicatol 
motions  observable  on  the  heavens.  This  quality  would  render  it 
a  hiffhly  convenient  measure  of  time^  and  it  is  aocordindy  adoptil 
for  that  purpose  in  all  observatories.  The  hands  of  a  mcbreal  cloak 
move  in  perfect  accordance  wml  the  apparent  motion  of  the  fi^ 
mament. 

But  for  civil  purposes,  uniformity  of  motion  is  not  the  on^  eo 
dition  which  must  be  fulfilled  by  a  measure  of  time.  It  is  equallj 
indispensable  that  the  intervds  mto  which  it  divides  duralkm  snonU 
be  marked  by  conspicuous  and  universally  observable  phenomraa.. 
Now  it  happens  that  the  intervals  into  which  the  diurnal  revolution 
of  the  heavens  divides  duration,  are  marked  by  phenomena  which 
astronomers  alone  can  witness  and  ascertain,  but  of  which  manldnd 
in  general  are,  and  must  remain,  altogether  unconscious. 

2452.  Oiml  day  —  noon  and  midnight,  —  For  the  purposes  of 
common  life,  mankind  by  general  consent  has  therefore  adopted  the 
interval  between  the  successive  returns  of  the  centre  of  the  sen's 
disk  to  the  meridian,  as  the  unit  or  standard  measure  of  time.  TUi 
interval,  called  a  civil  dat,  is  divided  into  24  equal  parts  ealM 
HOURS,  which  are  again  subdivided  into  minutes  and  seeonds  as 
already  explained  in  relation  to  sidereal  time.  The  hours  of  the 
dvil  cby,  however,  are  not  counted  from  0  to  24,  as  in  sidereal  tim% 
but  are  divided  into  two  equal  parts  of  12  hours,  one  oommeneiig 


AHVUAL  Mon<nr  w  thb  eabtel  188 

hmk  die  ontra  ol  the  iim  k  on  the  moridiaoi  tlie  moment  of  wlu^ 
\  called  HOON  or  hid-dat;  and  the  other  12  honn  later,  when  the 
autre  of  the  ton  moat  pua  the  meridian  below  the  horiaon;  the 
aoment  of  whieh  la  MiDinaHX. 

For  eiTil  pnrpoaey  diia  latter  moment  haa  been  adopted  aa  the 
Bsamenoenient  of  one  day,  and  the  end  of  the  other. 

2458.  Difirmce  heiwem  meaim  $ohr  and  iidereal  Htne.  —  A 
■k  dsy  is  efidendy  longior  than  a  sidereal  day.  If  the  ann  did 
Ml  dui^oe  iti  norition  on  the  firmament,  ita  oentre  would  return  to 
fta  moiidian  after  the  aame  intenral  that  elapaes  between  the  aoe- 
teannta  of  a  fixed  ater.  But  ainoe  the  aun,  aa  haa  been 
mofea  al  the  rate  of  about  1^  per  day  firom  west  to 
and  rinea  thia  motion  takea  place  upon  the  ecliptioi  which  ia 
'  to  the  eqpator  at  an  anj^e  <^  28^  28',  the  centre  c^  the  sun 

\  ita  right  aaoenaion  firom  day  to  day,  and  thia  inereaae  Tariea 

laiwuling  to  ita  pontion  on  the  ediptic.  when  the  circle  of  dedi- 
anSon  on  whioh  the  centre  of  the  aun  ia  placed  at  noon  on  one  day 
ainna  to  the  meridian  the  next  day,  the  centre  of  the  sun  will  haye 
Irfl  iL  and  will  be  fimnd  upon  another  circle  of  declination  to  the 
OMi  or  it;  and  it  will  not  conaequently  come  to  the  meridian  until  a 
far  WT""*—  later,  when  thia  other  circle  of  declination,  by  the  di- 
wnti  motion  of  the  heavena,  shall  come  to  coincide  with  the  meridian. 
Henoe  the  aolar  day  la  longer  than  the  sidereal  day. 

S464.  DUbreiiee  heiwem  amairent  noon  and  mean  noon.  —  But 
dMCy  fkom  the  oanae  juat  atated  and  another  which  will  be  presently 
aiphjnedi  the  daily  inereaae  of  the  aun's  riffht  ascension  ia  variable, 
Aa  dififarenee  between  a  sidereal  day  and  ue  interval  between  the 
SBBBeaHfv  tnmaitB  <tf  the  sun  is  likewise  variable,  and  thus  it  would 
UDow  thai  the  adar  daya  would  be  more  or  less  unequal  in  length. 

S466.  Meam  adlar  time — Equaiion  of  time. — Hence  has  arisen 
m  expedient  adq^  for  civil  purposes  to  efhce  this  inequality.  An 
tammaiy  aon  ia  conceived  to  accompany  the  true  sun,  making  the 
Maplele  revolution  of  the  heavena  with  a  rigorously  uniform  increase 
tf  nght  aacenaion  firom  hour  to  hour,  while  the  increase  of  the  right 
■■wffcfiffn  of  the  true  sun  thus  variea.  The  time  measured  by  the 
sotioii  of  thia  imaginary  sun  is  called  mxan  solar  time,  and  the 
lima  msaaiiiiiil  by  the  motion  of  the  true  sun  is  called  appabemt 
aoLUtsm. 

The  jiffffyr*^  between  thjs  apparent  and  mean  solar  time  is  called 

fa  ^IQUAnOM  OV  TIMX." 

The  variation  of  the  increase  of  the  sun's  rijght  ascension  being 
Naked  within  narrow  limits,  the  true  and  imagmary  suns  can  never 
hifa  asonder,  and  consequentlv  tiie  diffiBrence  between  mean  and 
iRiient  time  ia  never  consideraDle. 


i 


!Rie  time  indksated  by  a  wMmJ  is  9tfmm^  rtm^j  ^k^  im 
hj  an  exaotly  r^;alated  olodk  or  waioh  ip  nepn  fjme. 

The  oorrection  to  be  afiplied  to  i^qprnnt  time^  to  ledoo 
mean  time,  is  often  engraved  on  svii'diabi  where  it  is  atate 
mnch  ''tbe  enn  is  too  £ut  or  too  Aow." 

2456.  IXstance  of  the  mm. — Althongh  tbe  ptMfiWi  to  ^et 
with  the  greatest  practioal  jireeinon  the  oistuioe  of  die  son  fr 
eerth  is  attended  widi  great  diffieoltiesy  menv  phenomena  < 
ob0ar▼ado^  enpplyihe  means  of  asoertuuiiff  tnat  thb  distaap 
bear  a  yerj  (peat  proportion  tp  the  eutirs  Sameieri  or  io 
soeh  thaty  t>7  oomparison  inth  it,  a  line  8000  mileB  in  lei 
ahnostapomt  If,  for  example,  Uieai^MuwntdiBbuMeq^  the 
irf  the  son  jftom  any  fixed  star  tie  observed  HiiniiTtaneoQsly  in 
pkeeenpon  the  eaith,n6  nmtter  how  fkr  they  are  u^ 
wQl  be  disoovered  between  them,  nnless  means  of  lAaervalii 
oeptible  of  extraordinair  precision  be  resorted  ta  $he  expi 
by  irhvAi  the  anparent  aiqplioement  of  the  son's  eente  by  a 
of  pomtion  of  tne  observer  from  one  extremity  of  a  di>uneter 
eijrtti  to  the  other,  or,  what  is  the  same^  the  apparent  magnit 
the  diameter  of  the  eurth  ss  it  wonld  be  see(n  rann  thesnn,  hi 
aseertsined,  will  be  explained  hereafter.  Meanwhile,  howc 
may  be  stated  that  this  visual  angle  amounts  to  no  more  than 
or  about  the  hundredth  part  of  the  apparent  diameter  of  the 
seen  from  the  earth. 

Supplied  with  this  datum,  and  the  actual  magnitude  of  the 
tor  of  the  earth,  we  can  calculate  the  distance  of  the  sun  by  t 
explained  in  2298.  If  r  express  the  distance  of  the  sun,  an< 
diameter  of  the  earth,  we  shall  have 

2,062,660  „  ^^^ 

r=    '      ' — X  a  =  11,992X0. 

It  appears,  therefore,  that  the  distance  of  the  sun  is  equal  to 
diameters  of  the  earth,  and  since  the  diameter  of  the  earth  m^ 
about  7900  miles  (2389),  the  distance  of  the  sun  must  be 

11,992  X  7900  =  94,736,800  miles. 

or  very  nearly  NiNBTT-nvE  millions  of  milss. 

Since  the  mean  distance  of  the  earth  from  the  son  ha 
adopted  as  the  unit  or  standard,  with  reference  to  which  astroi 
distances  ^nerally  are  expressed,  it  is  of  the  highest  import 
ascertain  its  value  with  the  greatest  precision  which  oar  m 
observation  and  measurement  admit  By  elaborate  calcu 
based  upon  the  observations  made,  in  1769,  on  the  transit  of 
it  has  accordingly  been  shown  by  Professor  Enok^,  that  wb 
earth  is  at  its  mean  distance  from  the  sun,  the  semidiameter 
terrestrial  equator  subtends  at  the  sun  an  angle  of  8"'5776. 
ii  therefore  the  mean  equatorial  horizontal  penllax  of  the  sui 


AHNUAL  MOTION  Of  THB  BARTH.  185 

if  r  expieM  the  aemidiaiiieter  of  the  equaloTi  and  D  the  me^ 
(if  the  earth  from  the  suiii  we  shall  therefore  have 

206265  ^^^,^ 

^=¥5776^'  =  ^^^^''' 

\md  fliiiee  the  semidiameter  of  the  eqpator  measures  3962-8  miles 

■  ii889\  it  follows  that 

rV  D  =  95^3,452. 

an  the  numerical  results  of  ohservatkm  and  measurement 
liable  to  some  amoont  of  error,  it  Is  important^  when  pieciiiion 
is  lecinized,  to  know  the  limit  of  this  error,  in  order  to  appreciate 
fta  extent  to  which  sach  resnlts  are  to  be  relied  upon.  In  all  cases 
lUi  b  posriUe,  a  major  and  minor  limit  of  the  compated  or  obeerred 
fHDtity  being  assignable,  which  cannot  be  exceeded.  In  the  present 
esas  the  ^alne  of  d  cannot  yarj  from  the  troth  bj  more  than  its 
Ihfee-hnndredth  part;  that  is  to  saj,  the  actoal  mean  distance  ci 
>fhe  earth  from  the  snn,  or  the  semiaxis  major  of  the  orbit^  cannot 
fts  greater  than 

95,293,452  +  117,645  =  95,411,097  miks, 
trbsB  than 

95,293,452— 117,645  =95,175,807  miles. 

2457.  Linear  value  of  V  ai  the  tun'i  dutance,  —  Bj  what  has 
been  explained  in  2298,  it  af^pears  that  the  linear  Tsloe  of  I''  at  the 
son's  distance  is 

95,000,000^ 

206,265  ^^ 

2458.  Daily  and  hourly  apparent  motion  of  the  mm,  and  real 
fnotion  of  the  earth. — Since  the  son  moves  over  360^  of  the  heaTens 
in  365i  days,  its  daily  apparent  motion  most  be  59^-14,  or  354%^, 
which  beine  abont  twice  the  son's  apparent  diameter,  it  is  easy  U} 
remember  uat  Uie  diak  of  the  son  appears  to  more  in  Uie  firmament 
daily  ovtsr  a  space  nearly  cqoal  to  twice  its  own  apparent  diameter. 
Its  hoorly  apparent  motion  is 

Snce  V  at  the  son's  distance  is  eqoal  to  466  miles,  and  rinee  the 
real  orbitoal  motion  is  eqoal  to  that  which  the  son  woold  haTC  if  it 
mowed  roond  the  earth  in  a  year,  it  follows  that  the  daily  orbitoal 
reotioa  of  the  earth  is 

3548  X  466  =  1,653,368  miles, 
aad  its  motions  per  hoar,  mioote,  and  second,  are 

68,890  miles  per  hoar, 
1,148  miles  per  minote, 
19  1  miles  per  seoond. 

16* 


186  A8f itamifv. 

2469.  OrUio/A0eariheB^pAci,'--U^htitn^ 
oonsidered  the  path  of  the  eam  mrouid  tl|e  mx^  cribd  hf  miho- 
noBien  its  ORBir,  to  be  a  Qbcle,  io  tiio  eentre  of  whicii  the  eeoin 
of  the  sun  is  plaoed.    Thb  is  neailjr  ^nie^  bit  not  eiaedy  lo^  as 
will  appear  from  the  following  observed  phenomena. 

Let  a  telescope  sapf^ed  wuh  the  miflfooMlm  wfaes  teaAed  h 
2817,  be  directed  to  the  son,  and  tiie  wires  se  ai^MAsd  4M  ^ 
shall  ezaoUy  touch  the  npper  and  lower  limbS|  as  infy.  722.  Ifl 
the  obsenror  then  watch  tan  day  to  day  the  ippeasanse  of  fbe  4P 


JJ 


and  the  position  oi  the  wires;  hewillind  tha^afkerteevfauatiaM 
the  wires  will  no  longer  touch  the  sun,  but  will  perhaps  ftU  a  litl^ 
within  it^  as  represented  in/|^.  728.  And  after  •  fiiraier  lajpss  rf 
timoi  he  will  find,  on  the  other  hand,  that  they  fiill  a  little  wil|i^ 
it,  as  in  y^.  724. 

Now,  as  the  wires  throughout  such  a  series  of  observations  sie 
maintained  always  in  the  same  position,  it  follows  that  the  disk  of 
the  sun  must  appear  smaller  at  one  time,  and  larger  at  another— 
that,  in  fact,  the  apparent  magnitude  of  the  sun  must  be  variaUe. 
It  is  true  that  this  yariation  is  confined  within  very  small  limits,  but 
still  it  is  distinctly  perceptible.  What,  then,  it  may  be  asked,  must 
be  its  cause  ?  Is  it  possible  to  imagine  that  the  sun  realfy  under^ 
ffoes  a  chanae  in  its  size  f  This  idea  would,  under  any  drcum- 
stances,  be  absurd ;  but  when  we  have  ascertained,  as  we  may  doi 
that  the  chauee  of  apparent  magnitude  of  the  sun  is  regular  aal 
periodical  —  that  for  one  half  of  the  year  it  continually  diminishes 
until  it  attains  a  minimum,  and  then  for  the  next  half  year  it 
increases  until  it  attains  a  maximum — such  a  supposition  as  that 

incredible. 

K,  then,  an  actual  change  in  the  magnitude  of  the  sun  be  impos- 
sible, there  is  but  one  other  conceivable  cause  for  the  change  in  its 
apparent  magnitude — which  is,  a  corresponding  change  in  the 
earth's  distance  firom  it  If  the  earth  at  one  time  be  more  remols 
than  at  another,  the  sun  will  appear  proportionally  smaller.  TUs 
is  an  easy  and  obvious  explanation  of  the  changes  of  appearanes 
that  are  observed,  and  it  has  been  demonstrated  accordingly  to  be 
the  true  one. 

On  examining  the  change  of  the  apparent  diameter  of  the  sun,  it 
is  foand  that  it  is  least  on  the  1st  of  July,  and  greatest  on  the  31st 


AHNUAL  MOTIOK  OF  THB  BARTIL 


187 


of  December;  thai  firom  December  to  Jnly,  it  regularly  decreases; 
and  from  Jolv  to  December,  it  regularly  increases. 

Since  tbe  distance  of  the  earth  from  the  sun  must  increase  in  the 
•ame  ratio  as  the  apparent  diameter  of  the  sun  decreases,  and  vic^ 
wend  (1118X  the  variation  of  the  distance  of  the  earth  from  the  sun 
ii  erery  position  which  it  assumes  in  its  orbit  can  be  exactly  ascer" 
tmied.  A  plan  of  the  form  of  the  orbit  may  therefore  be  laid 
iovn,  haying  the  point  occupied  by  the  centre  of  the  snn  marked  in 
tL  Snch  a  plan  proves  on  geometric  examination  to  be  an  ellipse, 
the  plaM  of  the  sun  being  one  of  the  foci. 

2460.  Method  o/ducrtbtng  an  dlipae  —  its  foci,  axis,  and  eccen- 
triciiy,  — If  the  ends  of  a  thread  be  attached  to  two  points  less 
distant  from  each  other  than  its  entire  length,  and  a  pencil  be  looped 
in  the  thread,  and  moved  round  the  points,  so  as  to  keep  the  thread 
tigbt,  it  will  trace  an  ellipse,  of  which  the  two  points  are  the  EOOI. 

The  line  drawn  joining  the  foci,  continued  in  both  directions  to 
the  ellipse,  is  called  its  tbansy erse,  or  major  axis. 

Another  line,  passing  through  the  middle  point  of  this  at  right 
■gks  to  it,  is  called  its  minor  axis. 

The  middle  point  of  the  major  axis  is  called  the  centre  of  the 
dlipae. 

The  fractional  or  decimal  number  which  expresses  the  distance 
if  the  focus  from  the  centre,  the  semiaxis  major  being  taken  as  the 
nit^  is  called  the  eccentricity  of  the  ellipse. 

In  fi(/.  725,  0  is  the  centre,  s 
and  8  the  foci,  A  B  the  transverse 
axis. 

The  less  the  ratio  of  s  s'  to  A  b, 
or,  what  is  the  same,  the  less  the 
eccentricity  is,  the  more  nearly  the 
form  of  the  ellipse  approaches  to 
that  of  a  circle,  and  when  the  foci 
actually  coalesce,  the  ellipse  be- 
comes an  exact  circle. 

Kg.  725.  2AQ1,  Eccentricity  of  the  earth's 

orbit.  —  The  eccentricity  of  the 
elliptic  orbit  of  the  earth  is  so  small,  that  if  an  ellipse,  representing 
truly  that  orbit,  were  drawn  upon  paper,  it  would  be  distinguishable 
from  a  circle  only  by  submitting  it  to  exact  measurement.  The 
tteentrieity  of  the  orbit  has  been  ascertained  to  be  only  001679. 
The  semiaxis  major,  or  mean  distance,  being  10000,  the  greatest 
md  least  distances  of  the  earth  from  the  sun  will  be  — 

B  8  =  10000  +  001679  =  101679 
A  8=  10000  — 0  01679  =  0-98321. 


188 


ASTBOirOMr. 


The  difftrenoe  between  Uiefle  extreme  distanoee  b,  fliersfbRiy  onljr 
0-08858.  So  thet  the  differenee  between  the  flreetest  and  leul 
distances  does  not  amount  to  so  much  as  fonr  nandredths  of  the 
mean  distance. 

2402.  Perihdum  and  apMion  of  Ae  earA.  — The  positioDS  i 
and  By  where  the  earth  is  nearest  to,  and  most  dialaat  fkon,  Hi 
ann,  are  called  pebihsuon  and  aphxuok. 

The  positions  of  these  points  axe  asoertained  bj  obaerfiiig  dp 
places  of  the  snn  when  its  apparent  diameter  is  mi^est  and  umIl;. 
It  is  evident  from  what  has  been  stated  that  the  earth  ia  in  apW> 
lion  on  Ist  Jnlj,  and  in  perihelion  on  Ist  Jannaiy. 

Oontrary  to  what  might  be  ezpeotedi  therelbiey  the  earth  is  nun 
distant  from  the  snn  in  summer  than  in  winter. 

2408.   VariaJtionM  of  temperaturt  tkrough  Ae  jfeor. «— The  SM* 
cession  of  spring,  summcTi  antamn,  and  winter,  and  the  vaiktioBi    ' 
of  temperatore  of  the  seasons  —  so  fiur  as  these  Taiktions  depeni 
on  the  position  of  the  snn — will  now  reqmre  to  be  explained. 

The  mflnence  of  the  snn  in  heating  a  portion  of  the  eartfa'a  sn^ 

ftoCi  will  depend  partij  on  its  altitude  above  the  hoiuon.    The 

greater  that  altitude  is,  the  more  perpendicularly  the  rajs  will  Vh^ 

and  tiie  greater  will  be  their  calonfic  effect 

To  explain  this,  let  us  suppose  abod,^.  720,  to  represent  a 

beam  of  the  solar  light;  let  on 
represent  a  portion  of  the  earth's 
sur&oe,  upon  which  the  hem 
would  Ml  perpendicularly;  and 
let  0  E  represent  that  portion  on 
which  it  would  fall  obliquely ;  the 
same  number  of  rays  will  strike 
the  surfaces  0  D  and  o  E ;  but  the 
surface  o  £  being  obviously  sreater 
than  OD,  the  rays  will  necessarily  fall  more  densely  on  thelattw: 
aud  as  the  heating  power  must  be  in  proportion  to  the  density  of 
the  rays,  it  follows  that  o  d  will  be  heated  more  than  o  B  in  just  the 
same  proportion  as  o  E  is  greater  than  o  d.  But  if  we  would  com- 
pare two  surfaces  on  neither  of  which  the  sun's  rays  fall  perpendi- 
cularly, let  us  take  0  E  and  o  F.  They  fall  on  0  E  with  more  obli- 
auity  than  on  of;  but  CE  is  evidently  greater  than  OF,  and 
lierefore  the  rays,  being  diffused  over  a  larger  surface,  are  ksB 
dense,  and  therefore  less  effective  in  heating. 

The  calorific  effect  of  the  sun's  r^  on  a  surface  more  oblique  to 
their  direction  than  another  will  then  be  proportionably  leas. 

If  the  sun  be  in  the  zenith,  its  rays  will  strike  the  surface  ne^ 
pendicularly,  and  the  heating  effect  will  therefore  be  greater  tnaD 
when  the  sun  is  in  any  other  position. 

The  greater  the  altitude  to  which  the  sun  rises,  the  less  obliquely 


Fig.  726. 


ANNUAL  MOTION  OF  TlIE  EARTH.  }&9 

will  be  the  directioii  in  which  its  rays  will  strike  the  surface  at 
noou,  and  the  more  effective  will  be  their  heating  power.  So  far, 
then,  as  the  heating  power  depends  on  the  altitude  of  the  snn^  it 
will  be  increased  with  eveiy  increase  of  its  meridian  altitude. 

Hence  it  is  that  the  heat  of  summer  increases  as  we  approach  the 
equator.  The  lower  the  latitude  is,  the  greater  will  be  the  height 
to  which  the  sun  will  rise.  The  meridian  altitude  of  the  sun  at  the 
Bummer  solstice  being  everywhere  outside  the  tropics  forty-six 
d^;ree8  and  fif^-six  minutes  more  than  at  the  winter  solstice^  the 
heating  effect  will  be  proportionately  greater. 

Bat  this  is  not  the  only  cause  which  produces  the  greatly  superior 
heat  of  summer  as  compared  with  winter,  especially  in  the  higher 
latitudes.  The  heating  effect  of  the  sun  depends  not  alone  on  its 
altitude  at  midday;  it  also  depends  on  the  length  of  time  which  it 
is  above  the  horizon  and  below  it  While  the  sun  is  above  the 
horixon,  it  is  continually  imparting  heat  to  the  air  and  to  the  surfiice 
of  the  earth ;  and  while  it  is  below  the  horizon^  the  heat  is  con- 
tinually being  dissipated.  The  longer,  therefore, — other  things 
leiuff  Uie  same,  — the  sun  is  above  the  horizon,  and  the  shorter  time 
it  is  Delow  it,  the  greater  will  be  the  amount  of  heat  imparted  to  the 
earth  every  twenty-four  hours.  Let  us  suppose  that  between  sun- 
rise and  sunset,  the  sun,  by  its  calorific  effect,  imparts  a  certain 
amount  of  heat  to  the  atmosphere  and  the  surface  of  the  earth,  and 
that  from  sunset  to  sunrise  a  certain  amount  of  this  heat  is  lost : 
the  result  of  the  action  of  the  sun  will  be  found  by  deducting  the 
latter  fjrom  the  former. 

Thus,  then,  it  appears  that  the  influence  of  the  sun  upon  the 
seasons  depends  as  much  upon  the  length  of  the  days  and  nights  as 
upon  its  altitude ;  but  it  so  happens  that  one  of  these  circumstances 
depends  upon  the  other.  The  greater  the  sun's  meridional  altitude 
iSy  the  longer  will  be  the  days,  and  the  shorter  the  nights ;  and  the 
less  it  is,  the  longer  will  be  the  nights,  and  the  shorter  the  days. 
Thus  both  circumstances  always  conspire  in  producing  the  increased 
temperature  of  summer,  and  the  diminished  temperature  of  winter. 

2464.  ITAy  the  longest  dai/  is  not  also  the  hottest.  —  The  dog- 
days.  —  A  difficulty  is  sometimes  felt  when  the  operation  of  these 
causes  is  considered,  in  understanding  how  it  happens  that,  not- 
withstanding what  has  been  stated,  the  2l8t  of  June  —  when  the 
sun  rises  the  highest,  when  the  days  are  longest  and  the  nights 
shortest  —  is  not  the  hottest  day,  but  that,  on  the  contrary,  the 
dog-days,  as  they  are  called,  which  comprise  the  hottest  weather  of 
the  year,  occur  in  August;  and  in  the  same  manner,  the  2l8t  of 
December  —  when  the  height  to  which  the  sun  rises  is  least,  the 
days  shortest,  and  the  nights  longest  —  is  not  usually  the  coldest  day, 
but  that,  on  the  other  hand;  the  most  inclement  weather  occurs  at  a 
later  penod. 


190  ASTBOHomr. 

To  mlain  this,  so  &r  is  it  depends  on  tlie  posilioii  of  llie  Mi 
•ad  the  length  of  the  days  and  nights,  we  an  to  nomwHw  tha  M 
lowing  eircumstances :—  f. 

As  midmimmer  approachesi  the  gradual  inerease  of  ihe  teBM^i 
ratore  of  the  weather  has  beien  ezphdned  thos:  The  dm  * 
e<msiderably  longer  than  the  nights,  the  qoanti^  of  heat  in 

Sr  the  son  during  the  day  is  ffreater  than  the  qoantilj  lost  _ 
e  night;  and  the  entire  result  during  the  twenty-Amr  horn 
an  increase  of  heat  As  this  augmentation  takes  phoe  after 
sucoessiye  day  and  night,  the  general  tempenlove  oontmiMS  to 
crease.  On  the  2l8t  of  JunCi  when  the  day  is  kngesl^  aad 
idght  is  shortest,  and  the  sun  rises  UigheBty  this  angMiil 
rsMhes  its  maximum;  but  the  temperature  of  the  wcatlier 
not  therefore  oease  to  inerease.  After  the  2lBt  of  June  tlien  dik 
tinues  to  be  still  a  daily  augmentation  of  heat;  fe  the  mm  still  ci^ 
tinues  to  impart  more  heat  during  the  day  than  is  lost  during  Ai 
night.  The  temperature  of  the  weather  inll  therefore  only  cease  1^ 
increase  when,  by  the  diminished  length  of  the  day,  the  incressri 
length  of  the  night,  and  the  diminished  meridional  altitude  of  As 
sun,  the  heat  imparted  daring  the  day  is  just  balanced  by  the  hoi 
lost  during  the  night  There  will  be,  then,  no  further  incresse  of 
temperature,  and  the  heat  of  the  weather  will  have  attained  its 
maximum. 

But  it  might  occur  to  a  superficial  observer,  that  this  zeasooiBi 
would  lead  to  the  conclusion  that  the  weather  would  ocmtinue  to 
increase  in  its  temperature,  until  the  length  of  the  days  woill 
become  equal  to  the  length  of  the  nights ;  and  such  would  be  the 
case,  if  the  loss  of  heat  per  hour  during  the  night  were  equal  to  tibsi 

Sin  of  heat  per  hour  during  the  day.  But  such  is  not  the  esse; 
e  loss  is  more  rapid  than  the  gain,  and  the  consequenoe  isL  tiisi 
the  hottest  day  usually  comes  within  the  montii  of  Jmy^  but  wrqi 
long  before  the  day  of  the  autumnal  equinox. 

The  same  reasoning  will  explain  why  the  coldest  weathor  dom 
not  usually  occur  on  the  2l8t  of  Decemlier,  when  the  day  is  shorteit 
and  the  nieht  longest,  and  when  the  sun  attains  the  lowest  meridi- 
onid  altitude.  The  decresse  of  the  temperature  of  the  weather 
depends  upon  the  loss  of  heat  during  the  night  being  greater  thsa 
the  gain  durinff  the  day ;  and  until,  by  the  increased  length  of  the 
day  and  the  cuminished  length  of  the  night,  these  effectn  are  ba- 
lanced, the  coldest  weather  will  not  be  attained. 

These  observations  must  be  understood  as  applying  only  so  &r  ss 
the  temperature  of  the  weather  is  affected  by  the  sun,  and  by  the 
lensth  of  the  days  and  nights.  There  are  a  variety  of  other  kcsl 
and  geographical  causes  which  interfere  with  these  effects,  and  vary 
them  at  diffsrent  times  and  places. 

On  referring  to  the  annual  motion  of  the  earth  round  the  siiB|  it 


ANNUAL  MOTION  OF  THB  EARTH.  191 

appears  Uiat  the  position  of  the  sun  within  the  elliptic  orbit  of  the 
earth  is  such  that  the  earth  is  nearest  to  the  sun  about  the  1st  of 
Janoarj,  and  most  dbtant  from  it  about  the  1st  of  July.     As  the 
edorific  power  of  the  sun's  rajs  increases  as  the  distance  from  the 
Mjth  diminishes,  in  even  a  higher  proportion  than  the  change  of 
distaiioes,  it  might  be  expected  that  the  effect  of  the  sun  in  heating 
the  earUi  on  the  1st  of  cTanuary  would  be  considerably  greater  than 
QO  the  Ist  of  July.     If  this  were  admitted^  it  would  follow  that  the 
nnnal  motion  of  the  earth  in  its  elliptic  orbit  would  have  a  ten- 
dency to  diminish  the  cold  of  the  winter  in  the  northern  hemisphere, 
and  mitigate  the  heat  of  summer,  so  as  to  a  certain  extent  to  equalize 
the  seasons;  and,  on  the  contraiy,  in  the  southern  hemisphere, 
where  the  Ist  of  January  is  in  the  middle  of  summer,  and  the  1st 
of  July  in  the  middle  of  winter,  its  effects  would  be  to  aggravate  the 
eold  in  winter  and  the  heat  in  summer.    The  investigations,  how- 
evcTy  which  have  been  made  in  the  physics  of  heat,  have  shown 
thai  that  principle  is  governed  by  laws  which  counteract  such  effects. 
Like  the  operation  of  all  other  physical  agencies,  the  sun's  calo- 
rific power  requires  a  definite  time  to  produce  a  given  effect,  and  the 
heat  received  by  the  earth  at  any  part  of  its  orbit  will  depend  con- 
jointly on  its  distance  from  the  sun  and  the  length  of  time  it  takes 
to  traverse  that  portion  of  its  orbit     In  fact,  it  has  been  ascertained 
thai  the  heating  power  depends  as  much  on  the  rate  at  which  the 
sun  changes  its  longitude  as  upon  the  earth's  distance  from  it. 
Now  it  happens  that,  in  consequence  of  the  laws  of  the  planetary 
motions,  duicovered  by  Kepler,  and  explained  by  Newton,  when  the 
earth  is  most  remote  from  the  sun,  its  velocity  is  least,  and  conse- 
quently the  hourly  changes  of  longitude  of  the  sun  will  be  propor- 
tionally less.     Thus  it  appears  that  what  the  heating  power  loses 
by  augmented  distance,  it  gains  by  diminished  velocity ;  and  again, 
when  the  earth  is  nearest  to  the  sun,  what  it  gains  by  diminished 
distance,  it  loses  by  increased  speed.    There  is  thus  a  complete  com- 
pensation produced  in  the  heating  effect  of  the  sun,  by  the  dimi- 
nished velocity  of  the  earth  which  accompanies  its  increased  distance. 
This  period  of  the  year,  during  which  the  heat  of  the  weather  is 
asoally  most  intense,  was  called  the  canicular  days,  or  doq 
j    DATS.     These  days  were  generally  reckoned  as  forty,  commencing 
aboat  the  3d  of  July,  and  received  their  name  from  the  fact,  that  in 
ancient  times  the  bright  star  Sirius,  in  the  constellation  of  Canis 
major,  or  the  Great  Dog,  at  that  time  rose  a  little  before  the  sun, 
and  it  was  to  the  sinister  influence  of  this  star  that  were  ascribed 
the  bad  effects  of  the  inclement  heat,  and  especially  the  prevalence 
of  madness  among  the  canine  race.     Owing  to  a  cause  which  will 
be  explained  hereafter  (the  precession  of  the  equinoxes),  this  star 
ao  longer  rises  with  the  sun  during  the  hot  season. 


182 


ASTRONOMY. 


CHAP.  IX. 


THE  MOON. 


2465.  The  motm  an  object  of  popular  interest — Althongh  it  b 
in  mere  magnitude,  and  physically  considered,  ope  of  the  most  ia* 
ngnifioant  bodies  of  the  solar  system,  yet  for  yarioos  reasons  tht 
MOON  has  always  been  regarded  by  mankind  with  feelings  of  pio* 
found  interest,  and  has  been  invested  by  the  popnlar  mind  wHk 
various  influences,  affecting  not  only  the  physical  condition  of  dfe 
globe,  but  also  the  phenomena  of  the  organised  world.  It  has  beii 
as  much  an  object  of  popular  superstition  as  of  sdentifio  observatiorii 
These  circumstances  doubtless  are  in  some  degree  owing  to  ili 
striking  appearance  in  the  firmament,  to  the  various  changes  of 
form  to  which  it  is  subject,  and  above  all  to  its  proximity  to  tin 
earth,  and  the  close  alliance  existing  between  it  and  onr  planet 

2466.  Its  distance.  —  The  distance  of  lb 
moon  is  computed,  by  the  method  expIaSMl 
in  2828,  by  first  ascertaining  its  hornontd 
parallax. 

Lot  £  and  i/,  fg.  727,  be  the  opposite 
ends  of  a  diameter  of  the  earth,  and  let  M 
be  the  place  of  the  moon's  centre.  Let  s 
be  any  conspicuous  star  seen  near  the  mo<m 
in  the  heavens,  in  the  plane  of  the  pointB 
E,  e',  and  M.  The  apparent  distance  of  this 
star  from  the  moon's  centre  is  89  to  an  ob- 
server at  E,  and  it  is  s  /  to  an  observer  at  E*. 
The  difference  of  these  distances  x'f  is  the 
arc  of  the  heavens  which  measures  the  angle 
8m/,  or,  what  is  the  same,  the  angle  em^, 
under  which  the  diameter  Eif  of  the  earth 
would  be  seen  from  the  moon. 

Now  the  arcs  bs  and  8t^  can  be  and 
have  been  measured,  and  their  mean  difier- 
ence  si/  has  been  ascertained  to  be  114'  11^ 
=  6852'',  subject  to  a  slight  variation, 
from  a  cause  which  will  presently  be  ex- 
plained. 

It  appears,  from  what  has  been  explained 
in  2327,  that  half  the  angle  ems'  is  the 
moon's  honzontal  parallax,  which  is  therefore 
57'  6"  ==  3426". 

The  moon's  distance,  therefore,  computed 
Fig.  727.  by  the  formula  explained  in  2328,  is 


THB  HOOK.  198 

206265 

*"  =  -8S6-'**'=*'"^'"*' 

It  follows,  thereforBi  that  the  moon's  distance  is  abont  thirty 
times  the  earth's  diameter;  and  since  the  value  of  the  latter  is  7900 
Biks,  the  moon's  distance  is 

7900  X  80  =  237,000  mUes, 

m,  as  qypean  by  more  exact  computation,  237,630  miles. 

2467.  Linear  value  of  V  on  it,  —  Having  thus  ascertained  the 
aooo's  distance,  we  are  enabled,  by  the  method  exphdned  in  2319, 
to  ascertain  the  actual  length  measured  transversely  to  the  line  of 
won  on  the  moon  which  corresponds  to  the  visual  angle  of  1''. 
lys  length  18 

237630   --.  ., 

206266  =  ^'^^  °'^'- 

By  this  formula  any  space  upon  the  moon,  measured  by  its  visual 
lagle,  can  be  reduced  to  its  actual  linear  value,  provided  its  direc- 
Ibn  be  at  richt  angles  to  the  visual  ray,  which  it  will  be  if  it  be  at 
the  centre  of  the  lunar  disk.  If  it  be  between  the  centre  and  the 
edgeSy  it  will  be  foreshortened  by  the  obliquity  of  the  moon's  sur- 
bob  to  the  line  of  vision,  and,  consequently,  the  linear  value  thus 
ooBpQted  will  be  the  r^  linear  value  diminished  by  projection, 
i^ieh,  however,  can  be  easily  allowed  for,  so  that  the  true  linear 
fafaie  can  ba  obtained  for  every  part  of  the  lunar  disk. 

2468.  Us  apparent  and  real  diameter,  —  The  apparent  diameter 
of  the  moon  is  subject  to  a  slight  variation,  owing  to  a  correspond- 
ing variation  due  to  the  small  ellipticity  of  its  orbit.  Its  mean 
filoa  is  found  to  be  31'  V  or  1867". 

By  what  has  just  been  established  (2392),  therefore,  its  real 
diuneter  must  be 

1867  X  115  =  2147  miles. 

More  exact  methods  give  2153  miles. 

Since  the  superficial  magnitude  of  spheres  is  as  the  squares,  and 
tlieir  volume  or  solid  bulk  as  the  cubes,  of  their  diameters,  it  fol- 
lows that  the  superficial  extent  of  the  moon  is  about  the  fourteenth 
ptit  of  the  snr&ce,  and  its  volume  about  the  forty-ninth  part  of  the 
Mk,  of  our  globe. 

2469.  Apparent  and  real  motion.  —  The  moon,  like  the  sun, 
tppears  to  move  upon  the  celestial  sphere  in  a  direction  contrary  to 
tttt  of  the  diurnal  motion.  Its  apparent  path  is  a  great  circle  of 
t^  sphere,  inclined  to  the  ecliptic  at  an  angle  of  about  5°  8'  48'^ 
It  completes  its  revolution  of  the  heavens  in  27***  7^*  44"*-. 

This  apparent  motion  is  explained  by  a  real  motion  of  the  moon 
fooad  the  earth  at  the  mean  distance  aoove  mentioned,  and  in  the 
ti»e  in  whidi  the  apparent  revolution  is  completed. 

ni.  17 


Itt  ASTEovomr. 

2470.  JBourly  motumf  apparent  amd  rtal, — Sinee  tlie  time  fnkw 
bj  the  moon  to  make  a  complete  revoIntioDy  or  880^  of  the  betveii^ 
is  27''  7^*  44"*  or  655^-73^  it  follows,  that  her  mean  appurent  boImi 
per  dav  is  IS^"  IV  85'',  and  per  hoar  is  82^  42*,  whioh  m  a  Sttb 
more  than  her  mean  apparent  diameter.  The  rate  of  the  bmmh'i 
apparent  moUon  on  the  firmament  may  therefefe  be  lememberad  If 
the  fiict,  that  she  niOTea  orer  the  wngth  of  her  own  sppsRil 
diameter  in  an  honr. 

Since  the  linear  valne  of  1''  at  the  moon's  distMoe  is  1  15  tAi 
the  linear  valne  of  1'  is  6*9  miles,  and,  oonseqnentlyi  the  real  M6m 
of  the  moon  per  hour  in  her  orl^  is  -^ 

6-9  X  82-9  =  227  miles. 

Her  orbitnal  motion  is  therefore  at  the  rate  of  8-8  miles  per  minilii 

2471.  Orbii  eiltptical  —  Althoogh,  in  its  ^eral  fiinn  and  eh^ 
ncter,  the  path  of  the  moon  round  the  earth  is,  like  the  orbits  d 
the  plsnets  and  satellites,  cireolar,  jet  when  safamitCed  to  m 
dbsOTTation,  we  find  that  it  is  stiioUy  an  ellipse  or  ofval,  the 
of  the  earth  ooonpying  one  of  itsybet.  This  fiustesa  be 
bj  immediate  observation  npon  the  apparent  magnitode  of  Al 
moon.  It  will  be  easily  comprehended  that  any  c&mge  which  tti 
apparent  magnitnde,  as  seen  from  the  earth,  nndogoes,  oinsl  wrim 
from  corresponding  changes  in  the  moon's  distance  from  ns.  Tkm^ 
if  at  one  time  the  disk  of  the  moon  appears  larger  than  at  aiioChr 
time,  as  it  cannot  be  supposed  that  the  actnal  siie  <^  tiie  mom 
itself  could  be  changed,  we  can  only  ascribe  the  increase  of  thi 
apparent  magnitude  to  the  diminution  of  its  distance.  Now  we  fiii 
by  observation  that  such  apparent  changes  are  actually  observed  ia 
its  monthly  course  around  the  earth.  The  moon  is  subjeot  to  a 
small  though  perceptible  variation  of  apparent  size.  We  find  that 
it  diminishes  until  it  reaches  a  minimum,  and  then  gradumUy  iih 
creases  until  it  reaches  a  maximum. 

When  the  apparent  magnitude  is  least,  it  is  at  its  greatest  cB^ 
tance,  and  when  greatest,  at  its  least  distance.  The  positions  is 
which  these  distances  lie  are  directly  opposite.  Between  these  two 
positions  the  apparent  size  of  the  moon  undergoes  a  regular  aad 
gradual  change,  increasing  continually  from  its  minimam  to  ill 
maximum,  and  consequently  between  these  positioDs  its  distsnoi 
must  gradually  diminish  from  its  maximum  to  its  minimum.  If  m 
lay  down  on  a  chart  or  plan  a  delineation  of  the  course  or  path  thtf 
determined,  we  shall  find  that  it  will  represent  an  oval,  which  diftis 
however  very  little  from  a  circle ;  the  place  of  the  earth  being  neaier 
to  one  end  of  the  oval  than  the  other. 

2472.  Moon's  apsides — apogee  and  perigee — progreuion  of  As 
cipsu^.'^The  point  of  the  moon's  path  in  the  heavens  at  m\aA 
its  magnitude  appears  the  greatest,  and  when,  therefore,  it  is  near* 


THE  MOON.  195 

ftrthy  is  called  its  perigee  ;  and  the  point  where  itfl  apparent 
east,  and  where,  therefore,  its  distance  from  the  earth  is 
is  called  its  apogee.    These  two  points  are  called  the  mootC% 

I  positions  of  these  points  in  the  heavens  be  observed  aocu- 
r  a  length  of  time,  it  will  be  found  that  they  are  subject  to 
'  change ;  that  is  to  say,  the  place  where  the  moon  appears 
will  every  month  shift  its  position ;  and  a  corresponding 
rill  take  place  in  the  point  where  it  appears  largest  The 
Dt  of  these  points  in  the  heavens  is  found  to  be  in  the  same 
as  the  general  movement  of  the  planets;  that  is,  from  west 
>r  progressive.    Thb  phenomenon  is  called  the  proobes- 

THS  moon's  APSTBES. 

lie  of  this  progressicm  of  the  moon's  apsides  is  40^  68'  in  a 
or  common  year,  being  equivalent  to  6'  41"  per  day.  They 
intly  make  a  complete  revolution  in  8*85  years. 
Moom'$  node$ —  ascending  and  descending  node — their  re- 
9«.  —  If  the  position  of  the  moon's  centre  in  the  heavens 
red  from  day  to  day,  it  will  be  found  that  its  apparent  path 
at  circle,  making  an  angle  of  about  5^  with  the  ecliptic. 
h  consequently  crosses  the  ecliptic  at  two  points  in  opposite 
of  the  heavens.  These  points  are  called  the  moon's  nodes. 
eitioDs  are  ascertained  by  observing  from  time  to  time  the 
of  the  moon's  centre  from  the  ecliptic,  which  is  the  moon^s 
;  by  watching  its  gradual  diminution,  -and  finding  the  pdnt 
I  it  becomes  nothing;  the  moon's  centre  is  then  in  the 
and  its  position  is  the  node.  The  node  at  which  the  moon 
om  the  south  to  the  north  of  the  ecliptic  is  called  the  as- 
node,  and  that  at  which  it  passes  from  the  north  to  the 
called  the  descending  node. 
points,  like  the  apsides,  are  subject  to  a  small  change  of 
but  in  a  retrograde  direction.  They  make  a  complete  revo- 
f  the  ecliptic  in  a  direction  contrary  to  the  motion  of  the 
8-6  years,  being  at  the  rate  of  3'  W'-^  per  day. 

Rotation  on  its  axis.  —  While  the  moon  moves  round  the 
lus  in  its  monthly  course,  we  find,  by  observations  of  its 
ice,  made  even  without  the  aid  of  telescopes,  that  the  same 
ere  is  always  turned  towards  ns.  We  recognise  this  fact 
ving  that  the  same  marks  are  always  seen  in  the  same  posi- 

00  it.  Now  in  order  tliat  a  globe  which  revolves  in  a  circle 
a  centre  should  turn  continually  the  same  hemisphere 
hat  centre,  it  is  necessary  that  it  should  make  one  revolu- 
m  its  axis  in  the  time  it  takes  so  to  revolve.     For  let  us 

that  the  globe,  in  any  one  position,  has  the  centre  round 
t  revolves  north  of  it,  the  hemisphere  turned  toward  the 

1  tamed  toward  the  north.     After  it  makes  a  quarter  of  a 


ASTBOKOMT. 

I,  Aa  Awtre  ia  to  the  cast  of  it,  an^  the  hemwplMn  vUA 
wu  pnriotuly  turned  to  the  north  muat  now  be  tnrned  to  tiM  CMi 
Aftn  it  has  made  sDother  quarter  of  a  rcvoladon  the  oen tie,  will b 
noth  of  it,  and  it  muat  be  now  turned  to  the  sonth.  In  the  mm 
mannsr,  after  another  quarter  of  a  revolution,  it  must  be  tnnied  to 
the  weat     Aa  the  same  hemisphere  ia  snoccsstTlj  turned  lo  all  Ibe 

n'  I  of  the  ooapasa  in  one  revolution,  it  ia  evident  that  the  gkba 
mnat  make  a  single  revolntion  od  its  axis  in  that  time. 

It  appaan,  tlisn,  that  the  rotadpn  of  the  moon  upon  its  axis,  hein; 
woal  to  tlut  of  ita  revolution  in  its  orbit,  is  27^  7'  44"'  or  SiS*^ 
4v^  !nM  intetvala  of  light  and  darknees  to  the  inhabitaals  of  th« 
aoOBi  if  then  were  any,  would  then  bo  altogether  different  finni 
AoH  pnmded  in  the  planeta;  there  would  be  about  327*'  Spot 
•Mtinned  light  alternately  with  327"'  52"'  of  oootinucd  darkRW; 
A*  analogf,  then,  which,  as  will  hereafter  appear,  prevails  araODg 
dw  {dansta  with  regard  to  days  and  nights,  and  which  forma  a  maiD 
tajgBumit  in  &Tour  of  the  ooodusioa  that  they  are  inhabited  glebci 
Uko  tho  oarth,  does  not  hold  good  in  the  case  of  the  moon. 

S47&>  Adinaiiott  of  axig  of  rolation.  —  Although  u  a  gaoml 
prnpunlioa  it  be  true  that  the  same  hemisphere  of  the  mooD  ia  *!■ 
mji  toned  toward  the  earth,  yet  there  are  small  variatiooa  at  die 
•dge,  called  libi&tioDa,  which  it  is  necessary  to  Dob'cc.  The  ana  of 
the  moon  ia  not  exactly  perpendicular  to  its  orbit,  bat  is  inoliiied  at 
the  amall  angle  of  1°  SO*  W'S.  By  reason  uf  this  inclination,  the 
nnthem  and  southern  poles  of  the  moon  lean  alternately  in  a  ^gbt 
dcuree  to  and  from  the  earth. 

2476.  LAration  in  latitude. — When  the  north  pole  leans  towuili 
the  earth,  we  aee  a  little  more  of  that  region,  and  a  little  less  vbes 
it  leans  the  contrary  way.  This  variation  in  the  oorthem  anl 
Bonthem  regions  of  the  moon  visible  to  us,  is  called  the  libkatiom 

»  LATITDDS. 

2477.  Libratton  in  langkude.  —  In  order  that  in  a  strict  »en« 
the  tame  hemisphere  should  be  continually  turned  toward  the  earib, 
the  time  of  rotation  npon  its  aiip  must  not  only  he  equal  to  the  time  of 
rotation  in  its  orbit,  which  in  &ct,  it  is,  bat  its  angular  \elodtj«B 
its  axis  in  every  part  of  its  course,  muat  be  exactly  equal  to  its  » 
golar  velocity  in  its  orbit.  Now  it  happens  that  while  ita  aagaltf 
TClotutf  on  its  axis  is  rigorously  uniform  throughout  the  mcal^  iH 
angular  Tolodty  in  its  orbit  is  subject  to  a  slight  variation ;  the  eoa- 
aaqnence  of  this  is  that  a  little  more  of  its  eastern  or  weatera  edp 
ia  aeen  at  one  time  than  at  another.     This  is  oalled  the  UBBAXll)> 

at  LOMQITDDI. 

2478.  Diumai  UbratUm.  —  By  the  diurnal  motion  of  the  earA, 
WO  are  carried  with  it  ronnd  its  axis ;  the  stations  from  whiA  f* 
liaw  the  moon  in  the  morning  and  evenicg,  or  rather  when  it  liM 
•ad  when  it  sets,  are  then  different  according  to  Ute  UtJtado  of  th* 


IBBHWHI. 


187 


1  in  vhieh  »e  are  plucei].  TJy  tbuB  viciring  it  from  (iifferent 
re  sea  it  undi-'r  slighlly  diffureut  aspecls.  Tills  is  aootb^r 
*  vitmtiaii,  whk'h  wo  see  in  Its  eastern  anil  wealern  eilgoa; 

iJled  tbc  DfL'RSAL  LIBBATIO.V. 
t4T9.   Phatet  «/  the  moon. — While  the  moon  revolves  round  thft 
'     '  a  Ulamiiiaited  hcmiapherc  is  alwajs  presented  to  the  auD  ;   it 
refore  takes  various  poailioas  in  refcreooe  to  the  earth.     Id  Ji^. 
t,  the  effects  of  this  axe  exhibited.     Let  E  s  represent  the  direu- 


Fif.m. 


tNa  <if  tlie  ntn,  and  K  the  earth  ;  when  the  moon  is  at  N,  between 
tha  ma  and  the  earth,  its  illuminated  hemisphere  being  torned  to- 
■ard  ika  mn,  it«  dirk  heminphpro  vill  be  presented  toward  thn 
Mrth ;  it  will  therefore  Ijo  inviuble.  In  thia  poution  the  noon  i:t 
nid  to  be  in  cnKJU.NcnoN. 

Wben  it  move*  to  the  position  c,  the  enlightened  hemisphere  be- 
iig  Mill  preaeatcd  to  tbe  aun,  a  small  portion  of  it  only  is  turned 
to  A»  cutb,  and  it  appeara  as  a  thin  crescent,  a»  repnxented  ftt  r. 

When  the  moon  takn  the  poution  of  q,  at  right  angles  to  the 
warn,  it  ia  Mid  to  be  in  quasoatuse;  one  half  of  the  enlightened 
hwniiphare  onlj  is  then  presented  to  tbe  earlb,  and  the  moon  ap- 
jmn  balTed,  aa  represented  at  9. 

When  it  aniTca  at  tbe  pnutioo  O,  the  greater  part  of  the  en- 
KghtMwd  portion  ia  toned  to  the  earth,  and  it  ia  giblrauj,  appearing 
M  nnmonlcd  at  g. 

WbeD  Ibe  moon  eoroes  in  ofpoeition  to  the  son,  as  seen  nt  j, 
tht  «nlight«wd  hemisphere  ia  tamed  full  toward  tbe  earth,  snd  tho 
■DOB  w31  "nou  fnll,  aa  at  /,  nntera  it  be  obaonred  by  the  earth's 
ikdoT,  whien  ivelj  happenit.  In  tho  same  manner  it  is  shown  Hint 
it  O^  it  ia  agaiB  gibbons;  at  qI  it  is  halved,  and  at  c*  it  ia  a  cctfoent. 


198  ASTROKOMT. 

Wlwn  tha  moon  is  folli  bong  in  oppoaition  to  Iho  warn,  it  will  w^ 
oeHuily  be  in  the  meridian  at  midnight^  and  will  riaa  as  Uw  m 
aetai  and  set  as  tlie  sun  rises;  and  thns,  whene?er  the  enlishtsaii 
hemisphere  is  turned  toward  ns,  and  wlieni  therefimy  it  is  tSe  bhI 
eiqpaUB  of  ben^ting  ns,  it  is  np  in  the  finnanent  all  nUt; 
whereasy  when  it  is  in  oonjnnotion,  as  at  K.  and  tha  daik  hemisMi 
ia  tamed  toward  ns,  it  wooU  then  be  of  no  nse  to  ns^  and  is  a^ 
ooidingly  np  during  the  day.  The  poaition  at  Q  la  eaUad  the  ^lot 
aoartor/' and  at  gr  tha  <<  last  qoarte.''  The  porition  at  o  is  eili|i 
the  fliBt  oeCant;  o  tha  seeond  oetuit;  cT  tha  tUid  oetwt;  mm 
the  fcnrdi  ootant  At  the  iliataiid  fearthoetastoitfaaflBaBIIMf^ 
and  at  the  aeeond  and  third  oetanta  it  ia  gthbons.. 

SMO.  Sjpiodk  period  cr  eimmom  wumA. — TbamanBlmiiMi 
of  the  moon  in  the  heavens  is  modi  more  nfUi  win  Ihat  of- «• 
lan;  fbr  while  the  snnmakea  a  eompieto  sireait  of  theecKpllili 
•66-26  days,  and  therefixe  motes  Ofsr  It  at  aboot  61'  par  dqff  ii* 
moon  moral  at  the  rate  of  18^  IV8&*  (2470)  par  iSj.  A»4fe 
■m  and  moon  appear  to  mofo  'iit  the  same  direeliQB  in  the  lnj|^ 
mesl^  both  pvooeeding  from  w«st  to  esst,  the  moon  will|  aAsr  iii- 
JvaetioD,  depart  ftom  the  snn  toward  the  east  at  tha  into  of  dM 
12^9'  par  day.  If  then,  the  moon  be  in  eonjnnetion  with  tha  saa 
on  any  ffwen  day,  it  will  be  12^  9^  east  of  it  at  the  aame  time  oa 
the  fimcming  day;  24?  18'  east  of  it  after  two  da^  and  ao  on.  If, 
then,  the  sun  set  with  the  moon  on  any  eyening,  it  will,  at  the  mo- 
ment of  sunset  on  the  followiog  evening,  be  12^  9^  east  of  it,  and 
at  sunset  will  appear  as  a  thin  crescent,  at  a  considerable  altitude; 
on  the  succeeding  day  it  will  be  24^  18'  east  of  the  sun,  and  will 
be  at  a  still  greater  altitude  at  sunset,  aud  will  be  a  broader  oreaoent. 
After  seven  days,  the  moon  will  be  removed  nearly  90^  from  the 
sun ;  it  will  be  at  or  near  the  meridian  at  sunset  It  will  remsin 
in  the  heavens  for  about  six  hours  after  sunset,  and  will  be  seen  is 
the  west  as  the  half-moon.  Each  successive  evening  increanng  iU 
distance  from  the  sun,  and  also  increasing  its  breadth,  it  will  be 
visible  in  the  meridian  at  a  later  hour,  and  will  consequently  be 
longer  apparent  in  the  firmament  during  the  nisht — it  will  then 
be  gibbous.  After  about  fifteen  days,  it  will  be  180^  removed  tram 
the  suD,  and  will  be  full,  and  consequenily  will  rise  when  the  son 
sets,  and  set  when  the  sun  rises  —  being  visible  the  entire  ni^t 
After  the  lapse  of  about  twenty-two  days,  the  distance  of  the  moon 
from  the  sun  being  about  270^,  it  will  not  reach  the  meridian  until 
nearly  the  hour  of  sunrise ;  it  will  then  be  visible  during  the  lait 
six  hours  of  the  night  only.  The  moon  will  then  be  waning,  snd 
toward  the  close  of  the  month  will  only  be  seen  in  the  morning  be> 
fore  sunrise,  and  will  appear  as  a  crescent. 

If  the  earth  and  sun  were  both  stationary  ti  bile  the  moon  revolvei 
round  the  former,  the  period  of  the  phases  would  be  the  same  ti 


THX  MOON.  199 

od  of  the  moon.  But  from  what  hu  been  ezplaioedy  it 
Brident  tbat  while  the  moon  makes  its  apparent  reyolation 
leavens  in  about  27*3  days,  the  son  advances  through  some- 
ire  than  27^  of  the  heavens,  in  the  iame  direction.  Before 
n  can  reassume  the  same  phase,  it  must  have  the  same  po- 
slative  to  the  sun,  and  most,  therefore,  overtake  it     Bat 

moves  at  the  rate  of  about  1^  in  two  hours,  it  will  take 
ftn  two  days  to  move  over  27^.  Henoe  the  tynodic  period, 
*  month,  €ft  the  interval  between  two  successive  conjunctions, 

two  days  longer  than  the  sidereal  period  of  our  satellite, 
oact  length  of  the  synodic  period  is  29^  12^  14**  2*'*87,  or 
i9  mean  solar  days. 

.  Mast  and  deniUy.  —  The  methods  by  which  the  mass  or 
if  the  moon  has  been  ascertained  will  be  explained  here- 
neanwhile  it  may  be  stated  here  that  the  result  of  the  most 
olations  of  this  problem,  by  various  methods  and  on  different 
roves  that  the  mass  or  quantity  of  matter  composing  tho 
'  the  moon,  is  a  little  more  than  the  90th  part  of  the  mass 
larth ;  or,  more  exactly,  if  the  mass  of  the  earth  consist  of 
n  of  equal  parts,  the  mass  of  the  moon  will  be  equal  to 
of  these  parts. 

I  the  volume  or  bulk  of  the  moon  is  about  the  50th  part  of 
the  earth,  while  its  mass  or  weight  is  little  more  than  the 
irt  of  that  of  the  earth,  it  follows  that  its  mean  density  must 
B  more  than  half  the  density  of  the  earth,  and  therefore 
about  2-83  times  that  of  water. 

.  No  air  vpon  the  moon,  —  In  order  to  determine  whether 
:be  globe  of  the  moon  is  surrounded  with  any  gaseous  en- 
ike  tlie  atmosphere  of  the  earth,  it  is  necessary  first  to  con- 
bat  appearances  such  an  appendage  would  present,  seen  at 
on's  distance,  and  whether  any  such  appearances  are  dis- 
le. 

rding  to  ordinary  and  popular  notions,  it  is  difficult  to  sepa- 
I  idea  of  an  atmosphere  from  the  existence  of  clouds ;  yet  to 
\  clouds  Bomethiog  more  is  necessary  than  air.  The  prcsenco 
tr  is  indispensable ;  and  if  it  be  assumed  that  no  water  exist, 
rtainly  the  absence  of  clouds  is  no  proof  of  the  absence  of 
lOtphere.  Be  this  as  it  may,  however,  it  is  certain  that 
ne  no  clouds  upon  the  moon )  for  if  there  were,  we  should  im- 
tlj  discover  them,  by  the  variable  lights  and  shadows  they 
iroduce..  If  there  is,  then,  an  atmosphere  upon  the  moon, 
B  entirely  unaccompanied  by  clouds. 

of  the  effects  produced  by  a  distant  view  of  an  atmosphere 
iding  a  globe,  one  hemisphere  of  which  is  illuminated  by  the 

that  die  boundary,  or  line  of  separation  between  the  hemi- 

enlightened  by  the  sun  and  the  dark  hemisphere,  is  uo^ 


SOO  ABTXQHOMT.  ' 

■odden  and  shtrply  defined,  bat  k  gniAttl«-tlie  Iq^i  fiiiiilg  iM^ 
bj  ibw  degrees  into  the  darkneH. 

It  18  to  this  effect  npon  tbe  globe  of  the  etrth  tket  t«ili|jlt-% 
owing;  and  as  we  shall  see  hereafter,  aooh  a  gradnallMaig  mnrtf  i 
tbe  san's  light  is  disooTerable  cm  some  of  m  planelaj  vpm  tmk  \ 
an  atmosphere  is  obserred. 

Now,  if  such  an  e£bct  of  an  atmoephere  wm  prodneeJ  «po*4b 
■Mon,  it  would  be  perceived  bj  the  naked  eje,  and  stiU  men-It 
tinotlj  with  the  teleeoope.  When  the  moon  qipean  as  a  cnMlK^ 
ita  ooDcave  edge  is  the  bonndaiy  whidi  emntea  the  enBjMiil 
from  the  dad:  hemisphere.  When  it  is  in  the  <|nart«ra,  the  &l|ifv 
oi  the  semicirole  is  also  that  boondar^.  In  neither  of  these  Mf^ 
howoTer,  do  we  ever  discover  the  skghtest  indication  of  aij  Mjl 
I4>pearance  as  that  which  has  iost  been  deeoribed.  There  k% 
l^oal  &ding  away  of  the  light  into  the  darkness;  on  the  iM^ 
tnuTi  the  booodaiy,  though  serrated  and  irregnlar,  is  wnTOithiiii 
perroctlj  well  defined  and  sadden. 

All  these  ciroamstances  coonpire  to  prove  that  there  doea  iH 
emt  upon  the  moon  an  atmoq>lien  tmpM»  of  nfleMbg  H^^ 
any  aensible  degree. 

2488.  Ah$ence  of  air  indicated  by  ahseiice  of  re/ractum, — Bit 
it  may  be  oontendcMl  that  an  atmosphere  may  still  exist,  thongh  too 
attenuated  to  produce  a  sensible  twilight.  Astronomers,  however, 
have  resorted  to  another  test  of  a  much  more  decisive  and  delioile 
kind,  the  nature  of  which  will  be  uDderstood  by  explaining  a  simple 
principle  of  optics. 

Let  m  m',  fig.  729,  represent  the  disk  of  the  moon.     Let  a  a' 


^ ^ >>y     --^^ 

Pig.  129. 

represent  the  atmosphere  which  surrounds  it  Let  ame  and  sia'e 
represent  two  lines  touching  tbe  moon  at  m  and  m'f  and  proeesdisf 
towards  the  earth.  Let  sshe  two  stars  seen  in  the  direction  of  theee 
lines.  If  the  moon  had  no  atmosphere,  these  stars  would  appear  to 
touch  the  edge  of  the  moon  at  m  and  m\  because  the  raya  of  Kght 
from  them  would  pass  directly  towards  the  earth ;  but  if  the  awoa 
have  an  atmosphere,  then  that  atmosphere  will  possess  the  propeity 
which  is  common  to  all  transparent  media  of  refracting  lights  aadf 
in  virtue  of  sacli  property,  stars  in  such  positions  as  e^  ?,  behind  tbe 


THX  MOON.  201 

Igs  of  the  moon,  would  be  yisible  ei  the  earth,  for  the  nj  j^m, 
I  pewing  through  the  atmosphere,  would  be  bent  at  an  angle 
I  ttie  direction  m  ^^  and  in  like  manner  the  ray  t^  m'  would  be  bent 
i  the  angle  mV — so  that  the  stars  /  tf  would  be  visible  at  e'  ^, 
otwithstanding  the  interposition  of  the  edges  of  the  moon. 

This  reasoning  leads  to  the  conclusion  that  as  the  moon  moyes 
ler  the  face  of  the  firmament,  stars  will  be  continually  yisible  at 
I  edge  which  are  really  behind  it  if  it  have  an  atmosphere,  and  the 
Eleot  to  which  this  effect  will  take  place  will  be  in  proportion  to 
be  dennty  of  the  atmosphere. 

The  magnitude  and  motion  of  the  moon  and  the  relative  positions 
f  tlw  stars  are  so  accurately  known  that  nothing  is  more  easy,  cer- 
lia,  and  precise,  than  the  observations  which  may  be  made  with 
be  view  of  asoertaininff  whether  any  stars  are  ever  seen  which  are 
caaihly  behind  the  edge  of  the  moon.  Such  observations  have 
leen  made,  and  no  such  effect  has  ever  been  detected.  This  species 
if  obaervation  is  susceptible  of  such  extreme  accuracy,  that  it  is 
icrtain  that  if  an  atmosphere  existed  upon  the  moon  a  thousand 
iaea  less  dense  than  our  own,  its  presence  must  be  detected. 

Bessel  has  calculated  that  if  the  difference  between  the  apparent 
iiameter  of  the  moon,  and  the  arc  of  the  firmament  moved  over  by 
he  moon's  centre  during  the  oocultation  of  a  star,  oentrically  oc- 
ndted,  were  admitted  to  amount  to  so  much  as  2",  and  allowing  for 
he  poBoble  effect  of  mountains,  by  which  the  edge  of  the  disk  is 
lerratedy  taking  these  at  the  extreme  height  of  24,000  feet,  the 
ktmij  of  the  lunar  atmosphere,  whose  refraction  would  produce 
nch  an  effect,  would  not  exceed  the  968th  part  of  the  density  of 
he  earth's  atmosphere,  supposing  the  two  fluids  to  be  similarly  con- 
{titnted.  Nor  would  this  conclusion  be  materially  modified  by  any 
nippoeition  of  an  atmosphere  composed  of  gases  different  from  the 
KDstituents  of  the  earth's  atmosphere. 

The  earth's  atmosphere  supports  a  column  of  30  inches  of  mer- 
eary :  an  atmosphere  1000  times  less  dense  would  support  a  column 
of  three-tenths  of  an  inch  only.  We  may  therefore  consider  it  as 
m  established  fact,  that  no  atmosphere  exists  on  the  moon  having  a 
density  even  as  great  as  that  which  remains  under  the  receiver  of 
the  most  perfect  air-pump,  after  that  instrument  has  withdrawn  from 
it  the  air  to  the  utmost  extent  of  its  power. 

If  further  proofe  of  the  nonexistence  of  a  lunar  atmosphere  were 
nquired,  Sir  J.  Herschel  indicates  several  which  are  found  in  the 
pbenomena  of  eclipses.  In  a  solar  eclipse  the  existence  of  an  at- 
mosphere having  any  sensible  refraction,  would  enable  us  to  trace 
tbe  limb  of  the  moon  beyond  the  cusps  externally  to  the  sun's  disk, 
W  a  namfw  but  brilliant  line  of  light  extending  to  some  distance 
lioog  ltd  edge.  No  such  phenomenon  has,  however,  been  seen. 
If  there  were  any  appreciable  quantity  of  vapour  suspended  over 


SOa  AftTBONOllt. 

the  noon'i  sar&oe,  very  fkint  stars  oodit  to  din|ppter  l^iiiiJl 
before  the  moment  of  their  ooenltation  dj  tiie  iDtarpoatioa  of  lb 
moon's  edge.    Snch,  howeTer,  is  not  the  esse.    Wfam  oooaUed  # 
the  enlightened  edge  of  the  lunwr  disk,  the  light  of  the  moon  anp 
powers  them  and  renders  them  invisiblei  and  even  at  the  iaA  W^ 
the  glare  in  the  skj,  oansed'  bj  the  prozimitj  of  the  eulighfs I  '■ 
part  of  the  disky  renders  the  ooenltation  of  extnnelj  mimito  shlff  ■ 
moapd>le  of  observation.    Bnt  these  obetadee  are  wmawei  h  Hi  \ 
ease  of  total  sohur  edipses;  on  whioh  oeeasions  atan^  so  &mt  astsM^  I 
only  seen  by  the  aid  of  a  telesoope,  oome  np  eloM  to  the  fimb  titf 
oat  any  senaUe  diminntion  of  their  brightness,  and  nadem  flsta* 
tinolum  as  instantaneoos  as  the  largest  and  bri|^teBt  by  &e  kM> 
pontion  of  the  moon's  limb.  ^^ 

2484.  Mnmlighi  noi  muibfy  cahnfic — It  has  bog  been  m 
oitjeet  of  inqniry  whether  the  light  of  the  moon  has  any  Deai:  bil 
the  most  delicate  experiments  and  observations  have  fidnd  to  dsM 
tibia  property  in  it  The  light  of  the  moon  was  coDeefeed  into  IhV 
fbeoa  of  a  concave  mirror  of  sneh  msgnitnde  as  woold  have  bsilf 
snffieient,  if  exnosed  to  the  son's  light,  to  evaponto  gold  or  di# 
Bom.  Ilie  bnlb  of  a  difierential  thermometer,  sensitive  enoip  li 
show  a  change  of  temperature  amonnting  to  the  500tfa  part  of  a 
degree,  was  placed  ib  its  focns,  so  as  to  receive  npon  it  the  eoneett- 
trated  rays.  Yet  no  sensible  efiect  was  produced.  We  must,  then- 
fore,  oondnde  that  the  light  of  the  moon  does  not  possess  the  esl^ 
rifie  property  in  any  sensible  degree.  But  if  the  rays  of  the  mooo 
be  not  warm,  the  vulgar  impression  that  they  are  cold  is  ecfosBj 
erroneous.  We  have  seen  that  they  produce  no  effect  either  way  on 
the  thermometer. 

2485.  JVb  liquids  on  the  tnoon, — The  same  phymcal  tests  wUeh 
show  the  nonexistence  of  an  atmosphere  of  air  upon  the  moon  sie 
equally  conclusive  against  an  atmosphere  of  vapour.  It  nd^l) 
therefore,  be  inferred  that  no  liquids  can  exist  on  the  moon's  sn^ 
fiu)e,  since  they  would  be  subject  to  evaporation.  Sir  John  Hersokeli 
however,  ingeniously  suggests  that  the  nonexistence  of  Tsponr  it 
not  conclusive  against  evaporation.  One  hemisphere  of  the  moca 
being  exposed  continuously  for  328  hours  to  the  glare  of  snnahiiM 
of  an  intensity  greater  than  a  tropical  noon,  because  of  the  abseoee 
of  an  atmosphere  and  clouds  to  mitigate  it,  whil^  the  other  is  ibraa 
equal  interval  exposed  to  a  oold  far  more  rigorous  than  that  which 
prevails  on  the  summits  of  the  loftiest  mountains  or  in  the  pokr 
region,  the  consequence  would  be  the  immediate  evaporatioD  oif  all 
liquids  which  might  happen  to  exist  on  the  one  hemisphere,  and  the 
instantaneous  condensation  and  congelation  of  the  vaponr  on  the 
other.  The  vapour  would,  in  short,  be  no  sooner  formed  on  the 
enlightened  hemisphere  than  it  would  rush  to  the  vacuum  over  the 
dark  hemisphere,  where  it  would  be  instantly  condensed  and  eon- 


THE  MOON.  208 

lied,  an  efieet  which  Henohel  aptly  illustrates  bj  the  familiar 
perimeiit  of  the  cbtophobus.  The  coDsequence,  as  he  ob- 
rresy  of  this  state  of  thin^  would  be  absolute  aridity  below  the 
srtical  01111,  oonstant  accretion  of  hoar  frost  in  the  opposite  region, 
id  periiaps  a  narrow  lone  of  running  water  at  the  borders  of  the 
iC^tened  hemisphere.  He  conjectures  that  this  rapid  alternation 
f  gfaporation  and  condensation  may  to  some  extent  preserve  an 
inKbriiim  of  temperature,  and  mitigate  the  severity  of  both  the 
nmal  and  nocturnal  conditions  of  the  surface.  He  admits,  ncver- 
that  such  a  supposition  could  only  be  compatible  with  the 
of  the  absence  of  a  transparent  atmosphere  even  of  vapour 
rithin  extremely  narrow  limits ;  and  it  remains  to  be  seen  whether 
be  general  physical  condition  of  the  lunar  surface,  as  disclosed  by 
be  leleeoope,  be  not  more  compatible  with  the  supposition  of  the 
olal  afaeence  of  all  liquid  whatever. 

It  appears  to  have  escaped  the  attention  of  those  who  assume  the 
MwbUity  of  the  existence  of  water  in  the  liquid  state  on  the  moon, 
ihal^  IB  die  abeenoe  of  an  atmosphere,  the  temperature  must  neces- 
■lilj  be,  not  only  hr  below  the  point  of  congelation  of  water,  but 
sven  that  of  most  other  known  liquids.  Even  within  the  tropics, 
ad  under  the  line  with  a  vertical  sun,  the  height  of  the  snow  line 
km  not  exceed  16,000  feet  (2187),  and  nevertheless  at  that  elcva- 
tka,  and  still  higher,  there  prevails  an  atmosphere  capable  of  sup- 
potting  a  considerable  column  of  mercury.  At  somewhat  greater 
devmtiooa,  but  still  in  an  atmosphere  of  very  sensible  density,  mer- 
enry  is  congealed.  Analogy,  therefore,  justifies  the  inference  that 
the  total,  or  nearly  total,  absence  of  air  upon  the  moon  is  altogether 
ineompetible  with  the  existence  of  water,  or  probably  any  other 
body  in  the  liquid  state,  and  necessarily  infers  a  temperature  alto- 
gether incompatible  with  the  existence  of  organised  beings  in  any 
respect  analogous  to  those  which  inhabit  the  earth. 

Bat  another  conclusive  evidence  of  the  nonexistence  of  liquids  on 
the  moon  is  found  in  the  form  of  its  surface,  which  exhibits  none 
of  thoae  well-understood  appearances  which  result  from  the  loog- 
oontinQed  action  of  water.  The  mountain  formations  with  which 
the  entire  visible  surfiboe  is  covered  are,  as  will  presently  appear, 
miTenally  so  abrupt,  precipitous,  and  unchangeable,  as  to  be  utterly 
ineompetible  with  the  presence  of  liquids. 

2486.  Abmnce  of  air  deprives  solar  light  and  heat  of  their 
vtiUt^. — The  abeoice  of  air  also  prevents  the  diffusion  of  the 
solar  li^t  It  has  been  abready  shown  r923)  that  the  general 
diffnaion  of  the  sun's  light  upon  the  earth  is  mainly  due  to  the 
reflection  and  refraction  m  the  atmosphere,  and  to  the  light  reflected 
by  the  cloods ;  and  that  without  such  means  of  diffusion  the  solar 
hAi  would  only  illuminate  those  places  into  which  its  rays  would 
directly  penetrate.    Every  place  not  in  full  sunshine,  or  exposed  Ui 


904  A8TR<nroinr. 

■iWM  fllomimted  eai&08|  would  bi  bmdivsd  b  Aa  mctk' 
dftrknesB.    The  iky  at  DOOD'daj  wooM  be  intonidly  Mack  j ' 
beantafol  aiare  ai  oar  Annaiiieiit  in  the.  dqf-4ime  b  te  M'M 
leflaoted  colour  of  the  air.  ''-?] 

Thua  it  appears  that  the  abaenoe  of  ur  aiiiiat  daptivia  flip 
lUwiiinatinff  and  heating  ageno^  of  nearly  all  ite  vlQif' 
diffiiaion  of  light  and  no  retention  and  aeenmnlntion  of 
aa  an  atmoafdiere  snpplieay  prerail,  it  b  impoaaible  to  € 
eziatenoe  and  maintenance  <»  an  oiganiaedwoild  hamiig 
to  the  carUi. 


2487.  Am  ieenfrom  Ae  mamf  cmeartmm  ^  Amm 
ArmammL  —  U  the  moon  were  inhabited,  oflaanwra 
it  wonld  witncM  celeatial  phenomoia  of  a  aingyiir 
differing  in  nianr  reepeota  nrom  thoae  pwaented  to  tiM 
of  onr  globe.    The  heavena  woold  be  perpetnally  aanne 
leae.    The  stara  and  planets  woold  ahme  with  eatnMiidiiiaij^ 
dour  daring  the  long  night  of  828  honn.    TIm  inolination 
axis  being  only  5^,  there  wonld  be  no  smisible  obangpa  of 
The  year  wonld  consist  of  one  unbroken  monotony  of  eqninoK.  Bl' 
inhabitants  of  one  hemisphere  would  never  see  the  earth ;  whUa  ~ 
inhabitants  of  the  other  would  have  it  constantly  in  their  txmm 
by  day  and  by  night,  and  always  in  the  same.poaitioa.    Ta 


wno  inhabit  the  central  part  of  the  hemisphere  praaented  to  sl  mi 

irlNse 


earth  would  appear  stationaiy  in  the  lenith,  and  wonld 
it,  ncYer  rising  nor  setting,  nor  in  any  d^;ree  changing  ita 
in  relation  to  the  senith  or  horiion.  To  those  who  inhabit  _ 
intermediate  between  the  central  part  of  that  hemirahere  and' 
places  which  are  at  the  edge  of  the  moon's  cUsk,  the  earth 
appear  at  a  fixed  and  invariable  distance  from  the  lenith,  and  ahi 
at  a  fixed  and  invariable  azimuth;  the  distanoe  from  the  iMiithhriv 
everywhere  equal  to  the  distance  of  the  observer  frmn  tiie  ayUi 
point  of  the  hemisphere  presented  to  the  earth.  To  an  ohaatvaril 
any  of  the  places  which  are  at  the  edge  of  the  lunar  disk,  the  enA 
would  appear  perpetually  in  a  fixed  direction  on  the  horiaon. 

The  earth  shone  upon  by  the  sun  would  appear  as  the  moon 
to  us;  but  with  a  disk  having  an  apparent  diameter  grealai 
that  of  the  moon  in  the  ratio  of  79  to  21,  and  an  appanot 
fioial  magnitude  about  fourteen  times  greater,  and  it  woold 
quently  have  a  proportionately  illuminating  power. 

EarOi  light  at  the  moon  would,  in  fine,  be  about  fourteen  tiatt 
more  intense  than  moonlight  at  the  earth.  The  earth  wooU  p 
through  the  same  phases  and  complete  the  series  of  them  ia  fit 
same  period  as  that  which  regulates  the  succession  of  the  laatf 
phases,  but  the  corresponding  phases  would  be  separated  bv  Ai 
interval  of  half  a  month.     When  the  moon  is/alf  to  tiie  eartD|tb« 


THB  MOON.  205 

lew  to  the  moon,  and  tnce  versd :  when  the  moon  is  a 
he  earth  u  gibbons,  and  vice  versd, 
tores  of  light  and  shade  wonid  not,  as  on  the  moon,  be 
lenl  and  invariable.  So  fiir  as  they  would  arise  from  the 
iing  in  the  terrestrial  atmosphere,  thej  would  be  variable. 
an,  their  arrangement  would  have  a  certain  relation  to  the 
wing  to  the  effect  of  the  prevailing  atmospheric  currents 
>  the  line.*  This  cause  would  produce  streaks  of  lifht 
,  the  general  direction  of  which  would  be  at  right  angles 
rtfa'i  axis,  and  the  appearance  of  which  would  be  in  all 
imilar  to  the  bilts  which,  as  will  appear  hereafter,  are 
upon  some  of  the  planets,  and  which  are  ascribed  to  a 
calcanse. 

h  the  openings  of  the  clouds  the  permanent  geographical 
r  the  surfiboe  of  the  earth  would  be  apparent,  and  would 
szhibit  a  variety  of  tints  according  to  the  prevailing  cha- 
'  the  soil,  as  is  observed  to  be  the  case  with  the  planet 
I  at  an  immenselv  greater  distance.  The  rotation  of  the 
Q  its  axis  would  be  distinctly  observed  and  its  time  ascer- 
rhe  continents  and  seas  would  be  seen  to  disappear  in  suo- 

one  side  and  to  reappear  at  the  other,  and  to  pass  across 
f  the  earth  as  carried  round  by  the  diurnal  rotation. 
Why  the  fvM  disk  of  the  moon  is  faintly  visible  at  new 
Soon  after  conjunction,  when  the  moon  appears  as  a  thin 
bot  is  so  removed  from  the  sun  as  to  be  seen  at  a  suffi- 
tnde  after  sunset^  the  entire  lunar  disk  appears  faintly 
id  within  the  boms  of  the  crescent.  This  phenomenon 
led  by  the  effect  of  the  ^rth  shining  upon  the  moon  and 
Dg  it  by  reflected  light  as  the  moon  illuminates  the  earth, 
a  degree  of  intensity  greater  in  the  ratio  of  about  14  to  1. 
I  to  what  has  just  been  explained,  the  earth  appears  to  the 
rly  full  at  the  time  when  the  moon  appears  to  the  earth  as 
scent,  and  it  therefore  receives  then  the  strongest  possible 
on.  As  the  lunar  crescent  increases  in  breadth,  the  phase 
rth  as  seen  from  the  moon  becomes  loss  and  less  full,  and 
sity  of  the  illumination  is  proportionately  diminished. 
i  find,  that  as  the  lunar  crescent  passes  gradually  to  the 
he  complement  of  the  lunar  disk  becomes  gradually  more 
able,  and  soon  disappears  altogether. 
Physical  condition  of  the  moon's  surface, — If  we  examine 

carefully,  even  without  the  aid  of  a  telescope,  we  shall 
pon  it  distinct  and  definite  lineaments  of  light  and  shadow, 
tores  never  change ;  there  they  remain,  always  in  the  same 
tpon  the  visible  orb  of  the  moon.     Thus  the  features  that 

•  See  Chapter  on  the  tides  and  trade  winds. 
•  18 


8M  ASTROKOMt. 

oaaQpj  Us  eentn  now  have  occupied  tbe  same  position  thi 
■n  bamu  noOTd.      ^\e  have  ulresdy  alaU^d  thnt  the  first 
obnow  infarenoe  which  this  fuct  Eiiggc»t3,  is  that  the  i 
i^bm  of  the  mooQ  is  alirBja  preseoted  toward  the  earth, 
qoantly,  the  oth«r  heoiispherc  ia  never  ecea.     This  singuli 
twistio  which  ktbcbea  lo  the  mo^on  of  the  mooa  rouod  t 
■mmi  to  be  xgeiieral  characteristic  of  all  other  moons  la  th< 
Sr  WiUiun  Henchel.  bj  tbe  aid  of  bis  powerful  telescopes, 
iadiettiixu  vhich  render  it   prohablo  tliat  tlie   moous  of 
nrolTB  in  the.nme  manner,  each  presenting  oontiiiiumjr 
henuBphere  to  tha  planet.     Tbe  cause  of  this  pecoJitr  i 
been  attempted  to  be  cxplsinod  by  the  hypothesis  ihut 
■phwe  of  the  ntellitc,  which  is  turned  toward  tbe  pla 
eloapted  and  ptotuberant,  and  it  b  the  excess  of  iU  wi  ^ 
nakea  it  tend  to  direct  itself  always  toward  the  piiiow^,  is 
to  the  nnirernJ  priociplo  of  attraction.     B«  this  8>  it  _ 
effeot  is,  that  onr  sclunograpbical  knowledge  is  nec«saari)j' 
to  that  hemiipberc  whiob  is  turned  toward  ua. 

But  what  u  the  coudition  and  character  of  tbe  sarfiuM  of  Ik 
moon  f  What  arc  the  lineaments  of  light  and  shade  which  we  m 
npon  it?  There  is  no  object  outside  tbe  earth  with  which  tin  (alt- 
■oope  haa  afforded  us  xuch  minute  and  satisfactory  informatioii. 

it,  when  the  moon  h  a  crescent,  we  examine 


even  of  moderate  power,  the  concave  boundary,  which  is  thai  pot 
of  the  sorfaoe  where  the  enlightened  hemisphere  ends  and  tba  oirk 
hemisphere  begins,  we  shall  find  that  this  boundary  is  not  an  ercii 
and  regnkr  curve,  which  it  undoubtedlj  would  be  if  the  surimoi 
were  smooth  and  regular,  or  nearly  so.  If,  for  example,  the  lanu 
aurboe  resembled  in  its  general  characteristica  that  of  our  globt, 
supposing  that  the  entire  surface  is  land,  having  the  general  char*^ 
teristioB  of  the  oonlinonta  of  the  earth,  the  inner  boundary  of  tli 
Innar  crescent  would  still  he  a  regular  curve  broken  or  intemiptad 
only  at  particular  points.  Where  great  mountain  ranges,  like  tjuw 
of  tbe  Alps,  the  Andes,  or  the  Himalaya,  might  chance  to  cross  i^ 
these  lofty  peaks  would  project  vastly  elongated  shadows  along  tbs 
adjacent  plain;  for  it  will  be  remembered  tbat,  being  sitoated, il 
''  3  moment  in  i|nestion,  at  the  boundary  of  the  enlightened  ati4 


darkened  hemispheres,  the  shadows  would  be  those  of  eTeniic  ■ 
mornins ;  which  are  prodigiously  longer  than  the  objeota  thenuMm 
The  efiect  of  these  would  be  to  cause  gapa  or  irregolaritiefl  ia  ^ 


general  outline  of  the  inner  boundary  of  the  crescent.     With  ll 
rare  exceptions,  tbe  inner  boundary  of  the  crescent  prodacad  bf  a 
globe  like  tbe  earth  would  be  en  even  and  re^lar  curve. 

Snoh,  however,  ia  not  tbe  case  with  the  inner  boandaiy  of  A| 
lunar  orescent,  even  when  viewed  by  the  naked  eye,  and  atiS  1m 
ao  when  magnifled  by  a  telesoope. 


,  on  tba  oontruj,  ragged  mad  serrated,  snd  briUbiitljr 
mints  ire  bmd  in  the  dark  parts  at  some  diatanoe  from 
shadows  of  considerable  length  appear  to  break  into 
ed  Bur&ce.  The  meqnalities  thns  apparent  indicate 
letaristioB  of  the  Bur&ee.  The  bright  pranta  kos  within 
iapber^  aro  the  peaka  of  1d%  mountains  dnged  widv 
(.  Tbey  are  m  the  condition  with  which  all  traTellen 
in  Alpine  ooaotries  are  familiar; 
aAer  the  snn  has  set,  and  dadineaa 
has  set  in  over  the  valleya  at  the 
foot  of  the  chaio,  the  son  still 
continneB  to  illuminate  the  peaks 
above. 

The  sketch  of  the  lonar  omorat 
in  fiff.  780,  will  illnstiBte  these 
obMrrationR. 

The  Tisible  hemisphere  of  oar 
satellite  has,  within  the  last  quarter 
of  a  centniy,  been  subjected  to  the 
most  rigOToas  examination  which 
anvearied  indoatry,  aided  hj  the 
Tast  imprOTcmcnt  which  has  been 
effected  in  the  instruments  of  tele* 
Boopio  obserration,  rendered  possi- 
ahle;  and  it  is  no  exaggeration 
P^  f  SO.  ^'^  to  stute  that  we  possess  a 

chart  of  that  hemisphere  which  in 
detail  far  exceeds  anj  similar  representation  of  the 

le  selenogrspbical  obeerrers,  the  Pmssisn  astronomers, 
nd  H^Ier,  stand  pre-eminent.  Their  descriptive  work 
Hoode  contains  the  most  complete  collection  of  obserra- 
ph^sical  condition  of  oar  satellite,  and  the  chart,  mea- 
ches  in  diameter,  exhibits  the  most  complete  represen- 
le  lonar  snrface  extanL  Bcudes  this  great  work,  a 
ie  chart  wss  produced  by  Mr.  Rnssell,  from  observations 
,  seven-foot  reflector,  a  umilar  delineation  by  Lohrmann, 
a  very  complete  model  in  relief  of  the  visible  hemisphere 
Witte,  an  Hanoverian  lady. 

f  to  the  stodent  any  precise  or  complete  idea  of  the  mass 
on  oollected  by  the  researches  aod  labonrs  of  these  emi- 
in,  would  be  altoeether  incompatible  with  the  necessair 
work  like  that  wniob  we  have  undertaken.  We  sball 
oGoe  ourselves  to  a  selection  from  some  of  the  most  re- 
folta  of  those  works,  aided  by  the  telescopic  chart  of  the 
9  qnadrant  of  the  moon's  disk,  given  in  Plate  I.^  vluc\i 


hM  boan  Tsdneed  from  the  gml  ohut  flf  Be«  nd  MUkr,  1 

being  exactly  one  half  of  tlut  ut  the  ari|piuL 

2490.  QxmaAL  DiaoBiPTioir  or  thb  Mooa'a  Subi 

(«)  Dmr^tiMt  ^  Q»  dtort;  FU»»  £— Ike  ealiN  ivrfkM  of  d 
kMl^pheie  of  tka  moon  to  lUsklj  eorcnd  *ltt  ■ewrtriaene  ai 
xanew  of  Tulau  tataa,  ■"f"— *— ,  aad  bdgU^  !■  «fiU^  kev 
]^*k1«dw  of  A  dmUr  or  entar-Uka  Dim  to  ODoapleitaiH.  Hm 
qMOtioDof  OwalMrtof  th«8.B.qiiBclrDnt,  PUtel..  will  render  ttui 
^_.  .1.-   _^_  u_- J — ii  ^  Ijjg  jjjg^  jij  jijjj  differ  from  tlilj 


_    _  lin«ameDta  obierred  npos 

cf  Am  fdn  noon  uIm  putlj  froto  the  different  reScotiag  poirB| 
■atlar  MmporfBg  diffeMBt  parte  of  the  Iudu  aurfKCc,  and  partly, 
dlftraet  aapaa  etiditoh  fte  reya  of  the  ealsr  light  are  indtleut  iq 
If  Um  mihee  of  0ie  hmar  h«ntopber«  wpr(>  uuirurml;  lerel,  or  a 
ttaaa  an^ai  of  IncidMMawaaldbadetermiaed  by  tbc  posiUoo  ofti 
wlthreMOB  to  the  ewrtreof  tk«  illumtoated  hcmiepberc;  and 
eaaa,  tiie  Hota  wovld  be  more  legnlHr  and  would  larj  in  relntion  h 
to  tka  eanba  of  tha  Aak;  but,  owing  to  Ihe  gruit  iceqiutlitiBB  o(J 

tkeiMt  and  eoBplioMMImamtlalnoua  mum " 

fart  of  tka  turfkae,  and  the  paat  dei'iba  of  \ 

■M  nmninded  by  tbe  aicovlar  mooDiain  Vin^i^ 

the  lolaT  ra/a  are  ratgeot  to  eztrama  and  Inagdfaw 

thoee  linMmenta  and  farms  tinted  with  Taiwoa  ilttdM  of  pay  • 

with  wbioh  eray  eye  to  familiar. 

(e)  Siadam  niiUf  enly  in  (At  ^toMi — rtqr  wjy^f  i—iiirM  ^f  fc 
Apd(. — When  themooD  is  fiill,  ooBhadowsnpon  it  can  1m  seen,  be 
tut  poBiliOD,  tbe  Ttonal  ray  coinciding  with  the  laminsni  ray,  ea 
to  directly  interpowd  between  tbe  obBcrrer  and  its  ehadow.  As  tli 
pTogreea,  howerer,  the  Bhadows  gradaally  come  into  Tiew;  bee 
TisDal  TS7  Ig  inclined  at  a  gradually  inereailDg  angle  to  the  aolat  i 

"  It  moft  be  obaerred  that  tbe  chart  repreecnta  the  moon'a  dto 
aaan  on  the  (outh  meridian  in  an  aatronomieal  telescope.  As  thi 
mcnt  prodaces  an  inTerted  image,  the  sooth  pole  appaan  at  the 
and  the  north  pole  at  the  lowest  point  of  the  disk,  and  the  easteri 
on  the  ri^t  and  the  western  on  the  left  of  the  obserrer,  all  of  wh 
lions  are  the  reveree  of  those  which  the  same  points  haTe  what 
without  a  telesoope,  or  with  one  which  does  not  ioTert.  rha  It 
are  measured  east  and  west  of  the  meridian  which  tdsaoti  the  Ttoi 
Vbs  original  chart  is  engraied  in  four  separate  sbeeta,  each  repm 
qnadrant  of  the  Tisible  hemisphere.  The  names  of  the  Tanou 
grai^oal  redone  and  more  prominent  moontalna  are  indioatei 
ehMt,  and  have  been  taken  generally  from  those  of  amineot  aoi^t 
The  mesidlana  drawn  on  the  shart  diride  the  aarfltoe  into  loaaa, 
which  measures  Ato  degrees  of  longitude,  and  the  paralleto  to  tka 
diTide  it  into  looes,  haWng  each  tbe  width  of  fire  degree*  of  Utib 
moon's  diameter  being  less  than  that  of  the  earth  in  the  ratio  of  II 
a  degree  of  lanar  latitude  is  less  than  60  geagraphical  miles  in  I 
jsoportioo,  and  is,  therefore,  equal  to  16  geographieal  miles.  Thto 
a  aoale,  by  which  the  magnitudes  on  the  chart,  Plate  L,  may  be 
nataly  estimated. 


THE  MOON.  200 

fa  the  qnarten,  this  angle  haTing  increased  to  00^.  anil  the  houndary  of 

the  enlightened  hemisphere  being  then  in  the  centre  of  the  hemi<ipiipre 

prc'vntcii  to  the  observer,  the  position  is  moat  favourable  for  the  observation 

of  the  shadowfl  bj  which  chiefly,  not  only  the  forms  and  dispositions  nf 

the  monntainoiiB  masses  and  the  intervening  and  enclosed  valleys  nnd 

lafines  are  ascertained,  bat  their  heights  and  depths  are  measured.     This 

hlter  problem  is  solved  by  the  well-onderstood  principles  of  geometrical 

injection,  when  the  directions  of  the  visual  and  solar  rays,  the  position  of 

At  oljcet,  and  of  the  surface  on  which  the  shadows  are  projected,  are 

■sranllj  giveik 

(i)  Umjarm  paiehet,  called  oceans,  teat,  ^c,  proved  to  be  irregular  land 

mrfmeg,  —  Cniform  patches  of  greater  or  less  extent,  each  having  an  uni- 

km  gray  tint  more  or  less  dark,  having  been  supposed,  by  early  observers, 

ll  bt  lar^  collections  of  water,  were  designated  by  the  names,  Or e anus. 

UMMMf  Palvs,  Laccs,  Sixrs,  &c.     These  names  are  still  retained,  but  the 

hewascd  power  of  the  telescope  has  proved  that  such  regions  are  diver« 

iMad,  like  the  rest  of  the  lunar  surface,  by  inequalities  and  undulations, 

rf  permanent  fonns,  and  are  therefore  not,  as  was  imagined,  water  or  other 

Iqvid*  They  differ  firom  other  regions  only  in  the  magnitude  of  the  mountain 

Masaca  which  prevail  upon  them.     About  two-thinls  of  the  visible  hemi- 

■lime  of  the  moon  consists  of  this  character  of  surface.     Examples  of 

these  are  preaenCed  by  the  Mare  Nubium,  Oceanus  Procellarum,  Mare  11  u- 

Memm,  Ac.,  on  the  chart. 

(€)  ^iVer  tpoit,  mountfiint.  — The  more  intensely  white  parts  are  moun- 
tains of  varions  magnitude  and  form,  whose  height,  relatively  to  the  moon's 
■sgoitude,  greatly  exceeds  that  of  the  most  stupendous  terrestrial  emi- 
aenees ;  and  there  are  many,  characterised  by  an  abruptness  and  steepness 
which  sometimes  assume  tlie  position  of  a  vast  vertical  wall,  altogether 
without  example  upon  the  earth.  These  are  generally  disposed  in  broad 
massm,  lying  in  close  contiguity,  and  intersected  with  vast  and  deep 
Talle3rs,  gullies,  and  abysse«,  none  of  which,  however,  have  any  of  the 
characters  which  betray  the  agency  of  water. 

(/)  Clat*e»  of  circular  mountain  ranget.  —  Circular  ranges  of  mountains 
which,  were  it  not  for  their  vast  magnitude,  might  be  inferred  from  their 
form  to  have  been  volcanic  craters,  are  by  far  the  most  prevalent  arrange- 
ment. These  have  been  denominated,  according  to  their  magnitudes,  Bri.- 
WARK  Plaixs,  Rixo  Mol'ntai.ns,  Cr.\ters,  and  IIolks. 

{g)  Bulwark  plaint.  —  These  are  circular  areas,  varying  from  40  to  120 
miles  in  diameter,  enclosed  by  a  ring  of  mountain  ri<]ges,  mostly  contiguous, 
bat  in  some  cases  intersected  at  one  or  more  points  by  va^-t  ravine?.  The 
enclosed  area  is  generally  a  plain  on  which  mountains  of  less  height  are 
often  scattered.  The  surrounding  circular  ridge  also  throws  out  «pnr^, 
both  externally  and  internally,  but  the  latter  are  generally  shorter  than 
the  former.  In  some  cases,  however,  internal  spurs,  which  are  diametri- 
cally opposed,  unite  in  the  middle  so  as  to  cut  in  two  the  enclosed  plain. 
In  some  rare  cases  the  enclosed  plain  is  uninterruiitvd  by  mountains,  and 
it  is  almost  invariably  depressed  below  the  general  level  of  the  surrounding 
land.     A  few  instances  are  presented  of  the  enclosed  plain  being  convex. 

The  mountainous  circle  enclosing  these  vast  areas  is  seldom  a  single  ridge. 
It  consists  more  generally  of  several  concentric  ridges,  one  of  which,  how- 
ever, always  dominates  over  the  rest  and  exhibits  an  unequal  summit, 
broken  by  stupendous  peaks,  which  here  and  there  shdot  up  from  it  to  vast 
heights.  Occasionally  it  is  also  interrupted  by  smaller  mountains  of  the 
circular  form. 

Examples  of  bulwark  plains  are  presented  in  the  cases  of  Clavius,  Wal* 
ther,  RegiomontanuK,  Parbuch,  Aljthonso,  and  Ptolemieus. 


210  A8TR0N0MT.  j 

The  dimeter  of  CUTios  is  124  mUef,*  tod  Um  endoMd  ana  b  itf^M 
Bquan  miles.  One  of  the  peaks  of  the  soirowiduig  ridge  Aeoti  if  li#^ 
height  of  16,000  feet  jj 

The  diameter  of  PtolemaBus  is  100  miles,  and  it  endosas  aaaiaarfjI^S 
square  miles.  This  area  is  intersected  by  numeroiis  small  ridges^  aatihiaifl 
a  mile  in  breadth  and  100  feet  in  height  Ptolemmns  is  aarroaiM.MH 
Tory  high  mountains,  and  is  remarkable  for  the  predpitoiia  ahaiiatark9H 
inner  sides.  ^ 

The  other  bulwark  plains  aboTo  named  haTe  nearlj  the  aaina  diimlH 
but  less  dimensions.  ^ 

(A)  £in^  mountaint.  —  These  circular  formations  are  ob  a  amalhr  MriH 
than  the  bulwark  plains,  Tarying  Arom  10  to  60  miles  in  diamatar,  ni  iM 
are  generally  more  regular  and  more  exactly  droular  in  their  fona.  Am 
are  sometimes  found  upon  the  ridge  which  enoloaea  a  bulwark  plU%  ft3 
Interrupting  the  continuity  of  their  boundary,  and  sometimes  thej  an  mJB 
within  the  enclosed  area.  Sometimes  they  stand  in  the  nudst  of  tha  smIU 
Their  inner  declivity  is  always  steep,  and  tiie  enclosed  area,  which  it  alvM 
ooncave,  often  includes  a  central  mountain,  presenting  thus  tha  gaaHW 
character  of  a  Yolcanic  crater,  but  on  a  scale  of  niagnitade  without  eiaBriii 
in  terrestrial  yolcanoes.  The  surface  enclosed  is  always  lower  thai  bj 
region  surrounding  the  enclosing  ridge,  and  the  central  monntidn  often  liM  I 
to  such  a  height  that,  if  it  were  levelled,  it  would  fill  the  depresdon. 

(t)  Tycho,  a  ring  mountain.  —  The  most  remarkable  example  of  this  dsv  j 
is  Tycho  (see  chart,  Int  42°,  long.  \2^).  This  object  is  distingniihsUl 
without  a  telescope  on  the  lunar  disk  when  full ;  but,  owing  to  the  bbU* 
tude  of  other  features  which  become  apparent  around  it  in  the  phssd^  k  { 
can  then  be  only  distinguished  by  a  perfect  knowledge  of  its  positioa,  ui 
with  a  good  telescope.  The  enclosed  area,  which  is  very  nearly  eironlir, 
is  47  miles  in  diameter,  and  the  inside  of  the  enclosing  ridge  hu  Al 
steepness  of  a  wall.  Its  height  above  the  level  of  the  enclosed  plsin  ii 
16,000  feet,  and  above  that  of  the  external  region,  12,000  feet  Thena 
a  central  mount,  height  4,700  feet,  besides  a  few  lesser  hills  within  thi 
enclosure. 

(k)  Craters  and  holes.  —  These  are  the  smallest  formations  of  the  dreskr 
class.  Craters  enclose  a  visible  area,  containing  generally  a  central  nonid 
or  peak,  exhibiting  in  a  striking  manner  the  volcanic  character.  Boki 
include  no  visible  area,  but  may  possibly  be  craters  on  a  scale  too  small  t0 
be  distinguished  by  the  telescope. 

Formations  of  this  class  are  innumerable  on  every  part  of  the  viabli 
surface  of  the  moon,  but  are  no  where  more  prevalent  than  in  the  repas 
around  Tycho,  which  may  be  seen  on  a  very  enlarged  scale  in  Plats  11* 
which  represents  that  ring  mountain,  and  the  adjacent  region,  extending  ovtf 
sixteen  degrees  of  latitude,  and  from  sixteen  to  twenty  degrees  of  loDgitodc. 

(/)  Other  mountain  furmationa.  —  Besides  the  preceding,  which  are  tfc« 
most  remarkable,  the  most  characteristic,  and  the  most  prevalent,  then 
are  various  other  forms  of  mountain,  classified  by  Beer  and  Madler,  but 
which  our  limits  compel  us  to  omit. 

(m)  Singular  and  unexplained  optical  phenomenon  of  radiaiing  Urtah.'^ 
Among  the  most  remarkable  phenomena  presented  to  lunar  observer!,  i> 
the  systems  of  streaks  of  light  and  shade,  which  radiate  from  the  bordcn 
of  some  of  the  largest  ring  mountains,  spreading  to  distances  of  sannl 
hundred  miles  around  theiu.  Seven  of  the  mountains  of  this  class,  w-t 
Tycho,  Copernicus,  Kepler,  Pyrgius,  Anaxagorus,  Aristarchus,  and  Olber^ 

*  The  geographical  mile,  or  the  sixtieth  part  of  a  degree  of  the  eartk*! 
meridian. 


.  miBd  whieb  tbij  •xtnordinar;  ndiktion  U  nuui- 
ama,  1«u  conspioDonvlj  deTclopcd,  howsTgr,  m 
Solcr,  Proeliu,  Ariitillui,  Timochuii,  tui  (an* 

I  dUpIafod  when  the  moon  u  fall  iroimd  Tjcho,  are 
I.  «n  tk*  Mn«  Mftle  u  PUt«  II. 
Htkl  eommmic*  at  a  distanca  of  abont  20  uIIm  ont- 
1  «f  Tye^-  From  tliat  limit  the;  dJTCrga  and  OTar- 
1  pari  of  tha  Tidble  hMnitpbcrs.  On  the  B.  Uiaj 
jf  tfae  duk  ;  OD  tlie  E.  to  Haiiucl  and  Capnanni ;  on 
Nnbiam ;  on  the  N.  to  Alphonie ;  on  the  N.W.  to  th« 
0  tb«  W.,  BO  aa  to  aatar  nearly  th«  entire  aontli-wMteni 

ibis  when  the  Ron'i  nyi  fall  npon  the  rc^on  of  Tjcbo 
Mter  than  25°,  and  the  more  perpendicnlarlj  tbe  nqrt 
t*  fbU;  developed  the  phenomena  will  be.     Thej  are, 
X  in  their  Eplendour,  aa  rtprMcnted  in  Plate  IIL,  when 
Aa  the  moon  morei  from  oppoaitdon  to  the  Uat  qnuter, 
re  (radoally  diMppear,  ana  tbe  ilMdowB  of  the  monn- 
«  at  the  tame  time  gradually  bronght  into  Tie*,  ao  that 
BOOD  iiDdeif  oei  a  complete  trantformatioii.     This  change 
exhibited  by  holding  the  Plate  III.  before  a  window  to 
t  the  obKtrer  is  tnmed.     Ha  will  then  see  the  pheoemetM 
iDtad  on  the  fall  mnon.     Let  him  (hen  tuni  alow^  npon 
•  Etee  is  presented  to  the  window,  holding  the  paper  be- 
nd the  light     The  Plate  II.  will  (hen  be  seen  by  meana  of 
'  of  the  paper,  and  it  will  gradually  become  more  and  more 
at  aa  he  tnma  more  dlreEtly  towarda  the  light.* 
mountain  formntiong  generally  disappear  under  tha  aplen- 
idiating  BtrealiB,  aome  few,  as  will  be  perceiTed  on  Plate 
be  liaible  through  them. 

omerous  selenographic  obscrrera  hsTe  proposed  any  satia- 
lon  of  these  phenomena,  which  are  exhibited  nearly  ia  the 
-ound  the  other  ring  mouniaias  aboTe  named.     SchrGter 

0  be  mountains,  an  hypothesis  OTcrtumed  by  the  obserra- 
e  with  more  powerful  instrumenta.  Herachel,  the  elder, 
lea  of  streams  of  Uts;  Cassiui  imagined  they  might  he 
«n  CTen  tnggested  the  possibility  of  their  being  roadal 

1  that  these  ring  mountalaH  may  have  been  among  the  &rst 
"Bia^ona ;  and,  consequently,  the  points  to  which  all  the 

the  formation  of  our  tatellile  would  hare  been  attracted. 
la  produced  effeota.  anch  as  vitrification  or  oiydation,  which 
eetive  powera  of  the  eurface.  We  must,  however,  dismisa 
IS,  however  ingenious  and  allractive,  referring  those  who 

the  aubject  to  the  original  work. 

/  TV**- — This  region  is  crowded  with  hundreds  of  pesks, 
ers  (see  Plate  II.)  i  not  (he  leoft  vesiige  of  a  plnin  cno 
Bcovered.  Towarda  the  E.  and  S.K.  craters  predominate, 
cbuna  parallel  to  the  ring  are  mare  nutneroua.     On  the  S. 


with  B  telescope  having  a  prismalio  eye- 


212  ASTRONOlfT. 

tbe  motintftins  are  thickly  scattered  in  conftised  masses.  At  a  distanee  of 
16  to  25  miles,  craters  and  small  ring  mountjuns  are  seen,  few  being  cir- 
cular, but  all  approaching  to  that  form.  All  are  surrounded  bj  ateep  ram* 
parts. 

(o)  Wilhelm  I.  —  This  is  a  considerable  ring  mountain  8.E.  of  ^eho. 
The  altitude  of  its  eastern  parapet  is  10,000  feet,  that  of  its  western  bciog 
only  6,000.  Its  crest  is  studded  with  peaks ;  and  craters  of  Tarioos  ma^ 
nitudes,  heights,  and  depths,  surrounding  it  in  great  numbers,  and  giTiof 
a  varied  appearance  to  the  adjacent  region. 

(p)  Lcnpomontanus,  —  A  large  circular  range,  having  a  diameter  of  80 
miles,  enclosing  a  plain  of  great  depth.  The  eastern  and  western  ridfcs 
rise  to  the  height  of  12,000  to  18,000  feet  above  the  level  of  tbe  enclosed 
plain.  Its  shadow  sometimes  falls  upon  and  conceals  the  numerous  crtten 
and  promontories  which  lie  near  it.  The  whole  surrounding  region  it 
savage  and  rugged  in  the  highest  degree,  and  must^  according  to  Midler, 
have  resulted  from  a  long  succession  of  convulsions.  The  principal,  and 
apparently  original,  crater  has  given  way  in  course  of  time  to  a  series  of 
new  and  less  violent  eruptions.  All  these  smaller  formations  are  visible 
on  the  full  moon,  but  not  the  principal  range,  which  then  disappetn, 
though  its  place  may  still  be  ascertained  by  its  known  position  in  rdatioa 
to  Tycho. 

(q)  Magmu9. — ^This  range  N.W.  of  Tycho  (see  Plate  I.)  has  the  appes^ 
ance  of  a  vast  and  wild  ruin.  The  wide  plain  enclosed  by  it  lies  in  deep 
shade  even  when  the  sun  has  risen  to  the  meridian.  Its  general  heiglitii 
18,000  feet.  A  broad  elevated  base  connects  the  numberless  peaks,  ter- 
races, and  groups  of  hills  constituting  this  range,  and  small  craters  ire 
numerous  among  these  wild  nnd  confused  masses.  The  central  peak  a  if 
a  low  but  well-defined  hill,  close  to  which  is  a  crater-like  depression,  and 
other  less  considerable  hills. 

(r)  Analoffy  to  terrestrial  volcanoes  more  apparent  than  real  —  enlarged  viev 
of  Gasscndi. — The  volcanic  character  observed  in  the  selenographic  forma- 
tions loses  much  of  its  analogy  to  like  formations  on  the  earth's  surftce 
when  higher  magnifying  powers  enable  us  to  examine  the  details  of  what 
appear  to  be  craters,  and  to  compare  their  dimensions  with  even  the  most 
extensive  terrestrial  craters.     Numerous  examples  may  be  produced  to  il- 
lustrate this.     We  have  seen  that  Tycho,  which,  viewed  under  a  moderate 
magnifying  power,  appears  to  possess  in  so  eminent  a  degree  the  volctnie 
character,  is,  in  fact,  a  circular  chain  enclosing  an  area  upwards  of  fif^j' 
miles  in  diameter.     Gassendi,  another  system  of  like  form,  and  of  still 
more  stupendous  dimensions,  is  delineated  in  fy.  1,  Plate  lY.,  as  seea 
with  high  magnifying  powers.     This  remarkable  object  consists  of  tw9 
enormous  circular  chains  of  mountains ;  the  lesser,  which  lies  to  the  north, 
measuring  16^  miles  in  diameter,  and  the  greater,  lying  to  the  south,  en- 
closing  an  urea  60  miles  in  diameter.     The  area  enclosed  by  the  former 
is  therefore  214,  and  by  the  latter  2,827  square  miles.     The  height  of  tlie^ 
lesser  chain  is  about  10,000  feet,  while  that  of  the  greater  varies  from  3,50C* 
to  5,000  feet.     The  vast  area  thus  enclosed  by  the  greater  chain  include? - 
at  or  near  its  centre,  a  principal  central  mountain,  having  eight  peaks  aii«^ 
a  height  of  2,000  feet,  while  scattered  over  the  surrounding  encloinire  up- 
wards of  a  hundred  mountains  of  less  considerable  elevation  have  bee** 
counted. 

It  is  easy  to  see  how  little  analogy  to  a  terrestrial  volcanic  crater  is  pre~ 
sented  by  these  characters. 

The  preceding  selections,  combined  with  the  cbarts,  Plates  I,  H» 


THE  KEV;  VrRK 

PUBLIC  library! 


«MJU  criiTB  nvssiven  by  cjiem 


SEW 


THB  MOON.  218 

[9  and  ly,  will  serve  to  show  the  general  physical  character  of 
laoar  surface,  and  the  elaborate  accuracy  with  which  it  has  been 
)mitted  to  telescopic  examination.  In  the  work  of  Beer  and 
idler,  a  table  of  the  heights  of  aboye  1000  mountains  is  given, 
eral  of  which  attain  to  an  elevation  of  23,000  feet,  equal  to  that 
the  highest  summits  of  terrestrial  mountains,  while  the  diameter 
the  moon  is  little  more  than  one  fourth  that  of  the  earth. 
2491.  Olservatums  of  Henchd.  —  Sir  John  Herschel  says,  that 
oog  the  lunar  mountains  may  be  observed  in  its  highest  perfection 
true  volcanic  character,  as  seen  in  the  crater  of  Vesuvius  and 
swhere ;  but  with  the  remarkable  peculiarity  that  the  bottoms  of 
Dy  of  the  craters  are  very  deeply  depressed  below  the  general 
&oe  of  the  moon,  the  internal  depth  being  in  many  cases  two  or 
ee  times  the  external  height  In  some  cases,  he  thinks,  decisive 
rks  of  volcanic  stratification,  arisine  from  a  succession  of  deposits 
ejected  matter,  and  evident  indications  of  currents  of  lava 
iaming  outwards  in  all  directions,  may  be  clearly  traced  with 
rerfol  telescopes. 

!492.  ObiervcUions  of  the  Earl  of  Roste.  —  By  means  of  the 
at  reflecting  telescope  of  Lord  Rosse,  the  flat  bottom  of  the 
ter  called  Albategnius  is  distinctly  seen  to  be  strewed  with  blocks, 
visible  with  less  powerful  instruments;  while  the  exterior  of 
ther  (Aristillus)  is  intersected  with  deep  gullies  radiating  firom 
centre. 

1493.  Supposed  influence  of  the  moon  on  the  weather. — ^Among 
many  influences  which  the  moon  is  supposed,  by  the  world  in 
eral,  to  exercise  upon  our  elobe,  one  of  tiiose,  which  has  been 
It  universally  believed,  in  all  ages  and  in  all  countries,  is  that 
ch  it  is  presumed  to  exert  upon  the  changes  of  the  weather, 
hough  the  particular  details  of  this  influence  are  sometimes  pre- 
led  to  be  described,  the  only  general  principle,  or  rule,  which 
rails  with  the  world  in  general  is,  that  a  change  of  weather  may 
looked  for  at  the  epochs  of  new  and  full  moon :  that  is  to  say, 
he  weather  be  previously  fair  it  will  become  foul,  and  if  foul 

I  become  fair.  Similar  changes  are  also,  sometimes,  though  not 
xmfidentiy,  looked  for  at  the  epochs  of  the  quarters. 

II  question  of  this  kind  may  be  regarded  eitiier  as  a  question  of 
nee,  or  a  question  of  fact 

f  it  be  regarded  as  a  question  of  science,  we  are  called  upon  to 
bun  how  and  by  what  property  of  matter,  or  what  law  of  nature 
attraction,  the  moon,  at  a  distance  of  a  quarter  of  a  million  of 
es,  combining  its  efiects  with  the  sun,  at  four  hundred  times  that 
ance,  can  produce  those  alleged  changes.  To  this  it  may  be 
iily  answered  that  no  known  law  or  principle  has  hitherto  ex- 
ined  any  such  phenomena.  The  moon  and  sun  must,  doubtiessi 
itt  the  ocean  fA  air  which  surrounds  the  globe,  as  they  affeoi  \lkkQ 


S14  ABTBOROIIT. 

oeein  of  imiei^— prodoomg  efieoto  analogoBS  to  iUmx  Ut  wkm  At 
quantity  of  such  an  effect  is  estimated;  it  is  pnmd  to  bo  oaoh  m 
eoald  by  no  means  aocount  for  tbe  meteorologioal  dttDgeo  hm 
odVeitea  to. 

But  in  condooting  inyeetigations  of  this  kind  we  piooeod  aUt* 
gether  in  tbe  wrong  direotiony  and  begin  at  tbe  wrong  end.  when  wi 
oommenoe  witb  tbe  investigation  of  tbe  pbjiical  eanee  ef  dio  Wjfi 
posed  pbenomena.  Onr  first  business  is  carefnllj  and  neeoratslj  Is 
observe  tiie  pbenomena  of  tbe  cbanges  of  tbe  weathefi  urf  then  p 
pat  them  in  juxtaposition  with  tbe  contemporaneous  ehangsa  ef  M 
lunar  phases.  If  there  be  any  discoverable  correspoodenosji  it  that 
becomes  a  question  of  physios  to  assign  its  oanse. 

Snob  a  course  of  observation  has  been  made  in  varions  tkamfi^ 
toriea  witb  all  tbe  rigour  and  exactitude  neeessaiy  in  sneh  an  kh 
quiiji  and  has  been  continued  over  p«riods  of  time  so  extendedy  |i 
to  emoe  all  conceivable  effiscts  of  accidental  irregularitieB. 

We  can  imagine,  placed  in  two  parallel  columns^  in  jnxt^wsHioi^ 
the  series  of  epochs  of  the  new  and  full  moons,  and  the  qnariasi 
and  the  corresponding  conditions  of  the  weather  at  these  tmeii^  far 
fifty  or  one  hundred  years  back,  so  that  we  may  be  enaUad  to  a* 
amine,  as  a  mere  matter  of  fact,  the  conditions  of  the  weather  flbr 
one  thousand  or  twelve  hundred  full  and  new  moons  and  qnarteni 

From  such  a  mode  of  observation  and  inquiry,  it  has  reraited  eon- 
clusively  that  the  popular  notions  conoemiDg  the  influence  of  the 
lunar  phases  on  the  weather  have  no  foundation  in  theory,  and  no 
correspondence  with  observed  facts.  That  the  moon,  by  her  mft 
tation,  exerts  an  attraction  on  our  atmosphere  cannot  be  dounsd; 
but  the  effects  which  that  attraction  would  produce  upon  the  wealhir 
are  not  in  accordance  with  observed  phenomena ;  and,  therefbr^ 
these  effects  are  either  too  small  in  amount  to  be  appreoiablo  in  As 
actual  state  of  meteorological  instruments,  or  they  are  obliteiatsl 
by  other  more  powerful  causes,  from  which  hitherto  they  have  not 
been  eliminated.  It  appears,  however,  by  some  series  <a  ohauf^ 
tions,  not  yet  confirmed  or  continued  through  a  sufficient  period  of 
time,  that  a  slight  correspondence  may  be  discovered  between  lbs 
periods  of  rain  and  the  phases  of  the  moon,  indicating  a  veiy  fbsUs 
influence,  depending  on  the  relative  position  of  that  luminary  to  the 
sun,  but  having  no  discoverable  relation  to  the  lunar  attnuilioB. 
This  is  not  without  interest  as  a  subject  of  scientific  inquiiyi  and  is 
entitled  to  the  attention  of  meteorologists ;  but  its  influence  is  ss 
feeble  that  it  is  altogether  destitute  of  popular  interest  as  a  wsalhcr 
prognostic.  It  may,  therefore,  be  stated  that,  as  far  as  obeervatfatt 
combined  with  theory  has  afforded  any  means  of  knowledge,  tben 
are  no  grounds  for  tbe  prognostications  of  weather  erroneously  sap* 
posed  to  be  derived  from  the  influence  of  the  sun  and  moon. 

Those  who  are  impressed  with  the  feeling  that  an  o^nion  so  oi* 


THE  MOON.  :215 

nraallr  ent0rteiii6d  erm  in  oonnkiae  remote  from  each  other,  as 

that  which  pteanmes  ao  infloeooe  of  the  moon  oyer  the  changes  of 

tte  wmiher,  will  do  well  to  remember  that  againat  that  opinion  we 

kMW  not  hm  ofqpoaed  mere  theory.    Naj.  we  have  abandoned  for 

.lh«  ocMBinn  the  aapport  that  aoienee  mi^  afford,  and  the  light  it 

■i^dhftahad  on  the  n^gatire  of  this  qoeatiODi  and  have  dealt  with  it 

•i  ft  aaen  qineatioD  of  &ot    It  matten  littlOi  ao  &r  as  thia  qnestion 

is  oonMsmadj  in  what  manner  the  moon  and  snn  may  prodoee  an 

cfiMt  OB  the  weather^  nor  even  whether  they  be  active  oanses  in 

yrfnmg  audi  efieet  at  alL    The  point,  and  the  only  point  of  im- 

porJMioo,  ii^  whether,  regarded  as  a  mere  maUer  qf/aeif  any  eor- 

leapnndfnfie  between  the  ohangea  of  the  moon  and  those  of  the 

weather  ezistsr    And  a  short  examination  of  the  recorded  faets 

fnwm  that  it  doxs  rot. 

MM.  (khar  mippoied  hnar  mjhteneei. — ^Bnt  meteorolomal  phe- 
BOBena  are  not  the  only  effiBCts  imputed  to  oar  satellite;  £at  body, 
Ska  oomets^  is  made  zeaponsible  for  a  vast  variety  of  interferences 
with  esjBnuaed  natore.  The  ctrenlation  of  the  juices  oi  vegetables, 
Ao  ^oantios  of  grain,  the  fkte  of  the  vintage,  are  all  laid  to  its  ao- 
esnt:  and  timbw  mnst  be  feUed,  the  harvest  cut  down  and  gathered 
ii^  aoa  tho  joke  of  the  grape  expressed,  at  times  and  under  oir- 
OHMlBoeea  regdaled  by  &e  aspects  of  the  moon,  if  excellence  be 
hoped  ftr  in  tb(Me  produets  of  the  scnL 

Aoeoiding  to  popular  belief,  our  satellite  also  presides  over  human 
msladiea;  and  ue  phenomena  of  the  sick  chamber  are  governed  by 
As  lunar  phases;  nayv  the  very  marrow  of  our  bones,  and  the  weiffht 
cf  oar  bodies,  sidGar  increase  or  diminution  by  its  influence.  Nor 
ii  its  iapated  power  oonfined  to  physical  or  organio  effects;  it  noto- 
aondj  governs  mental  derangement. 

If  theae  opinions  respectii^  lunar  mfluences  were  limited  to  par- 
tiwlar  oonntnes^  they  would  m  less  entitled  to  serious  consideration ; 
hU  it  ia  a  enriooa  &ot  that  many  of  them  prevail  and  have  pre- 
uSed  m  qnarters  of  the  earth  so  distant  and  unconnected,  that  it  is 
Monlt  to  imsfpne  the  same  error  to  have  proceeded  from  the  same 


Ov  limits^  and  the  olijeets  to  which  this  volume  is  directed, 
lendor  it  impossible  here  to  notice  more  than  a  few  of  the  principal 
ph jrioal  and  phyHologJcal  influencea  imputed  to  the  moon ;  nor  even 
with  foapect  to  theae  can  we  do  more  uian  indicate  the  kind  of  ez- 
amiaalion  to  whidi  they  have  been  submitted,  and  the  conclusions 
which  have  been  deduced  from  it 

M95.  The  red  motm,  —  Gkudeners  g^ve  the  name  of  Red  Moon 
to  that  moon  which  is  fuU  between  the  middle  of  April  and  the 
dooe  of  May.  Aooording  to  them  the  light  of  the  moon  at  that 
seaaon  exoreisea  an  injurious  influence  upon  the  young  shoots  of 
planla^    They  say  that  when  the  aky  is  dear  the  leaves  and  buda 


su 


ASTBOiroinr. 


«ipoMd  to  the  lunar  light  redden  tnd an  kHIed tiff  hjftM^llil 
time  when  the  thermometer  exposed  to  the  ttnoaplMre  jftal  ~ 
many  degrees  above  the  fieenng  point  Thej  mj  abo  Art 
elooded  Ay  intercepts  the  moot? s  light  it  prevents  these  '"^^ 
eonsequences  to  the  plants^  althon|^  the  oneamstanoes  of 
tore  are  the  same  in  both  eases.  Nothbg  is  more  eaij  fh^lb 
explanation  oi  these  eflfeets.  The  leaves  and  flowen  of  phlli  lb 
atrong  and  powerful  radiatonrof  heat;  when  the  sl^  is  ehririMr 
thOTUorelose  temperature  and  may  be  froaen;  if|OiL  toe  oAirliijI^ 
the  aky  be  clouded,  their  temperature  is  msintained  ftr  Ae  *" 
above  stated.  ' 

The  moon,  therefore,  has  no  oonneedon  whatever  witli  tUri^l^^ 
and  it  is  certain  that  plants  would  suflbr  ondM  the  ana  d^'^^jri 
stances  whether  the  moon  is  above  or  below  tiie  horiiao.  Ilil|ip|f^^ 
is  quite  true  that  if  the  moon  be  above  ihehoriioO|  thejplaataeriiilii' 
suffor  unless  it  be  visible ;  because  a  dear  d^  \A  inffi^easslli^b' 
much  to  the  production  of  the  iojuty  to  the  plants  as  to   ~ 


bility  of  the  moon;  and,  on  the  other  hand,  the  same  dooiawfti 
veil  the  moon  and  intercept  her  light  give  back  to  thephnlill  iA 
warmth  which  prevents  the  injury  here  adverted  to.     The  pofihr 
opinion  is  therefore  right  as  to  the  effedj  but  wrong  as  to  the 
and  its  error  will  be  at  once  discovered  by  showing  that  on  a 
night,  when  the  moon  is  new,  and,  therefore,  not  visible^  the  phrti 
may  nevertheless  suffer. 

2496.  Supposed  influence  an  timber.  —  An  opinion  is  gsnsnllr 


entertained  tnat  timber  should  be  felled  only  during  the 
the  moon ;  for  if  it  be  cut  down  during  its  increase,  it  will  not  b 
of  a  good  and  durable  quality.     This  impressico  prevuls  in  vsiioBI 
countries.     It  is  acted  upon  in  England,  and  is  made  the  groonlrf 
le^lation  in  France.     The  forest  laws  of  the  latter  eoontiyialv* 
diet  the  cutting  of  timber  during  the  increase  of  the  moon,    flu 
same  opinion  prevails  in  Brazil.     Sigpor  Francisco  Pinto,  an  CM* 
nent  agriculturist  in  the  province  of  £spirito  Santo,  afikmed,  as  tb 
result  of  his  experience,  that  the  wood  which  was  not  felled  at  tb 
full  of  the  moon  was  immediately  attacked  by  worms  and  veiy  sooa 
rotted.     In  the  extensive  forests  of  Germany,  the  same  opinion  is 
entertained  and  acted  upon.     M.  Duhamel  du  Moncean,  a  celehnlBd 
French  agriculturist,  has  made  direct  and  positive  experiments  tat 
the  purpose  of  testing  this  quesdon ;  and  has  clearly  and  eondo- 
sively  shown  that  the  qualities  of  timber  felled  in  different  parts  of 
the  lunar  month  are  the  same. 

2497.  Supposed  lunar  influence  on  vegetables.  — It  is  an  apho^ 
ism  received  by  all  gardeners  and  agriculturists  in  Europe,  thil 
vegetables,  plants,  and  trees,  which  are  expected  to  flourish  sad 
grow  with  vigour,  should  be  planted,  grafted,  and  pruned,  doriog 
the  increase  of  the  moon.     This  opinion  is  altogether  erroneoaa 


THE  MOON.  217 

The  inoreafle  or  deereise  of  the  moon  has  no  appreciable  influence 
OD  the  phenomena  of  vegetation ;  and  the  experiments  and  obeer- 
Tatioos  of  sevend  French  agrionlturista,  and  especially  of  M. 
Dihamel  da  Monoeau  (already  alluded  to)  have  clearly  established 
tUi. 

2408.  Sitppoied  Ittnar  influence  an  wine-making, — ^It  is  a  maxim 
of  wine-growers,  that  wine  which  has  been  made  in  two  moons  is 
aefer  of  a  good  quality,  and  cannot  be  clear. 

To  this  we  need  only  answer,  that  the  moon's  rays  do  not  affect 
the  temperature  of  the  air  to  the  extent  of  one  thousandth  part  of  a 
degree  ci  the  thermometer,  and  that  the  difference  of  temperatures 
d  any  two  neighbouring  places  in  which  the  process  of  making  the 
vine  of  the  same  soil  and  yintafle  might  be  conducted,  may  be  a 
thousand  times  greater  at  any  given  moment  of  time,  and  vet  no 
me  ever  imagines  that  such  a  circumstance  can  affect  the  quality  of 
the  wine. 

2499.  Supposed  lunar  influence  on  the  complexion.  —  It  is  a 
pRvalent  popular  notion  in  some  parts  of  Europe,  that  the  moon's 
light  is  attended  with  the  effect  of  darkening  the  complexion. 

That  light  has  an  affect  upon  the  colour  of  material  substances 
is  a  fact  well  known  in  physics  and  in  the  arts.  The  process  of 
Ueaching  by  exposure  to  the  sun  is  an  obvious  example  of  this  class 
of  &ct0.  Vegetables  and  flowers  which  grow  in  a  situation  excluded 
from  the  light  of  the  sun  are  different  in  colour  from  those  which 
have  been  exposed  to  its  influence.  The  most  striking  instance, 
however,  of  the  effect  of  certain  rays  of  solar  light  in  blackening  a 
light^coloured  substance,  is  afforded  by  chloride  of  silver,  which  is 
a  white  substance,  but  which  immediately  becomes  black  when  acted 
upon  by  the  rays  near  the  red  extremity  of  the  spectrum.  This 
substance,  however,  highly  susceptible  as  it  is  of  having  its  colour 
affected  by  light,  is,  nevertheless,  found  not  to  be  changed  in  any 
sensible  degree  when  exposed  to  the  light  of  the  moon,  even  when 
that  light  is  condensed  by  the  most  powerful  burning  lenses.  It 
would  seem,  therefore,  that  as  fisir  as  any  analogy  can  be  derived 
from  the  qualities  of  this  substance,  the  popular  impression  of  the 
influence  of  the  moon's  rays  in  blackening  the  skin  receives  no 
support. 

2500.  Supposed  lunar  influence  on  putrefaction.  —  Pliny  and 
Plutarch  have  transmitted  it  as  a  maxim,  that  the  light  of  the  moon 
facilitates  the  putrefaction  of  animal  substances,  and  covers  them 
with  moisture.  The  same  opinion  prevails  in  the  West  Indies,  and 
in  South  America.  An  impression  is  prevalent,  also,  that  certain 
kinds  of  fruit  exposed  to  mooDlight  lose  their  flavour  and  become 
soft  and  flabby;  and  that  if  a  wounded  mule  be  exposed  to  the 
light  of  the  moon  during  the  night,  the  wound  will  be  irrithted,  and 
frequently  become  incurable. 

III.  10 


1 


218  ASTBONOMT. 

8aoh  elfeots,  if  real,  may  be  explained  upon  tibe  same  prrBciphi 
aa  those  by  which  we  have  already  ezpfained  the  effiscta  imputed  to 
the  red  moon.  Animal  subatancea  exposed  to  a  clear  sky  at  night, 
are  liable  to  receive  a  deposition  of  dew,  which  humidity  has  a  ten- 
dency to  accelerate  putrefaction.  But  this  effect  will  be  prodneod 
if  the  sky  be  clear,  whether  the  moon  be  above  the  hoiriion  or  Bot 
The  moon,  therefore,  in  this  case,  is  a  witness  and  not  an  igeit; 
and  we  must  acquit  her  of  the  misdeeds  imputed  to  her. 

Supposed  lunar  influence  on  sheU-Jish.  — It  is  a  Terj  andenl  re- 
mark, that  oysters  and  other  shell-fish  become  larger  during  the  in- 
crease than  during  the  decline  of  the  moon.     This  maxim  is  mat- 
tioned  by  the  poet  Luoilius,  by  Aulus  Gellins,  and  others ;  and  the 
members  of  the  academy  dd  Cimento  appear  to  have  taeitlyadantp    ) 
ted  \ij  since  they  endeavour  to  give  an  explanation  (^  it     Theftdy    ^ 
however,  has  been  carefully  examined  by  Rohault,  who  baa  eooh    - 
pared  shell-fish  taken  at  all  periods  of  the  lunar  month|  and  fiMod 
that  they  exhibit  no  difference  of  quality. 

2501.  Supposed  lunar  influence  on  the  marrow  of  anuRofc.—  ' 
An  opinion  is  prevalent  among  the  butchers  that  the  marrow  Ibaid  < 
in  the  bones  of  animals  varies  in  ouantity  according  to  the  pban  =< 
of  the  moon  in  which  they  are  slaughtered.  This  question  hn  > 
also  been  examined  by  Rohault,  who  made  a  series  of  obeervatioDS 
which  were  continued  for  twenty  years  with  a  view  to  test  it;  sod  : 
the  result  was,  that  it  was  proved  completely  destitute  of  fonnda- 
tion. 

2502.  Supposed  lunar  influence  on  tJie  weight  of  the  humm    : 
hody.  —  Sanctorius,  whoso  name  is  celebrated  in  phyncs  for  the    i 
invention  of  the  thermometer,  held  it  as  a  principle  that  a  healthy 
man  gaiucd  two  pounds  weight  at  the  beginning  of  every  lunar    ; 
month,  which  he  lost  toward  its  completion.     This  opinion  appean    - 
to  be  founded  on  experiments  made  upon  himself;   and  aflMi 
another  instance   of  a  fortuitous  coincidence  hastily  generalised.    ■ 
The  error  would  have  been  corrected  if  he  had  continued  his  obser* 
vations  a  sufficient  length  of  time. 

2503.  Supposed  lunar  influence  on  births,  —  It  is  a  prevalent 
opinion  that  births  occur  more  frequently  in  the  decline  of  the  mooo  ~ 
than  in  her  increase.  This  opinion  has  not  been  tested  by  compiriog 
the  number  of  births  with  the  periods  of  the  lunar  phases ;  hat  the 
attention  directed  to  statistics,  as  well  in  this  country  as  abroad, 
will  soon  lead  to  the  decision  of  this  question.* 

2504.  Supposed  lunar  influence  on  incubation.  —  It  is  a  maxim 
handed  down  by  Pliny,  that  eggs  should  be  put  to  cover  when  the 


*  Other  sexual  phenomena,  such  as  the  period  of  gestation,  vnlgsrlx 
iupposed  to  have  some  relation  to  the  lunar  month,  have  no  relation  wbtt- 
OYer  to  that  period. 


TH£  MOON.  219 

is  new.     In  Fruioe  it  b  a  maxim  generallj  adopted,  that  the 

are  better  and  more  successfiillj  reared  when  they  break  the 
at  the  foil  of  the  moon.  The  experiments  and  observations 
.  Oiroa  de  Busareinpues  have  given  conntenanoe  to  this  opin- 

But  such  observations  require  to  be  multiplied  before  the 
m  can  be  considered  as  established.  M.  Girou  inclines  to  the 
Ml  that  during  the  dark  nights  about  new  moon  the  hens  sit  so 
itnrbed  that  £ej  either  kill  their  young  or  check  their  devel- 
ni  bj  too  much  heat ;  while  in  moonlight  nights,  being  more 
mM,  uoB  effect  is  not  produced. 
05.   Suppo9ed  lunar  infiuence  on  mental  derangement  and 

kmnan  maladiei.  —  The  influence  on  the  phenomena  of  human 
dies  imputed  to  the  moon  is  very  ancient  Hippocrates  had  so 
i;  a  faith  in  the  influence  of  celestial  objects  upon  animated 
rsy  that  he  expressly  recommends  no  physician  to  be  trusted 
IS  rnnorant  of  astronomy:  Qalen,  following  Hippocrates,  mdn- 
d  £e  same  opinion,  especially  of  the  influence  of  the  moon 
oe  in  diseases  the  lunar  periods  were  said  to  correspond  with  the 
sssion  of  the  sufferings  of  the  patients.  The  critical  days  or 
i  (as  they  were  afterward  ealled),  were  the  seventh,  fourteenth, 
twenty-fost  of  the  disease,  corresponding  to  the  intervals  be- 
n  the  moon's  principal  phases.  While  the  doctrine  of  alchym- 
|>revailed,  the  human  body  was  considered  as  a  microcosm ;  the 
t  representing  the  sun,  the  brain  the  moon.     The  planets  had 

ite  proper  influence :  Jupiter  presided  over  the  lungs,  Man 

the  hver,  Saturn  over  the  spleen,  Venus  over  the  kidneys,  and 
corj  over  the  oigans  of  generation.  Of  these  grotesque  no- 
I  there  is  now  no  relic,  except  the  term  hinacy,  which  still 
jpDStes  unsoundness  of  mind.  But  even  this  term  may  in  some 
•ee  be  said  to  be  banished  from  the  terminology  of  medicine, 
it  has  taken  refuge  in  that  receptacle  of  all  antiquated  absurdi- 

of  phraseology  —  the  law.  Lunatic,  we  believe,  is  still  the 
I  for  the  subject  who  is  incapable  of  managing  his  own  aflairs. 
klthough  the  ancient  faith  in  the  connection  between  the  phases 
he  moon  and  the  phenomena  of  insanity  appears  in  a  great 
nee  to  be  abandoned,  yet  it  is  not  altogether  without  its  votaries ; 
have  we  been  able  to  ascertain  that  any  series  of  observations 
lucted  on  scientific  principles  has  ever  been  made  on  the  pheno* 
ta  of  insauity,  with  a  view  to  disprove  this  connection.  We 
e  even  met  with  intelligent  and  well-educated  physicians  who 

maintain  that  the  paroxysms  of  insane  patients  are  more  violent 
;n  the  moon  is  full  than  at  other  times. 

506.  Examples  produced  by  Faber  and  RamazzxnL  —  Ma- 
>lus  Faber  gives  an  instance  of  a  maniac  who,  at  the  very  mo- 
lt of  an  eclipse  of  the  moon,  became  furious,  seised  upon  a 
rd,  and  fell  upon  every  one  around  him.    Ramaszini  lelatea 


aSO  IBTEONOMT. 

ttat^in  tli«  qwbmio  fefw  whioh  qweid  am  Ililjia  fth«  javl8i^ 
pitieiitB  died  in  an  anoBiial  number  on  the  Slit  of  Janvny,  at  Al 

BomeDt  of  a  lunar  eelipee. 

Without  disputing  this  &ct  (to  aaoertain  whieh,  howwer.  it  wpM 
be  neoeasary  to  have  statiatical  retama  of  the  daily  deatfia;,  il  atf 
be  objeoted  that  the  patients  who  thoa  died  in  aodi  moBben  lil  ill 
moment  of  the  eolipae,  might  have  had  their  imagmnliimi  bU|[ 
ezoited,  and  tiieir  rears  wrooght  upon  by  the  appranoh  ef  VI 


event,  if  popular  opinion  invested^  it  with  dan^.    Xhaft  aadHk 


i^dnion  was  not  unlikely  to  preyail,  is  evident  from  Urn 
have  been  reoorded. 

At  no  veiy  distant  period  from  that  time,  m  Auansl^  Itt^  |r|| 
related  that  patients  in  considerable  numbers  were,  liy  (■te#^ 
physiciansi  shut  up  in  chambers  well  dosed,  wanned,  and  psrfWi^ 
with  a  view  to  escape  the  injurious  influence  of  the  aolir  adte 


which  happened  at  that  time  i  and  such  was  the 
persons  of  nH  classes,  that  the  numbers  who  flocked  to 
were  so  great  that  the  eoclesiastics  found  it  impossible  to 
that  rite.    An  amusing  anecdote  is  related  of  a  village  onrale 
Paris,  who,  with  a  view  to  ease  the  minds  of  his  flock,  and  to  gri( 
the  necessary  time  to  get  through  bis  business,  seriously 
them  that  the  eclipse  was  postponed  for  a  fortnight. 

2507.  Exampiet  of  Valitmteri  and  Bacon. — Two  of  die 
remarkable  examples  reoorded,  of  the  supposed  influence  of  Ai 
moon  on  the  human  body,  are  those  of  YaUisnieri  and  Bacon.  Tit 
lisnieri  declares  that,  being  at  Padua,  reooverioff  from  a  tefioM 
illness,  he  suflfered,  on  the  12th  of  May,  1706,  during  the  ed^ 
of  the  sun,  unusual  weakness  and  shivering.  Lunar  edipaee  new 
happened  without  making  Bacon  faint;  and  he  did  not  reoover  Ui 
senses  till  the  moon  recovered  her  light 

That  these  two  striking  examples  should  be  admitted  in  proof  ef 
the  existence  of  lunar  mfluence,  it  would  be  necessary,  aaya  ![• 
Arago,  to  establish  the  fact,  that  feebleness  and  pusilhmimitf  ef 
character  are  never  connected  with  high  qualities  of  mind. 

2508.  Supposed  influence  on  cutaneous  affections,  —  Heauiet 
considered  that  cutaneous  maladies  had  a  manifest  connection  with 
the  lunar  phases.  He  says  that  he  himself  observed,  in  the  yev 
1760,  a  patient  afflicted  with  a  scald-head  (ieigne),  who,  during  the 
decline  of  the  moon,  suffered  from  a  gradual  increase  of  the  maladj, 
which  continued  until  the  epoch  of  the  new  moon,  when  it  had 
covered  the  face  and  breast,  and  produced  insufferable  itching.  Am 
the  moon  increased,  these  symptoms  disappeared  by  degrees;  tiie 
face  became  free  from  the  eruption ;  but  the  same  effects  wera  rs- 
produced  after  the  full  of  the  moon.  These  periods  of  the  dkesM 
continued  for  three  months. 

Henuret  also  stated  that  he  witnessed  a  similar  oorrespondeoee 


THE  MOON.  2'Jl 

letween  the  lunar  phases  aod  the  distemper  of  the  itch ;  hot  the 
utamstaDoes  were  the  reverse  of  those  in  the  former  case ;  the 
Daladj  attaining  its  mazimum  at  the  full  of  the  moon,  and  its 
ainimum  at  the  new  moon. 

Without  disputing  the  aceoracy  of  these  statements,  or  throwing 
■J  Bnq[>iGion  on  the  good  £uth  of  the  phjsidan  who  has  made 
km,  we  mayoheerve  that  such  £u:tB  jmove  nothing  except  the 
hrtoitooa  cdncidenoe.  If  the  lektion  of  cause  and  eSeet  had 
insled  between  the  lunar  phases  and  the  phenomena  of  these  dis- 
iNDpeiVy  the  same  cause  would  have  continued  to  produce  the  same 
Art  in  like  drcnmstances ;  and  we  should  not  be  left  to  depend 
br  the  proof  of  lunar  influence  on  the  statements  of  isolated  cases, 
nenrring  under  the  ohservation  of  a  phjsician  who  was  himself  a 
ttliever. 

2509.  Remarkable  rate  adduced  by  Hoffman.  —  Maurice  Hoff- 
Baa  relates  a  case  whieh  came  under  his  own  practice,  of  a  joung 
nmaiiy  the  daiuhter  of  an  epileptic  patient  The  abdomen  of  this 
fA  became  inflated  every  monUi  as  the  moon  increased,  and  regu- 
Illy  resumed  its  natural  form  with  the  decline  of  the  moon. 

Now,  if  this  statement  of  Hoffman  were  accompanied  by  all  the 
kBoesBaiy  details,  and  if,  also,  we  were  assured  that  this  strange 
Ifaoi  continued  to  be  produced  for  any  considerable  length  of  dme, 
he  relation  of  cause  and  effect  between  the  phases  of  the  moon 
ad  the  malady  of  the  girl  could  not  legitimately  be  denied ;  but 
eoeiving  the  statement  in  so  vague  a  form,  and  not  being  assured 
hat  the  effect  continued  to  be  produced  beyond  a  few  months,  the 
cgitimate  conclusion  at  which  we  must  arrive  is,  that  this  is  another 
sample  of  fortuitous  coincidence,  and  may  be  classed  with  the  ful- 
Qment  of  dreams,  prodigies,  &c.,  &c. 

2510.  Catet  o/ nervous  diseoMes.  —  As  may  naturally  be  ex- 
Mcted,  nervous  diseases  are  those  which  have  presented  the  most 
leqoent  indications  of  a  relation  with  the  lunar  phases.  The  cele- 
mted  Mead  was  a  strong  believer,  not  only  in  the  lunar  influence, 
at  in  the  influence  of  all  the  heavenly  bodies  on  all  the  human. 
le  cites  the  case  of  a  child  who  always  went  into  convulsions  at  the 
aoment  of  full  moon.  Pyson,  another  believer,  cites  another  case 
f  a  paraWtic  patient  whose  disease  was  brought  on  by  the  new 
Doon.  Menuret  records  the  case  of  an  epileptic  patient  whose  fits 
etomed  with  the  full  moon.  The  transactions  of  learned  societies 
bound  with  examples  of  giddiness,  malignant  fever,  somnambu- 
ism,  &c.,  having  in  their  paroxysms  more  or  less  corresponded  witL 
he  lunar  phases.  Gall  states,  as  a  matter  having  fallen  uiidor  his 
»wn  observation,  that  patients  suffering  under  weakness  of  iiitcUoct 
lad  two  peri<xls  in  the  mouth  of  peculiar  excitement;  and,  in  a 
vork  published  in  London  so  recently  as  1829,  wc  are  assured  that 
liese  epochs  aro  between  the  new  and  full  moon. 

19* 


I 


i!!22  ASTRONOMY. 

2511.  OUertfatums  of  Dr,  Olben  on  imane  paiieniM.  —  Agtinst 
all  these  instances  of  the  supposed  effect  of  lunar  influenoe,  we 
have  little  direct  proof  to  offer.  To  establish  a  negative  is  not  easj. 
Yet  it  were  to  be  wished  that  in  some  of  our  great  asylums  for  ia- 
sane  patients,  a  register  should  be  preserred  of  the  exact  times  of 
the  access  of  all  the  remarkable  paroxysms;  a  subsequent  ooo- 
parisoo  of  this  with  the  age  of  the  moon  at  the  time  of  their  oooa^ 
rence,  would  furnish  the  ground  for  legitimate  and  safe  oonolosioDS. 
We  are  not  aware  of  any  scientific  physician  who  has  expreidj 
directed  his  attention  to  tlus  question,  except  Dr.  Olbers  of  BrewD, 
celebrated  for  his  discovery  of  the  planets  Pallas  and  Yesta.  Ha 
states  that,  in  the  course  of  a  long  medical  practicCi  he  was  mm 
able  to  discover  the  slightest  trace  of  any  conneotioa  between  tk 
phenomena  of  disease  and  the  phases  of  ike  moon. 


2512.  Influence  not  to  he  hcutily  refected.  — lo  the  spirit  of  im 
philosophy,  M.  Arago,  nevertheless,  recommends  caution  in  deoidiiig   ^ 
against  this  influence.     The  nervous  system,  says  he,  is  in  many  ]■-    ; 
stances  an  instrument  infinitely  more  delicate  than  the  most  smi   ^ 
apparatus  of  modem  physics.     Who  does  not  know  that  the  dfro-   ; 
tory  nerves  inform  us  of  the  presence  of  odoriferous  matter  in  air,    , 
the  traces  of  which  the  most  refined  physical  analysis  would  £ul  to 
detect?     The  mechanism  of  the  eye  is  highly  affected  by  that 
lunar  light  which,  even  condensed  with  all  the  power  of  the  lamit 
burning  lenses,  fails  to  affect  by  its  heat  the  most  susceptible  ther- 
mometers, or  by  its  chemical  influence,  the  chloride  of  silver;  yet 
a  small  portion  of  this  light  introduced  through  a  pin-hole  wUl  be 
sufficient  to  produce  an  instantaneous  contraction  of   the  pupil; 
nevertheless,  the   integuments  of  this  membrane,  so  sensible  to 
light,  appear  to  be  completely  inert  when  otherwise  affected.     The 
pupil  remains  unmoved,  whether  we  scrape  it  with  the  point  of  a 
needle,  moisten  it  with  liquid  acids,  or  impart  to  its  surface  electric 
sparks.     The  retina  itself,  which  sympathises  with  the  pupil,  ii 
insensible  to  the  influence  of  the  most  active  mechanical  agents. 
Phenomena  so  mysterious  should  teach  us  with  what  reserve  we 
should  reason  on  analogies  drawn  from  experiments  made  upon  in- 
animate substances,  to  the  far  different  and  more  difficult  caae  of 
organised  matter  endowed  with  life. 


( 


THE  TIDES  AND  TRADE  WINDS.  '228 


CHAP.  X. 

THE  TIDKS  AND  TRADS  WINDS. 

2513.  Oorretpondence  beftoeen  the  recurrence  of  the  tides^  and 
tkfB  diurnal  appearance  of  the  moon,  —  The  phenomena  of  the  tides 
of  the  ocean  are  too  remarkable  not  to  have  attracted  notioe  at  an 
earlj  period  in  the  progress  of  knowledge.  The  intervals  between 
the  epochs  of  high  and  low  water  everywhere  corresponding  with 
the  intervals  between  the  passage  of  the  moon  over  the  meridian 
ibove  and  below  the  horizon,  suggested  naturally  the  phvsical  con- 
Beetion  between  these  two  effects,  and  indicated  the  probability  of 
Ihe  eanse  of  the  tides  being  found  in  the  motion  of  the  moon. 

2514.  Erroneout  notions  of  the  lunar  influence, — There  are  few 
«h}eet8  in  physical  science  about  which  more  erroneous  notions 
fnvmil  among  those  who  are  but  a  little  informed.     A  common 
ilsft  isy  that  the  attraction  of  the  moon  draws  the  waters  of  the 
ttrth  toward  that  side  of  the  globe  on  which  it  happens  to  be  placed, 
nd  that  consequently  they  are  heaped  up  on  that  side,  so  that  the 
lemis  and  seas  acquire  there  a  greater  depth  than  elsewhere ;  and 
(hat  high  water  will  thus  take  place  under,  or  nearly  under,  the  moon. 
Bat  this  does  not  correspond  with  the  fact.     High  water  is  not  pro- 
duced merely  under  the  moon,  but  is  equally  produced  upon  those 
puts  most  removed  from  the  moon.     Suppose  a  meridian  of  the 
ftfth  so  selected,  that  if  it  were  continued  beyond  the  earth,  its 
plane  would  pass  through  the  moon ;  we  find  that,  subject  to  certain 
Mxiifications,  a  great  tidal  wave,  or  what  b  called  htt/h  watery  will 
ke  formed  on  both  sides  of  this  meridian ;  that  is  to  say,  on  tho 
■de  next  the  moon,  and  on  the  side  remote  from  the  moon.    As  the 
■000  moves,  these  two  great  tidal  waves  follow  her.     They  are  of 
floorse  separated  from  each  other  by  half  the  circumference  of  the 
globe.     As  the  globe  revolves  with  its  diurnal  motion  upon  its  axis, 
every  part  of  its  surface  passes  successivelv  under  these  tidal  waves ; 
lad  at  all  such  parts,  as  they  pass  under  them,  there  is  the  pheno- 
menon of  high  water.     Hcuco  it  is  that  in  all  places  there  are  two 
tides  daily,  having  an  interval  of  about  twelve  hours  between  them. 
Now,  if  the  common  notion  of  the  cause  of  the  tides  were  well 
foanded,  there  would  be  only  one  tide  daily — viz.,  that  which  would 
tike  place  when  the  moon  is  at  or  near  the  meridian. 

2515.  The  moon'g  attraction  alone  will  not  explain  the  tides. — 
That  the  moon's  attraction  upon  the  earth  simply  considered  would 
Bot  explain  the  tides  is  easily  shown.     Lot  us  suppose  that  the 


whole  mass  of  matter  on  tbe  earth,  including  the  waters  which  fu- 
ti»llj  cover  it,  were  ftttracled  eqnallj  by  the  moon ;  they  wobW 
then  be  ecjualty  drawn  toward  that  body,  and  no  reason  woald  eiiit 
why  they  ehould  be  heaped  under  tbe  moon ;  for  if  they  were  d«ti 
with  the  same  force  as  that  with  which  tbe  solid  globe  of  the  eirtli 
nndcr  tbcm  is  drawn,  there  would  be  no  reason  for  supposiog  that 
tbe  waters  would  have  a  greater  tendency  to  collect  towani  the  mam 
tban  the  solid  bottom  of  uie  ocean  on  which  they  reaL  Id  short,  the 
whole  mass  of  tbo  earth,  solid  and  Quid,  being  drawn  wilb  tbe  nme 
force,  would  equally  lead  toward  the  moon ;  and  its  parts,  whetfair 
Bolid  or  Suid,  wonid  preserve  among  themselves  tbe  eame  rclatin 
position  as  if  they  were  not  attracted  at  all. 

2516.  Tides  cauted  hy  the  difference  of  the  altrartiotu  on  Jif- 
/erent  parU  of  the  earth.  —  When  we  observe,  however,  in  a  mM 
composed  of  various  porticlea  of  matter,  that  the  relative  anaagfr 
ment  of  these  particles  is  distarbcd,  some  bi^iug  driven  in  cwlaiB 
directions  more  than  others,  tbe  inference  is,  that  the  eompowat 
parts  of  such  a  mass  must  be  placed  under  theopera^oD  of  diSiaicel 
forces;  those  which  tend  more  than  others  in  a  certaia  ^jtctiot 
being  driven  with  a  proportionally  greater  force.  Such  is  the  «■■ 
with  tbe  earth,  placed  under  the  attraction  of  the  moon.  And  itii 
is,  in  fact,  what  must  happen  under  tho  operation  of  an  attractjn 
force  like  that  of  gravitation,  which  diminishes  in  its  inteDsitj  h 
tbe  square  of  the  distance  iacreaaes. 

Let  A,  B,  c,  D,  £,  F,  o,  H,  fit/.  731,  represent  the  globe  of  ibt 
earth,  and,  to  simplify  the  explanatian,  let  us  first  suppoae  the  edin 


Fig.  731, 

surface  of  the  globe  to  be  covered  with  water.  Let  m,  the  moca, 
be  placed  at  the  distance  m  ii  from  the  nearest  point  of  tbe  nu^ 
^  the  earth.  Now  it  will  be  apparent  that  the  various  p 
the  earth's  surfaco  are  at  difTcrent  disLiucea  from  the  t 
A  and  G  are  more  rt'mole  th»Q  ii ;  k  aud  ¥  still  more  rei. 
aad  I  more  distant  again,  and  D  more  remote  tbata  tU.  Th* 
tion  wbich  the  tnooo  ezerdses  at  h  is,  therefon^  giMt«r  tin 


CD  TID18  AXD  TBABB  WINM.  SSB 


■fttdkiloniM  nfeAndo^nd  iim  graite  Ouui  thai  which  it 
aft  B  and  W}  and  the  attnation  which  it  ezaroiaes  at  d  la 
of  alL  Now  thia  attnetion  eqnaUy  affiMta  matter  in  erery 
aad  eooditioB.  It  afiaeta  the  partidea  of  fluid  as  well  as  aolid 
;  but  then  ia  thia  di&nenee,  thai  where  it  acta  upon  aolid 
r,  the  eoapeneatpaita  of  wUdi  are  at  difierent  diatancea  frran 
i^mtA  A&nbf  adgeot  to  diflEuEont  attncdonay  it  will  not  diatarb 
ha  irialiia  aiiaageiaent^  ainee  aneh  diatnrbaneea  or  diaamnflementB 
■a  pwfgnted  hy  the  coheaJon  whieh  chaiaoteriaes  a  aolid  body;  bot 
Hi  »  BOft  the  eaaa  with  floidbiy  the  partiolea  of  which  are  mobOe. 
^Bia  alii  art ifli  iriiioh  the  mom  eaereiaea  upon  the  ahell  of  water, 
MJk  is  coBeetad  imine&tely  vnder  it  near  the  point  z,  ia  greatw 
Ant  wUeh  it  enraiaea  iqwQ  the  aolid  maai  of  the^be;  oon* 
*  r  there  will  be  a  greater  tendency  of  thia  attractKm  to  draw 
idbkh  veali  upon  the  aufaee  at  h  toward  the  mooa,  than 
the  aolid  naaa  of  the  earth  which  ia  more  distant 
Aa  the  iaid,  by  ita  natore^  ia  free  to  obey  thia  ezoeaa  of  attrao- 
it  will  neceiaarily  hmp  itaelf  up  in  a  pile  or  ware,  over  h, 
m  eooTex  protaberaneei  aa  repreaented  between  r  and  i, 
S^  water  wul  take  place  at  h,  immediately  under  the  moon. 
ter  whidi  thna  cdlleota  at  h  will  necessarily  flow  from  tfie 
B  and  7,  where  thersbie  there  will  be  a  dimmished  quantity 
aflse  ptoportooQ. 

Baft  laft  na  now  oonaider  what  hi^ipens  to  that  part  of  the  eerth 
a.  Heva  the  watersy  beinff  more  remote  from  the  moon  than  the 
■U  wrnaa  of  tibe  earth  nnder  themy  will  be  leas  attractedi  and  con- 
wqatBalAj  will  hare  a  leaa  tendency  to  gravitate  toward  the  moon. 
Iha  solid  mass  of  the  earth,  dh,  will,  as  it  werCi  recede  flxmi  the 
nfteiB  aft  ih  in  virtoe  of  the  excess  of  attnetion,  leaying  these 
wafteia  behind  it,  which  will  thna  be  heaped  up  at «,  ao  as  to  form 
a  ooDfez  nrotabeianee  between  I  and  4  nnular  exactly  to  tiiat 
winefa  W6  hate  already  deaoribed  between  r  and  u  Aa  the  differ- 
anea  between  the  attnetion  of  the  moon  on  the  waten  at  a  and  die 
aofid  eurth  under  the  waten  is  neariT  the  aame  aa  the  diffurenoe 
httufiiin  ila  attnetion  on  the  latter  and  upon  the  waten  at  n,  it  fol- 
lava  that  the  hdght  of  the  fluid  protabennoes  at  a  and  it  aro  equal, 
h  other  woidai  the  heighia  of  the  tidea  on  opposite  sides  of  the  earthy 
the  one  being  under  tM  moon  and  the  other  most  remote  from  it, 
•nequaL 

It  appeara,  therefore,  that  the  cause  of  the  tides,  so  far  as  the 
mUm  of  the  moon  is  ooDcemed,  is  not,  as  is  Tulgarl^  supposed,  the 
rneni  attraction  of  the  moon;  since,  if  that  attnetion  were  equal 
en  nD  the  component  parte  of  the  earth,  there  would  assuredly  be 
We  aro  to  look  for  the  cauae,  not  in  the  attraction  of  the 
baft  in  the  megwalii^  of  ita  attraction  on  different  parts  of 
The  peater  tUa  inequality  is,  the  greater  will  be  thia 


S26  ASTRONOMT. 

lidos.  Henoe,  as  the  moon  is  snbject  to  a  slight  Ywna&m.  of  im 
tsDoe  from  the  earth,  it  will  follow,  that  when  it  is  at  ks  lent 
distaDce,  or  at  the  poiot  called  perigee,  the  tides  will  be  the  gnstiit; 
and  when  it  is  at  the  greatest  mstance,  or  at  the  point  called  d|pcj^ 
the  tides  will  be  least  ]  not  because  the  entire  attraotioo  of  As 
moon  in  the  former  case  is  greater  than  in  the  latter,  bet  beoMl 
the  diameter  of  the  globe  bearing  a  greater  proportion  to  the  kmm 
distance  than  the  greater,  there  will  be  a  greater  tM€fiuilH(|f  ef  ife> 
traction. 

2517.  UjffecU  of  9un*s  aUradion. — It  will  oeoor  to  those  lb 
bestow  on  these  observations  a  little  refleetioni  that  all  whieh  li 
have  stated  in  reference  to  the  efieots  produced  bj  the  attnetiai  rf 
the  moon  upon  the  earth,  will  also  be  applicable  to  the  attiaoln  of 
the  sun.  This  is  undoubtedly  true ;  but  in  the  case  of  the  son  Ik 
effects  are  modified  in  some  very  important  respects.  The  smi  ii  il 
400  times  a  greater  distance  than  the  moon,  and  the  actual  amonl 
of  its  attraction  on  the  earth  would,  on  that  account,  be  160^000 
times  less  than  that  of  the  moon ;  but  the  mass  of  the  mm  mmk 
that  of  the  moon  in  a  much  greater  ratio  than  that  of  160,000  to  L 
It  therefore  possesses  a  much  greater  attracting  power  in  Tiitas  rf 
its  mass  compared  with  the  moon,  than  it  loses  by  its  greater  difr 
tance.  It  exercises,  therefore,  upon  the  earth  an  attraoticm  elM^ 
mously  greater  than  the  moon  exercises.  Now,  if  the  simple  amoul 
of  its  attraction  were,  as  is  commonly  supposed,  the  cause  of  the 
tides,  the  sun  ought  to  produce  a  vastly  greater  tide  than  the  mooa 
The  reverse  is,  however,  the  case,  and  the  cause  is  easily  expIainedL 
Let  it  be  remembered  that  the  tides  are  due  solely  to  the  ineqnslitj 
of  the  attraction  on  different  sides  of  the  earth,  and  the  greater  thsl 
inequality  is,  the  greater  will  be  the  tides,  and  the  less  that  » 
equality  is,  the  less  will  be  the  tides. 

In  the  case  of  the  sun,  the  total  distance  is  12,000  diameten  d 
the  earth,  and  coDsequently  the  diffiBrcnce  between  its  distances  tnm 
the  one  side  and  the  other  of  the  earth  will  be  only  the  12,000lk 
part  of  the  whole  distance,  while  in  the  case  of  the  moon,  the  toldi 
distance  being  only  30  diameters  of  the  earth,  the  difference  of  di^ 
tances  from  one  side  and  the  other  is  the  30th  part  of  the  whok 
distance.  The  inequality  of  the  attraction,  upon  which  alone,  sal 
not  on  its  whole  amount,  the  production  of  the  tidal  wave  depend^ 
is  therefore  much  greater  in  the  case  of  the  moon.  According  to 
Newton's  calculation,  the  tidal  wave  due  to  the  moon  is  greater  is 
height  than  that  due  to  the  sun  in  the  ratio  of  58  to  23,  or  2|  to  1 
very  nearly. 

2518.  Cause  of  spring  and  neap  tides.  —  There  is,  therefore,! 
solar  as  well  as  a  lunar  tide  wave,  the  former  being  much  less  ele* 
vated  than  the  latter,  and  each  following  the  luminary  from  whicb 
k  takes  its  name.     When  the  sun  and  moon,  therefore,  are  either 


TUE  TIDES  AND  TRADE  WINDS.  227 

QD  the  same  side  of  the  earth,  or  on  the  opposite  sides  of  the  earth — 
JO  other  worda,  when  it  is  new  or  full  moon  —  their  efiects  in  pro- 
dooiDg  tides  are  combined,  and  the  spring  tide  is  produced,  the 
hcijriit  of  which  is  equal  to  the  solar  and  luuar  tides  taken  together. 
On  the  other  hand,  when  the  sun  and  moon  are  separated  from 
earii  other  hy  a  distance  of  one  fourth  of  the  heavens,  that  is,  when 
the  moon  is  in  the  quarters,  the  effect  of  the  solar  tide  has  a  ten- 
dency to  diminish  that  of  the  lunar  tide. 

The  tides  produced  by  the  combination  of  the  lunar  and  solar  tide 
VATee  at  the  time  of  new  and  full  moon  are  called  spring  tides  ; 
and  those  produced  by  the  lunar  wave  diminished  by  the  effect  of 
the  aoUur  wave  at  the  quarters  are  called  neap  tides. 

2519.    Why  the  tides  are  not  produced  directly  under  lite  moon. 

'-—  If  physical  effects  followed  immediately,  without  any  appreciable 

interval  of  time,  the  operation  of  their  causes,  then  the  tidal  wave 

produced  by  the  moon  would  be  on  the  meridian  of  the  earth  directly 

noder  and  opposite  to  that  luminary ;  and  the  same  would  be  true  of 

the  wfAu  tides.     But  the  waters  of  the  globe  have,  in  common  with 

ftU  other  matter,  tho  property  of  inertia,  and  it  takes  a  certain  in- 

terrel  of  time  to  impress  upon  them  a  certain  change  of  position. 

Henoe  it  follows  that  the  tidal  wave  produced  by  the  moon  is  not 

fanned  immediately  under  that  body,  but  follows  it  at  a  certain  dis- 

tuiee.     In  oonsequence  of  this,  the  tide  raised  by  the  moon  does  not 

tdM  phoe  for  two  or  three  hours  after  the  moon  passes  the  meridian ; 

and  as  the  action  of  tho  sun  is  still  more  feeble,  there  is  a  still 

graster  interval  between  the  transit  of  the  sun  and  occurrence  of  the 

solar  tide. 

2520.  Priming  and  lagging  of  the  tides,  —  But  besides  these 

droamstanoes,  the  tide  is  affected  by  other  causes.     It  is  not  to  the 

separate  effect  of  either  of  these  bodies,  but  to  the  combined  effect 

of  bothy  that  the  efiects  are  due ;  and  at  every  period  of  the  month, 

the  time  of  actual  high  water  is  either  accelerated  or  retarded  by  the 

son.     In  the  first  and  third  quarters  of  the  moon,  the  solar  tide  is 

westward  of  the  lunar  one ;  and,  consequently,  the  actual  high  water, 

which  is  the  result  of  tho  combination  of  the  two  waves,  will  be  to 

the  westward  of  the  place  it  would  have  if  the  moon  acted  alone, 

and  the  time  of  high  water  will  therefore  be  accelerated.     Id  the 

second  and  fourth  quarters  the  general  effect  of  tho  sun  is,  for  a 

Bimilar  reason,  to  produce  a  retardation  in  the  time  of  high  water. 

This  effect,  produced  by  the  sun  and  moon  combined,  is  what  is 

commonly  oalled  fkk^  priming  and  lagging  of  the  tides.    The  highest 

spring  tides  occur  when  the  moon  passes  the  meridian  about  an  hour 

aher  the  sun;  for  then  the  maximum  effect  of  the  two  bodies 

eoineides. 

2521.     Researches  of  Whexcdl  and  Lubbock. — The  subject  of 
the  tides  has  of  late  years  received  much  attention  from  several  scv 


228  ASTROKOMT. 

entifio  iDvesHgators  id  Europe.  The  disoiumoiiB  held  at  die  anonl 
meetings  of  the  British  Association  for  the  Advancement  of  Seienoei 
on  this  subject,  have  led  to  the  development  of  mnch  naefiil  infisp- 
mation.  The  labours  of  Professor  Wnewell  have  been  espedillj 
valuable  on  these  questions.  Sir  John  Lnbbook  has  alao  pabliriwd 
a  valuable  treatise  upon  it.  To  trace  the  results  of  these  inverti- 
ffations  in  all  the  details  which  would  render  them  clear  and  intd- 
ligible,  would  greatly  transcend  the  necessary  limits  of  this  vqIoim.  - 
We  shall,  however,  briefly  advert  to  a  few  of  the  moet  xemaifaUa  e 
points  connected  with  these  questions.  r 

2522.  Vvlf/ar  and  corrected  e9tahlitihment — The  apparent  tine  . 
of  high  water  at  any  port  in  the  afternoon  of  the  day  or  new  or  MI  s 
moon,  is  what  is  usually  called  the  establtahmeni  of  the  part,  tto-  3 
feasor  Whewell  calls  this  the  vulgar  establishment,  and  ne  calbtte  -m 
corrected  establishment  the  mean  of  all  the  intervals  of  the  tides  snd  ms 
transit  of  half  a  month.    This  corrected  establishment  is  eoBM*    ^ 

Suently  the  luni-tidal  interval  corresponding  to  the  day  on  wUek   ^m 
le  moon  passes  the  meridian  at  noon  or  midnight  cr 

2523.  Diurnal  inequality/.  —  The  two  tides  immediatelv  fblhmg   %^ 
one  another,  or  the  tides  of  the  day  and  night,  vary,  both  in  bsig^   r 
and  time  of  high  water  at  any  particular  place,  with  the  distance  of    ^ 
the  sun  and  moon  from  the  equator.     As  the  vertex  of  the  tide  wan  . — 
always  tends  to  place  itself  vertically  under  the  luminary  which  pro*    ^ 
duces  it,  it  is  evident  that  of  two  consecutive  tides,  that  which  happeu   . 
when  the  moon  is  nearest  the  zenith  or  nadir  will  be  greater  thsn   — 
the  other ;  and,  consequently,  when  the  moon's  declination  is  of  tk  ^ 
same  denomination  as  the  latitude  of  the  place,  the  tide  which  eo^  ^ 
responds  to  the  upper  transit  will  be  greater  than  the  opposite  tnnti  r^ 
and  vice  versdj  the  difference  being  greatest  when  the  san  and  moOB  -^ 
are  in  opposition,  and  in  opposite  tropics.     This  is  called  the  VflCt^  < 
NAL  TNEQUALITY,  bccause  its  cyclc  is  one  day ;  but  it  varies  greallj  -^ 
at  different  places,  and  its  laws,  which  appear  to  be  governed  hj  ^ 
local  circumstances,  are  very  imperfectly  known. 

2524.  Local  effects  of  the  land  %ipon  the  tides,  —  We  have  BOt  mm 
described  the  principal  phenomena  that  would  take  place  were  tba  ? 
earth  a  sphere,  and  covered  entirely  with  a  fluid  of  uniform  depth.  -^ 
But  the  actual  phenomena  of  the  tides  are  infinitely  more  eoiDpIi-  3 
cated.  From  the  interruption  of  the  land,  and  the  irregular  fivn  ^ 
and  depth  of  the  ocean,  combined  with  many  other  disturbing  ci^ 
cumstances,  among  which  are  the  inertia  of  the  waters,  the  ftwtioB  ^ 
on  the  bottom  and  sides,  the  narrowness  and  length  of  the  channebi  « 
the  action  of  the  wind,  currents,  difference  of  atmospheric  piuawuti 
&c.,  &c.,  great  variation  takes  place  in  the  mean  times  and  heights 

of  high  water  at  platvs  differently  situated. 

2525.  Velocity/  of  tidal  wave,  —  In  the  open  ocean  the  ereslof     j 
tide  travels  with  enormous  velocity.     If  the  whole  sorftoe  liCit 


THE  TIDES  AND  TRADE  WINDS.  229 

eorered  with  water,  the  sammit  of  the  tide  wave,  being 

nuinlj  goyerned  bj  the  moon,  would  everywhere  follow  the  moon's 

tnnat  At  the  nme  interval  of  time,  and  consequently  travel  round 

the  earth  in  a  litUe  more  than  twenty-four  hours.     But  the  circum- 

ftrenoe  of  the  earth  at  the  equator  beinff  about  25,000  miles,  the 

fdoeity  of  propagation  would  therefore  be  about  1,000  miles  per 

hour.    The  actual  velocity  is,  perhaps,  nowhere  equal  to  this,  and  is 

very  different  at  different  places.     In  latitude  60^  south,  where 

thm  is  no  interruption  from  land  (excepting  the  narrow  promontory 

of  Palaconia),  the  tide  wave  will  complete  a  revolution  in  a  lunar 

day,  and  consequenUy  travel  at  the  rate  of  670  miles  an  hour.     On 

cmmining  Mr.  Whewell's  map  of  cotidal  lines,  it  will  be  seen  that 

tiie  great  tide  wave  from  the  Southern  Ocean  travels  from  the  Cape 

of  Good  Hope  to  the  Azores  in  about  twelve  hours,  and  from  the 

Aiorea  to  the  sonthermost  part  of  Ireland  in  about  three  hours  more. 

In  the  Atlantic,  the  hourly  velocity  in  some  cases  appears  to  be  10^ 

latitude,  or  near  700  miles,  which  is  almost  equal  to  the  velocity  of 

Bound  Uirough  the  air.     From  the  south  point  of  Ireland  to  the 

north  point  of  Scotland,  the  time  is  eight  hours,  and  the  velocity 

about  160  miles  an  hour  along  the  shore.     On  the  eastern  coast  of 

Britain,  and  in  shallow  water,  the  velocity  is  less.     From  Buchan- 

neaa  to  Sunderland  it  is  about  60  miles  an  hour;  from  Scarborough 

to  Cromer,  85  miles;  from  the  North  Foreland  to  London,  80 

miles ;  from  London  to  Richmond,  13  miles  an  hour  in  that  part  of 

the  river.    (Whewell,  Phil  Trans.  1833  and  1836.)    It  is  scarcely 

neeeasary  to  remind  the  reader  that  the  above  velocities  refer  to  the 

transmisfiion  of  the  undulation,  and  are  entirely  different  from  the 

Telocity  of  the  current  to  which  the  tide  gives  rise  in  shallow  water. 

252G.   Range  of  the  tides.  —  The  difference  of  level   between 

high  and  low  water  is  affected  by  various  causes,  but  chiefly  by  the 

eonfiguration  of  the  land,  and  is  very  different  at  different  places. 

In  deep  inbends  of  the  shore,  open  in  the  direction  of  the  tide  wave 

and  gradually  contracting  like  a  funnel,  the  convergence  of  water 

causes  a  very  great  increase  of  the  range.     Hence  the  very  high 

tides  in  the  Bristol  Channel,  the  Bay  of  St.  Malo,  and  the  Bay  of 

Fondy,  where  the  tide  is  said  to  rise  sometimes  to  the  height  of  one 

i       hundred  feet.     Promontories,  under  certain  circumstances,  exert  an 

ooposite  influence,  and  diminish  the  magnitude  of  the  tide.     The 

i       oiMerved  ranges  are  also  very  anomalous.     At  certain  places  on  the 

I      south-east  coast  of  Ireland,  the  range  is  not  more  than  three  feet, 

[      while  at  a  litUe  distance  on  each  side  it  becomes  twelve  or  thirteen 

i       feel;  and  it  is  remarkable  that  these  low  tides  occur  directly  opposite 

I       the  Bristol  Channel,  where  (at  Chepstow)  the  difference  between 

high  and  low  water  amounts  to  sixty  feet.     In  the  middle  of  the 

I       PKific  it  amounts  to  only  two  or  three  feet.     At  London  Docks, 

•       the  average  range  is  about  22  feet;  at  Liverpool,  155  feet;  at 

!  HI.  20 


280  ASIEOHOICT* 

PortRDoatli,  12-5  feet;  at  PIjmoiifth|  alio  12-6  ftrt|  at  BnM,  IS 
feet 

2527.  7%(2b  a^ecfe^  2>y  A«  omoMAere. — Berides  iiie  mmiflnoi 
eausee  of  irregalaritj  depending  on  the  kxsal  ciieiimBtaiietB,  tht  tidm 
are  also  affected  by  the  atate  of  the  atmoaphen.  Aft  BM^  At 
height  of  high  frater  Tariea  inYenelj  as  the  heifl^t  of  the  hanMHK 
and  rises  more  than  eight  inches  for  a  fell  of  aoont  half  aa  iath.m 
the  barometer.  At  Liverpooly  a  fell  of  one-tenth  of  an  iaek  ia.ili 
barometer  corresponds  to  a  rise  in  the  river  Mersey  of  about  a»  iiiBk; 
and  at  the  London  Bocks,  a  fell  of  one-tenth  of  an  indi  oomamfe 
to  a  rise  in  the  Thames  of  about  seven-tenths  of  an  isdi.  li^a 
low  buometer,  therefore,  the  tide  may  be  expeoted  to  be  hU^jdl 
vice  vend.  The  tide  is  also  liaUe  to  be  distorbed  by  wincHL^k 
John  Lubbock  states  that,  in  the  Solent  hurricane  of  JainHpj.% 
1889,  there  was  no  tide  at  Gainslxwongh,  which  is  iwenty-ife  wtBm 
up  the  Trent — a  circumstance  unknown  before.  At  SaItnianih»od|f 
five  miles  up  the  Ouse  from  the  Humber,  the  tide  went  on  ^W/% 
and  never  flowed  unUl  the  river  was  dry  in  some  I^sMa :  whib.i* 
Ostend,  toward  which  the  wmd  was  blowing,  ccmtrary  eSaeAa  upe 
observed.  Durins  strong  north-westerly  pm  the  tide  maiks  hl^k 
water  earlier  in  the  Thames  than  otherwise,  and  does  not  ^^ve  ss 
much  water,  while  the  ebb  tide  runs  out  bite,  and  marks  lower;  bet 
upon  the  gales  abating  and  weather  moderating,  the  tides  put  in  aal 
rise  much  higher,  while  they  also  run  longer  before  lu^  water  is 
marked,  and  with  more  velocity  of  current:  nor  do  they  run  onftss 
long  or  so  low. 

2528.  The  trade  winds,  —  The  great  atmospheric  currents  thv 
denominated,  from  the  advantages  which  navigation  has  deriiel 
from  them,  as  well  as  other  currents  arising  from  the  same  esosM^ 
are  produced  by  the  uneaual  exposure  of  the  atmospherio  oosn^ 
which  coats  the  terrestrial  globe,  to  the  action  of  solar  heat;  the 
expansion  and  contraction  that  air,  in  common  with  all  gMSOiP 
bodies,  suffers  from  increase  and  diminution  of  temperature;  thi.j 
tendency  which  lighter  fluids  have  to  rise  through  heavi«r|  ndp  k 
fine,  the  rotation  of  the  earth  upon  its  axis. 

The  regions  in  which  the  trades  prevail  are  two  great  trofiifld 
belts  extending  through  a  certain  limited  number  of  degreea  north 
and  south  of  the  line,  but  not  prevailing  on  the  line  itodf,  the  st* 
mospherical  character  of  which  is  an  almost  constant  calm.  IW 
permanent  currents  blow  in  the  northern  tropical  belt  from  the  north-  r 
east,  and  in  the  southern  from  the  south-east  f 

On  the  other  hand,  in  the  higher  latitudes  of  both  bemiqpheni  r 
the  prevalent  atmospheric  currents  are  directed  from  west  to  etft|  r 
redressing,  as  it  were,  the  disturbance  produced  by  the  trades.  : 

To  understand  the  cause  of  these  phenomens,  it  is  neecsssij  ti  ' 
remember  that  the  sun,  never  departing  more  than  28)®  tnm  tb   } 


parts  of  either  hemisphere;  while  the  air  thus  displaced, 
by  its  buoyancy  above  its  due  level,  and  unsustaincd  by  any 

preirsurc,  flows  down  towards  either  pole,  and,  being  cooled 
oarse  and  rendered  heavier,  it  descends  to  the  surface  of  the 
.t  those  upper  latitudes  from  which  the  air  had  been  sucked 
ttds  the  line  by  its  previous  ascent. 

mstant  circulation  and  an  interchange  of  atmosphere  between 
ertropical  and  extratropical  regions  of  the  earth  would  thus 
»lace,  the  air  ascending  from  the  intertropical  surface  and 
owing  towards  the  extratropical  regions^  where  it  descends  to 
ftLoe  to  be  again  sucked  towards  the  line. 

in  this  view  of  the  effects,  the  rotation  of  the  earth  on  its 
not  considered.  In  that  rotation  the  atmosphere  participates, 
r  which  rises  from  the  intertropical  surface  carries  with  it 
3citj  of  that  sur&ce,  which  is  at  the  rate  of  about  1,000  miles 
r  from  west  to  east.  This  velocity  it  retains  to  a  considerable 
after  it  has  passed  to  the  higher  latitudes  and  descended  to 
rfiioe,  which  moving  with  much  less  velocity  from  west  to 
lerc  is  an  effective  current  produced  in  that  direction  equiva- 
the  excess  of  the  eastward  motion  of  the  air  over  the  eastward 

of  the  sur&ce  of  the  earth.  Hence  arises  the  prevalent 
rd  winds,  especially  at  sea,  where  causes  of  local  disturbance 
i  frequent,  which  are  so  familiar,  and  one  of  the  effects  of 
has  been,  that,  while  the  average  length  of  the  trip  of  good 
vessels  from  New  York  to  Liverpool  has  been  only  twenty 
hat  of  the  trip  from  Liverpool  to  New  York  has  been  thirty- 


8SS  Aswumina. 

wkjf  with  the  effeot  of  the  diffaimM  of  diair  velooitifli.  EBnae  the 
Birooe,  and  the  objeote  upon  it,  aie  earned  ewtward  ftt  a  mvdi 
sreater  rate  than  the  air  which  has  joat  descended  ficom  the  higher 
EititadeSy  they  will  strike  aj^ainst  the  air  with  a  jfinee  proportioiiai  ts 
the  diflbrence  of  their  velocitiesi  and  this  finroe  will  have  a  diieetioa 
contrary  to  that  of  the  motion  of  the  sox&oe,  thaiis  to  Mgr«  fitMi 
east  to  west 

Bat  it  most  be  coiuidered  that  this  eastward  fbioei  doA  lo  fhs 
motion  of  the  earth's  sorfiuWi  is  combined  with  the  films  with  wUsh 
tibfl  sir  moves  from  the  extratropieal  regioBs  tovmida  4i0  JiM 
Thnsi  in  the  northern  hemispherei  die  fme  eistwnd  ii  eemUMl 
with  the  motion  of  the  air  from  aimrth  to  sonth,  Mid  the  iMhsrt 
of  ihese  forces  is  that  north-east  eoirent  which  aotnallj  piwiwb| 
whiloi  for  like  reasons,  sooth  of  the  line,  the  motion  of  theiirlMi 
sooth  to  north,  being  combined  with  the  force  esstwudy  jftoHmm 
the  sooth-eastern  corrent  which  prsTsils  sooth  of  the  line. 

Were  any  Gonsiderable  mass  of  sir,  as  Sir  J.  Heiaohol  ^kmam^ 
to  be  sudidEffi^  transferred  from  beyond  the  tropics  to  the  k 
the  difiference  of  the  rotary  velocities  proper  to  the  two  ' 
wooH  be  so  great^  as  to  prodoce,  not  merely  a  wind,  bat 
of  the  most  destructive  violence ;  and  the  same  observation  woaU 
be  equally  applicable  to  masses  of  air  transported  in  the  eontrOT 
direction.  But  this  is  not  the  case ;  the  advance  of  the  air  ■  \ 
gradual,  and  all  the  while  the  earth  is  continually  acting  on  the  ah",'  jl 
and  by  the  friction  of  its  surface  accelerating  or  retarding  its  velotttf.  JI 
Supposing  its  progress  to  cease  at  anv  point,  this  cause  woold  almost  |^ 
immediately  communicate  to  it  the  aencient  or  deprive  it  of  tibe  «►  j 
cessive  motion  of  rotation,  after  which  it  would  revolve  quietly  witb 
the  earth  and  be  at  relative  rest.  We  have  only  to  call  to  mind  thi 
comparative  thinness  of  the  coating  of  air  with  which  the  g^obek  |^ 
invested  (2323)  and  its  immense  mass,  exceeding,  as  it  does,  dsi  |i 
weight  of  the  atmosphere  at  least  100,000,000  times,  to  apprsciill 
the  absolute  command  of  any  extent  of  territory  of  the  eirth  OW 
the  atmosphere  immediately  incumbent  upon  it. 

It  appears,  therefore,  that  these  currents,  as  they  wpproeoh  Ikl 
equator  on  the  one  side  and  the  other,  must  gradual^  lose  ihlit 
force ;  their  exciting  cause  being  the  difference  of  the  magnitads  H 
the  parallels  of  latitude;  and  this  difference  beinir  evanesoent  mu 
the  line,  and  very  inconsiderable  within  many  degrees  of  it^  At 
equalising  force  of  the  earth  above  described  is  allowed  to  teke  fail 
effect :  but,  besides  this,  the  currents  directed  from  the  two  jpoin 
encounter  each  other  at  the  line,  and  destroy  each  other's  fonik  ■ 
Hence  arises  the  prevalence  of  those  calms  which  ohaneteiiA  ^ 
the  line. 


9.  Apparent  and  real  magnitude.  —  Owing  to  the  ellipticity 

earth's  orbit,  the  distaDce  of  the  sun  is  subject  to  a  periodical 

CD,  which  causes,  as    has   been  already  explained,  a  corre- 

Dg  variation  in  its  apparent  magnitude.    Its  CTeatest  apparent 

ter,  when  in  perihelion,  is  32'  35"'6,  or  195^''6,  and  its  least 

int  magnitode,  when  in  aphelion,  is  31'  30"^  or  1890".    Its  :  \i 

apparent  diameter  is  therefore  1923". 

las  been  already  (2457)  shovm  that  the  linear  yalne  of  1'^  at  .  \ 

u'b  distance  is  466  miles.     It  follows,  therefore,  that  the  ac-  | 

ngth  of  the  diameter  of  the  globe  of  the  sun  is 

1923  X  466  =  896,118  miles. 


il  magnitude  of  the  sun  may  also  be  easily  inferred  in 
numbers  from  that  of  the  moon.  The  apparent  diameter  of 
)on  being  equal  in  round  numbers  to  that  of  the  sun,  and  the 
»  of  the  sun  being  400  times  greater  than  that  of  the  moon, 
)W8  that  the  real  diameter  of  the  sun  must  be  400  times 
r  than  that  of  the  moon.     It  must,  therefore,  be 

2153  X  400  =  861,200  miles. 

thods  of  calculation  susceptible  of  closer  approximation  than 
it  has  been  found  that  the  magnitude  is  882,000  miles,  or 
times  tho  diameter  of  the  earth. 

0.  Magnitude  of  the  sun  illustrated,  —  Magnitudes  such  as 
'  tho  sun  so  far  transcend  all  standards  with  which  the  mind 
liar,  that  some  stretch  of  imagination,  and  some  effort  of  the 
landing,  arc  necessary  to  form  a  conception,  however  imper- 


I 
?     ■     . 

I 


384 

S681.  Surfaet  and  Wukm.  —  Since  tli«  snr&oea  of  riaha  A 
M  the  Bqiures,  and  tfacir  volnmea  aa  the  oubee,  of  their  OMHli^i 
it  KQamt  that  th«  surface  of  the  lun,  most  be  12,500  times,  nf  Ik 
Ttdnme,  1,400,000  times,  gKsXat  tb&n  those  of  the  earth. 

Una,  to  fora  a  globe  liae  the  mm,  it  would  be  neoeaeaiy  to  nD 
nearly  fourteen  huodred  thousand  globes  like  the  earth  into  one. 

It  ia  found  by  consideria^  the  balks  of  the  different  planets,  Ibll 
if  aU  the  planeta  and  satellites  in  the  solar  ajatem  were  mooldtd 
bto  a  rinf^e  globe,  that  globe  would  still  not  ezoeed  the  fife-W 
dredA  part  the  globe  of  the  san  :  in  other  w<vds,  the  hnlk  of  ttf 
■U  ia  ne  hundred  times  greater  than  the  aggregate  bulk  of  a&  lb 
rest  of  the  bodiea  of  the  system. 

2682.  Jb  MOM  and  dentify.  —  By  methods  of  calcnlalioQ  nJ 
obeerration,  which  will  be  exjJained  hereafter,  the  ratio  of  the  mm 
tt  matter  «ompoeiDg  the  globe  of  the  nm,  to  the  maai  of  bmM 
conpwDg  the  earth,  has  ^a  ascertained  to  be  254,036  to  1. 

By  comparing  this  proportion  of  the  quantities  of  pondenUt 
matter  in  the  sun  and  earth  with  their  relative  Tolumes,  it  will  U 
evident  that  the  mean  dcosity  of  the  matter  oompoaiog  tbe  m 
must  be  about  tout  dines  less  than  the  mean  density  of  the  matlar 
oompoung  the  earth ;  for  although  the  volume  of  the  sun  eioeeJi 
that  of  the  earth  ia  the  ratio  of  1,400,000  to  1,  its  weight  er  ■■■ 
exceeds  that  of  the  earth  in  the  lesser  ratio  of  355.000  to  1,  ihi 
latter  rado  being  four  times  less  than  the  former.  Bulk  for  U^ 
therefore,  the  sun  is  four  times  lighter  than  the  earth. 

Since  the  mean  density  of  the  earth  is  567  times  that  of  *■!■ 
(2393),  it  follows  that  the  mesn  density  of  the  sun  is  li2tiam,K 
abont  one  half,  greater  tbao  that  of  water. 

From  the  comparative  lightne^  of  the  matter  compooDgit,  B«^ 
ichel  infers  the  probability  that  au  intense  heat  preTuls  in  ila  ial^ 
lior,  by  which  its  elasticity  is  reiuforced,  and  rendered  otpeUa  of 
reaisting  the  almuat  inconceivable  pressure  due  to  ita  intriono  ffV^ 
fation,  without  oollapsiug  into  smaller  dimensions. 

2533.  Form  and  rotation  ^axU  of  ro(af ioh.  ^  AlthooA  l> 
tninda  nnacoustomed  to  the  rigour  of  scientiSo  reeearoh,  it  aigbt  f- 
pear  sufficiently  evident,  without  further  demoDstratioo,  thai  a* 
ann  is  globular  in  its  form,  yet  tbc  njorc  exact  methods  parsned  in 
the  iuTestigation  of  physics  dcoiaod  that  we  should  find  more  eae> 
elusive  proof  of  the  sphericity  of  the  solar  orb  than  the  men  fW 
that  the  disk  of  the  sun  is  always  circalar.  It  is  barotv  potsAik, 
Itowever  improbable,  that  a  flat  circular  disk  of  matter,  toe  fim  ef 
which  should  always  be  presented  to  the  earth,  might  be  tke  fina 
of  the  snn;  and  indeed  there  are  a  great  variety  of  atba  fiwM 
which,  by  a  pertioalar  arrangement  of  their  motjoni,  might  fCHHt 
to  thee™'  'Mfsolar  appenranoe  aa  well  aa  a  globe  ot  wgbut.   A 


THE  SUN.  285 

pvore,  theiiy  that  a  body  is  globalar,  something  more  is  necessary 
tiban  the  mere  hot  that  it  always  appears  circular. 

When  a  telescope  is  directed  to  the  san^  we  discover  upon  it  cer- 
lun  marks  or  spots,  of  which  we  shall  speak  more  folly  presently. 
"We  observe  that  these  marks,  while  they  preserve  the  same  relative 
positkm  with  respect  to  each  other,  move  regularly  from  one  side  of 
the  son  to  the  other.  They  disappear,  and  continue  to  be  invisible 
fv  a  certain  time,  come  into  view  again  on  the  other  side,  and  so 
«ioa  more  pass  over  the  son's  disk.  This  is  an  effect  which  would 
•widently  be  produced  by  marks  on  the  surface  of  a  globe,  the  globe 
itelf  revolving  on  an  axis,  and  carrying  these  marks  upon  it.  That 
this  b  the  case,  is  abundantly  proved  by  the  fact  that  the  periods  of 
rotation  for  all  these  marks  are  found  to  be  exactly  the  same,  viz., 
aboot  twenty-five  davs  and  a  quarter,  or  more  exactly  25***  7^'  48"*. 
Such  is,  then,  the  time  of  rotation  of  the  sun  upon  its  axis,  and 
thai  it  is  a  globe  remains  no  longer  doubtful,  since  a  globe  is  the 
oaly  body  which,  while  it  revolves  with  a  motion  of  rotation,  would 
always  present  the  cireular  appearance  to  the  eye.  The  axis  on 
whidi  the  sun  revolves  is  very  nearly  perpendicular  to  the  plane  of 
die  earth's  orbit,  and  the  motion  of  rotation  is  in  the  same  direction 
u  the  motion  of  the  planets  round  the  sun,  that  is  to  say,  from  west 
to  east. 

2534.  Spots.  —  One  of  the  earliest  fruits  of  the  invention  of  the 
tdascope  was  the  discovery  of  the  spots  upon  the  sun  ;  and  the  ex- 
mination  of  these  has  gradually  led  to  some  knowledge  of  the 
physical  constitution  of  the  centre  of  attraction  and  the  common 
fKUitain  of  light  and  heat  of  our  system. 

When  we  submit  a  solar  spot  to  telescopic  examination,  we  dis- 
cover its  appearance  to  be  that  of  an  intensely  black  irregularly 
shaped  patch,  edged  with  a  penumbral  fringe.  When  watched  for 
a  considerable  time,  it  is  found  to  undergo  a  gradual  change  in  its 
form  and  magnitude;  at  first  increasing  gradually  in  size,  until  it 
attains  some  definite  limit  of  magnitude,  when  it  ceases  to  increase, 
and  soon  begins,  on  the  contrary,  to  diminish ;  and  its  diminution 

Set  on  gradually,  until  at  length,  the  bright  sides  closing  in  upon 
e  dark  patch,  it  dwindles  first  to  a  mere  point,  and  finally  disap- 
pears altogether.  The  period  which  elapses  between  the  formation 
of  the  spot,  its  gradual  enlargement,  subsequent  diminution,  and 
final  disappearance,  is  very  various.  Some  spots  appear  and  disap- 
pear very  rapidly,  while  others  have  lasted  for  weeks  and  even  for 
months. 

The  magnitude  of  the  spots,  and  the  velocities  with  which  tbo 
matter  composing  their  edges  and  fringes  moves,  as  they  increase 
and  decrease,  are  on  a  scale  proportionate  to  the  dimensions  of  the 
oib  of  the  sun  itself.     When  it  is  considered  that  a  space  upon  the 


286  ASTRONOMY. 

son's  disk,  the  apparent  breadth  of  which  is  only  a  minate,  aetoallj 
measure  (2457) 

466  X  60  =  27,960  miles, 

and  that  spots  have  been  frequently  observed,  the  apparent  length 
and  breadth  of  which  have  exceeded  2^,  the  stupendous  magmtode 
of  the  regions  they  occupy  may  be  easily  conceived. 

The  velocity  with  which  the  luminous  matter  at  the  edges  of  the 
spots  occasionally  moves,  during  the  gradual  increase  or  dinunatioD 
of  the  spot,  has  been  in  some  cases  found  to  be  enormous.  A  wfoi, 
the  apparent  breadth  of  which  was  90",  was  observed  by  Majer  to 
close  in  about  40  days.  Now,  the  actual  linear  dimensionB  of  sodi 
a  spot  must  have  been 

466  X  90  =  41,940  miles. 

and  consequently,  the  average  daily  motion  of  the  matter  oompoaiiig 
its  edges  must  have  been  1050  miles,  a  velocity  eqoi^ndent  to  44 
miles  an  hour. 

2535.  Cause  of  the  spots  ^-physical  stcUe  of  the  sim's  mr/Ke. 
Two,  and  only  two,  suppositions  have  been  proposed  to  explain  the 
spots.  One  supposes  them  to  be  scorise,  or  dark  scales  of  incom- 
bustible matter,  floatiDg  on  the  general  surface  of  the  sun.  The 
other  supposes  them  to  be  excavations  in  the  luminous  matter  which 
coats  the  sun,  the  dark  part  of  the  spot  being  a  part  of  the  solid 
non-luminous  nucleus  of  the  sun.  In  this  latter  hypothesis  it  is 
assumed  that  the  sun  is  a  solid  non-luminous  globe,  covered  with  i 
coating  of  a  certain  thickness  of  luminous  matter. 

That  the  spots  are  excavations,  and  not  mere  black  patches  on  the 
surface,  is  proved  by  the  following  observations  :  If  we  select  a  spot 
which  is  at  the  centre  of  the  sun's  disk,  having  some  definite  fbnn, 
such  as  that  of  a  circle,  and  watch  its  changes  of  appearance,  when, 
by  the  rotation  of  the  sun,  it  is  carried  toward  the  edge,  we  find, 
first,  that  the  circle  becomes  an  oval.  This,  however,  is  what  wonU 
be  expected,  even  if  the  spot  were  a  circular  patch,  inasmuch  u  a 
circle  seen  obliquely  is  foreshortened  into  an  ovid.  But  we  find 
that  as  the  spot  moves  toward  the  side  of  the  sun's  limb,  the  black 
patch  gradually  disappears,  the  penumbral  fringe  on  the  in«de  of 
the  spot  becomes  invisible,  while  the  penumbral  fringe  on  the  out- 
side of  the  spot  increases  in  apparent  breadth,  so  that  when  the  spot 
approaches  the  edge  of  the  sun,  the  only  part  that  is  visible  u  tbe 
external  penumbral  fringe.  Now,  this  is  exactly  what  would  ocear 
if  the  s[)ot  were  an  excavation.  The  penumbral  fringe  is  produced 
by  the  shelving  of  the  sides  of  the  excavation,  sloping  down  to  its 
dark  bottom.  As  the  spot  is  carried  toward  the  edge  of  the  sao, 
the  height  of  the  inner  side  is  interposed  between  the  eye  and  the 
bottom  of  the  excavation,  so  as  to  conceal  the  latter  from  view. 


TWm&oaof  Um ioiMrihdriiig lode tin taldng  tlw  dinotioa  of 
^  hat  tt  nka  Or  verj  BMrh,  iKmipJihai  in  Appanot  braadth, 
and  eeues  to  be  TiaiU^  vfails  too  nir&ae  of  the  ualriiia  lide  next  . 
tbo  adge  at  the  Mut  becoming  searij  peipeiidiculw  to  Uta  line  of 


I  </ ia  fall  brndtL 

!•  ahoct,  all  the  fanatioui  of  uneannoe  which  the  qiota  titidei|^, 
M  tbn  an  arricd  noiid  bj  the  ntatioa  of  the  nm,  clunging 
ftav  artamw  and  ym&nd  with  ngard  to  the  snn'a  centre,  an 
MMt^  aaA  as  wobU  be  frodoced  ]»  an  exoanlion,  and  not  Moll 
mA  M  m  dadfc  Midi  on  toe  foUr  inmae  would  ondwgo. 

i&SO-  Am  iaaitfwf  l^  twa  -atmaigiittru,  mm  AimmoM  amd  A« 
ilftir  MOM-fcoNMOMi^  —It  maj  )m  conpiwdj  then,  aa  prare^  that 
Ihi  ^ota  OB  tba  ann  an  e«anluiM;  iu>d  ti»t  the  ai^wnnt  bhok- 
aaa  ia  ncodtwed  tgr  4"  £m^  Atat  tlw  part  cooatitatuig  the  daik 
Mrtka  <H  th«  ifftk  ia  «Bhn  a  n^i|■CB  toi^Ij  deaititnte  of  light,  tm 
\j  cumpariaon  go  mucii  Idsa  luminoua  thaa  tbo  geocral  surface  of 
l^e  euQ  %i  lo  appear  bkck.  This  fuct,  combined  with  tbo  sppear- 
Hce  of  the  pcnuaibnl  edges  of  the  spole,  has  led  to  tha  suppoaj- 
lioD,  adTftDced  bj  Sir  W.  Herscbe],  wbicli  appears  scareetT  to  admit 
«f  doubt,  that  Uie  BoIiU,  opaque  nucleus,  or  globo  of  the  bud,  is 
inTL-iUd  with  at  least  two  atmospheres;  that  which  is  next  the  sua 
being,  Hke  oar  own,  noa- luminous,  aod  the  superior  one  being  that 
alone  in  w lush  ligbt  and  beat  are  evolved;  at  all  events,  whether 
Itififi  llnta  bo  ia  the  gaseous  state  or  not,  the  esisteDOO  of  two 
■neb,  OM  pUced  above  tbe  other,  the  superior  one  being  luminous, 
■eeros  to  be  exempt  from  doubt. 

2537.  Spots  may  not  be  black.  —  We  are  not  warraoled  in  as- 
■Btoiog  that  the  black  portion  of  the  spots  are  sur&ces  really 
deprivad  of  light,  for  the  most  intense  artificial  lights  nbioh  can  be 
pndoced,  such,  for  example,  as  that  of  a  piece  of  quiok-limo  ex- 
pned  to  the  aetiooof  the  compound  blow- pipe,  when  seen  projected 
tn  the  aun'a  disk,  appear  a^  dark  as  tbe  spots  themselves ;  an  effect 
vhicb  naat  be  nscribed  to  the  infinitely  superior  splendour  of  the 
■la'a  ligbL  AH  that  can  be  legitimaiel}'  inferred  respecting  tbo 
qwts,  thea,  is,  not  that  they  are  destitute  of  light,  but  that  tbej 
tie  incomnaably  leas  brilliant  than  the  general  surface  of  the  sun. 

2538,  &toU  vartablt. — The  preyaienoe  of  apota  on  tbe  sun's 
&k  is  both  variable  and  irteguW.  Sometimes  the  disk  will  be 
f'.L.L.ti.ly  riiv.-;(i'J  of  them,  and  will  continue  so  for  weeks  or 
::  1:11  ';.ie?  they  will  be  spread  over  certajn  parts  of  it  in 
infason.  Bomotifliea  the  spota  will  be  amall,  but  nnmerons ; 
wniuna  indrridaal  ^oto  wui  appear  of  vast  extent ;  sometimei 
Aejwill  ba  """'^^H  m  gronpi,  the  penumbna  or  fiingea  being  ia 

nmim&m.  of  eMh  qiot  ia  also  inlgeat  lo  great  and  irregolar 
WPtfiaik    A  ^D|  hM  ttmni  ud  wUwd  ia  kn  than  twentj* 


ftvr  hotm,  wbila  « 


•  hftven 


I  thartppa 


tion  tot  nine  or  ten  weeks,  or  dnring  nculy  three  eosapleta  lenb 
Horn  (£  the  sun  npon  ila  axio. 

A  lu^  spot  has  ■omelimeB  been  olwerTed  paSdenl;  to  tmaVt 
into  a  great  number  of  niull  ones. 

'""'".  J^-evail  generaOKin  tteo  paraild  tOMi.  —  The  ooljm- 
of  re^piluit^  wnidh  «ua  be  Mid  to  attend  these  nmvk- 
mens  IB  tbeir  pontion  ofKn  the  ann.   inieyireinvariililj 


.  IB  tiieir  positMm  a[ 
moderstdj  brosd  vHieB  psisllel  tot) 
sepsisted  fnm  it  by  s  ipsee  sercnl  iegrses  in  faresdth.  *  Ihi 
"  ind  this  ifMS  whidi  thnt  s^sistes  tiie  mmfat 
itely  dlTeetod  *  ' 
mpu^iu  the  li 

T  spoli  1 
in^.TS: 


ter  put  of  188S  snd  the  b^pnug 
of  1887,  when  t  la^  nnmber  of  spoi"  ^  "  -  -'-^ 


y -.;— -|..— ... 


the  sun's  equator,  and  mm'  nn'  the  northern,  and  p^  q^  the 
•on them  macular  zones. 

2540.  Obterealioni  and  draviinga  of  M.  Capocei.  —  The  utio- 
uomen  who  have  within  the  last  quartet  of  a  oentory  made  the  most 
important  oontributions,  b;  their  obserratione  and  leiesichea,  to  tiiil 


p'SSfll^ 


« 


^1 


m^ 

^-A. 

m,-        ......  I 

•y    ., ,  I 

r-~ 


r 


THE  SUN.  239 


•nkjccly  are  M.  Gapocei,  of  Naples^  Br.  Pastorff^  of  Frankfort  (on 
the  Oder},  and  Sir  John  HeracneL 

M.  Capocci  made  a  series  of  observations  on  the  spots  which 

vere  developed  on  the  son's  disk  in  1826,  when  he  recognised  most 

of  the  characters  above  described.     He  observed  that,  during  the 

bcRase  of  the  spot  from  its  first  appearance  as  a  dark  point,  the 

€ilfe8  were  sharply  defined,  without  any  indication  of  the  gradually 

hmg  away  of  the  fringes  into  the  dark  central  spot,  or  into  each 

ether;  a  character  which  was  again  observed  by  Sir  J.  Herschel,  in 

1837.    He  found,  however,  that  the  same  character  was  not  main- 

I        tuned  when  the  sides  began  to  contract  and  the  spots  to  diminish  : 

I        during  that  process  the  edges  were  less  strongly  defined,  being 

^        apptreotly  covered  by  a  sort  of  luminous  atmosphere,  which  often 

[        extended  so  completely  across  the  dark  nucleus  as  to  throw  a  thin 

*        tbeid  of  light  across  it,  after  which  the  spot  soon  filled  up  and 

diappeared.     Capocci  concurs  with  Sir  W.  Herschel  in  regarding 

i       tbe  internal  fringes  surrounding  the  dark  nucleus  as  the  section  of 

:       tile  inferior  stratum  of  the  atmosphere  which  forms  the  coating  of 

the  son;  he  nevertheless  thinks  that  there  are  indications  of  solid 

as  well  as  gaseous  luminous  matter. 

Capocci  also  observed  veins  of  more  intensely  luminous  matter 
on  the  fringes  converging  towards  the  nucleus  of  the  spot,  which  he 
compares  to  the  structure  of  the  iris  surrounding  the  pupil  of  the 
eye. 

The  drawings  of  the  spots  observed  by  M.  Capocci,  given  in 
Plate  v.,  will  illustrate  these  observations.  It  is  to  be  regretted, 
however,  that  he  has  not  given  any  measures,  either  in  his  memoirs 
or  upon  his  drawings,  by  which  the  position  or  magnitude  of  the 
^lots  can  be  determined. 

2541.  ObtervationM  and  drawing$  of  Dr,  PaUorff^  in  1826.  — 
Dr.  Pastorff  commenced  his  course  of  solar  observations  as  early  as 
1319.  He  observed  the  spots  which  appeared  in  1826,  of  which 
he  published  a  series  of  drawings,  from  which  we  have  selected 
^ose  given  in  Plate  YL,  from  observations  made  in  September  and 
^ctober,  contemporaneously  with  those  of  M.  Capocci.     Pastorff 

Rves  the  position  of  all,  and  the  dimensions  of  the  principal  spots, 
le  numbers  on  the  horixontal  and  vertical  lines  express  the  appa- 
'^nt  distances  of  the  spots  severally  from  the  limb  of  the  sun  in 
.^h  direction.  The  actual  dimensions  may  be  estimated  by  observ- 
'^g  that  1''  measured  at  right  angles  to  the  visual  ray  represents 
4w  miles. 

2542.  Obaervatiom  and  drawings  of  Pastorff,  in  1828. — In 
^lay  and  June,  1828,  a  profusion  of  spots  were  developed,  which 
%ere  observed  and  delineated  by  Pastorff  with  the  most  elaborate 
Accuracy. 

In  Plate  Yn.y  fy.  1  represents   the  positions  of  the  spots  as 


MO  Aflnovovr. 

they  appeared  on  die  &k  of  tiie  nm  on  fhe  84Ui  of  MagTi 
▲.M.,  Kud  Jigs,  2|  3,  4,  and  5,  repreeeni  their  fbirnis  and  ■ 
The  letters  A,  b,  g,  d,  in  Jig.  \  giv9  .the  peMona  of 
marked  by  the  same  letters  in,^^  2,  8,  4,  woi  5. 

The  dimensions  of  the  prindpal  ripot  rf  the  group  A  Mn  rfip 
pendoos ;  measured  in  a  plane  at  rijdit  anglea  to  uo  rkMtl  Hm^4i 
leneth  was  406  X  100  =46,600  ndleiiy  and  the  hmdth  466  iC0D 
=  27,960  miles. 

The  apparent  breadth  of  the  bhok  bottom  of  dw  spot  «aa40^ 
wbioh  oorreroonds  to  an  actoal  breadth  Of  466  X  40a=UyllO 
miles.  So  that  the  globe  of  the  earth  micht  pass  ihroag|h  Ma 
hole,  leaving  a  distance  of  upwards  of  5000  miles  between  His** 
Ihoe  and  the  edges  of  the  chasm. 

The  superficial  dimensions  of  the  serersl  groups  of  iqpots  tkund 
on  the  sun  on  the  24th  of  May,  at  10  A.  M.,  including  the  abrffim 
aides,  were  calculated  to  be  as  follows :— - 


) 


Groap  A,  prinoiiwl  spot OM^OOO^M  |i 

Ditto,  snuOler  spoto TM^OOOyM  I 

Group  B ^  SM^OOQ^OOi  l 

Group  0 282,000^m  f 

Group  D 804,000,000 

Total  area 2,490,000,000        j^ 

Thus  it  appears  that  the  principal  spot  of  the  group  A  corereJ  i  ^ 
space  equal  to  little  less  than  five  times  the  entire  surfitce  of  iki  ' 
earth;  and  the  total  area  occupied  by  all  the  spots  coUeetivdlf  \ 
amouDted  to  more  than  twelve  times  that  surface.  .    '^ 

On  the  days  succeeding  the  24th  of  May,  all  the  spots  wers  ok>  ^ 
served  to  change  their  form  and  magnitude  from  day  to  day.  Ik  h 
ffreat  spot  of  Uie  group  a,  which  even  when  so  dose  to  the  limb  d  | 
tne  sun  as  5',  or  a  sixth  of  the  apparent  diameter,  still  measanl  F 
80^'  by  40",  was  espcially  rapid  in  its  variation.  Its  shelving  ndo^  ^ 
as  well  as  its  dark  bottom,  were  constantly  varied,  and  luminfNi  }i 
clouds  were  seen  floating  over  the  latter.  ^_ 

After  the  disappearance  of  this  large  spot,  and  several  of  dn  ^ 
lesser  ones  of  the  other  groups,  a  new  spot  of  considerable  msfli*  ^ 
tude  made  its  appearance  on  the  13th  of  June,  at  the  eastern  eag^  ^f 
of  the  disk,  which  gradually  increased  in  magnitude  for  eidbt  daja  M 
On  the  21st  of  June,  at  half-past  9  in  the  morning,  the  disk  of  tii  ^i 
sun  exhibited  the  spots  whose  position  is  represented  in  Jig,  6,  Fbto  ^ 
YII,  and  whose  forms  and  magnitudes  are  indicated  in  j^t.  7,  8,By  ^ 
and  10.  * 

The  chief  spot  of  the  group  a  was  nearly  droular,  and  measonl }'. 
W  in  apparent  diameter,  the  diameter  of  its  dark  base  being  aboift  !^ 
30",  which,  without  allowing  for  projection,  represent  actual lu^glb  ^ 
of  466  X  64  =  29,824  miles,  and  466  X  30  =  13,980  mileB,  tk  k 


^THX  8UK.  241 

« 

bdng  sbove  8}  times,  and  the  latter  nearly  1}  times  the 
■Ktli's  diameter.  The  process  of  formation  of  this  spot,  surrounded 
ij  Ifuninons  clouds,  was  clearly  seen.  The  shelving  sides  were 
nrened  by  luminous  ravines  or  rills,  converging  towaids  the  centre 
iC  tlie  black  nucleus,  and  exhibiting  the  appearance  which  Gapocci 
ssBpaied  to  the  stacture  of  the  ins. 

On  the  same  day  (the  2l8t),  another  large  spot,  b,  fin*  8,  appeared, 
vbich  measuied  60"'  by  40"'. 

Fastorff  rejects  the  supposition  that  these  spots  were  the  mere  re- 
qipearanoes  of  those  which  had  been  observed  on  the  24th  of  May, 
■nee  they  differed  essentially  in  their  form,  and  still  more  in  their 

2648.  Obiervations  of  Sir  J.  Ilerschel  in  1837.  — Sir  J.  Her- 
i^,  at  the  Cape  of  Good  Hope,  in  1837,  observed  the  spots  which 
at  that  time  appeared  upon  the  sun,  and  has  given  various  drawings 
d  them  in  his  Cape  Observations.  These  diagrams  do  not  differ  in 
tnj  respect  in  their  general  character  from  those  of  Capocci  and 
hstorff.  Sir  J.  Herschel  recognised  on  this  occasion  the  striated 
or  radiated  appearance  in  the  fringes  already  noticed  by  Capocci  and 
hstorff.  He  thinks  that  this  structure  is  intimately  connected  with 
tlie  physical  agency  by  which  the  spots  arc  produced. 

2544.  Boundary  of  fringes  distinctly  defined.  —  It  is  observed 
bv  Sir  J.  Herschel,  that  one  of  the  most  universal  and  striking 
ofaaracterB  of  the  solar  spots  is,  that  the  penumbral  fringe  and  black 
ipoi  are  distinctly  defined,  and  do  not  melt  gradually  one  into  the 
)Cher.  The  spots  are  intensely  black,  and  the  penumbral  fringe  of 
I  perfectly  uniform  degree  of  shade.  In  some  cases  there  are  two 
inances  of  fringe,  one  lighter  than  the  other ;  but  in  that  case  no 
Atermizture  or  gradual  fading  away  of  one  into  the  other  is  appa- 
rent. ''The  idea  conveyed,"  observes  Sir  J.  Herschel,  "is  more 
Jiat  of  the  successive  withdrawal  of  veils, — the  partial  removal  of 
lefinite  films, — than  the  melting  away  of  a  mist  or  the  mutual  dilu- 
tion of  gaseous  media.''  This  absence  of  all  graduation,  this 
iharply  marked  suddenness  of  transition,  is,  as  Sir  J.  Herschel  also 
Dotices,  entirely  opposed  to  the  idea  of  the  easy  miscibility  of  the 
luminous,  non-luminous,  and  semi-luminous  constituents  of  the  solar 
envelope. 

2545.  Solar  facuhs  and  lucuJes,  —  Independently  of  the  dark 
spots  just  described,  the  luminous  part  of  the  solar  disk  is  not  uni- 
formly bright.  It  presents  a  mottled  appearance,  which  may  be 
eompared  to  that  which  would  be  presented  by  the  undulated  and 
agitated  surface  of  an  ocean  of  liquid  fire,  or  to  a  stratum  of  lumi- 
nous clouds  of  varying  depth  and  having  an  unequal  surface,  or  the 
ippearance  produced  by  the  slow  subsidence  of  some  flocculent 
ciiemical  precipitates  in  a  transparent  fluid,  when  looked  at  perpen- 
dicularly from  above.     In  the  space  immediately  around  the  edgea 

m.  21 


/ 


&49  ASnOHOMT. 

of  the  spots  ezteiunTe  spaoes  an  obtenred,  abooorerad  wiik  9km(^ 
defioed  carved  or  branohing  streaks,  mono  intenaely  luodnoai  Imi 
the  other  parts  of  the  disk,  amoo^  which  apota  olleD  bnak  cut 
These  seTeral  varieties  in  the  intoDsity  of  the  hrightneaa  of  the  dak 
have  been  differently  designated  by  the  tenna  /aeuin  and 
These  appearances  are  generally  more  pxevaleiit  and  itaoii|^ 
near  the  edges  of  the  disk. 

2546.  Incandtaccnt  coating  of  the  tun  gateouM. — ^VaiioaaattMito 
have  been  made  to  ascertain  by  the  direct  test  of  obaeryationy  wl^ 
pendently  of  conjecture  or  hypothesis^  the  phyaieal  alate  of  lb 
luminous  matter  which  coats  the  globe  of  the  auiiy  wheHiar  it  b 
solid,  liquid,  or  gaseous. 

That  it  is  not  solid  is  admitted  to  be  proved  eonekumly  ly  ki 
extraordinary  mobility,  as  indicated  by  the  rapid  motian  of  Iks    : 
edses  of  the  spots  in  clonng ;  and  it  is  contended  thaft  a  fliii » 
pable  of  moving  at  the  rate  of  44  miles  per  hoar  oaonot  be  wol\ 
to  be  liquid,  an  elastic  fluid  alone  admitting  of  snch  a  motifn. 

2547.  TtH  of  this  proposed  hjf  Arago,  —  Arago,  has,  hxmmmf 
suggested  a  physical  test,  by  which  it  appears  to  be  proved  thai  thii 
luminous  matter  must  be  gaseous ;  in  short,  that  the  ann  mast  b 
invested  with  an  ocean  of  flame,  since  flame  is  nothing  mon  tbsa 
aeriform  fluid  in  a  state  of  incandescence  (1584).  This  test  pro- 
posed is  based  upon  the  properties  of  polarised  light 

It  has  been  proved  that  the  light  emitted  from  an  inoandosflMt 
body  in  the  liquid  or  solid  state,  issuing  in  directiona  very  ofaliiiai 
to  the  surface,  even  when  the  body  emitting  it  is  not  amooth  or 
polished,  presents  evident  marks  of  polarisation ;  so  that  aooh  a  bo^, 
when  viewed  through  a  polariscopio  telescope,  will  present  two  m- 
ages  in  complementary  colours  (1290).  But,  on  the  other  hand,  ao 
signs  of  polarisation  are  discoverable,  however  obliqae  may  be  tb 
direction  in  which  the  rays  are  emitted,  if  the  luminoaa  matter  b 
flame. 

2548.  Il$  result. — The  light  proceeding  from  the  diak  of  the  sai 
has  been  accordingly  submitted  to  this  test  The  raya  proeeediBg 
from  its  borders  evidently  issue  in  a  direction  as  obliqae  as  poasibb 
to  the  surface,  and  therefore,  under  the  condition  moot  &voaraUe 
to  polarisation,  if  the  luminous  matter  were  liquid.  Neverthekfl^ 
the  borders  of  the  double  image  produced  by  the  polariaoope  show 
no  signs  whatever  of  complementary  colours,  both  being  eqoallj 
white,  even  at  the  very  edges. 

This  test  is  only  applicable  to  the  luminous  matter  at  or  near  tb 
edge  of  the  disk,  because  it  is  from  this  only  that  the  raya  isne 
with  the  necessary  obliquity.  But  since  the  sun  revolves  on  iti 
axis  (2533),  every  part  of  its  surface  comes  in  succession  to  the  odgt 
of  .the  disk;  and  thus  it  follows  that  the  light  emanating  from  evoy 
part  of  it  is  in  its  natural  or  nnpolarised  statOy  even  when  issoi^ 


nttMir.  24S 


m  99VJ  WBOn  CMBOQk 

)•  3nU  mil  praoahfy  imveiied  with  a  douhk  gaMetnu  coating. 
.1*  Alt  Ifce  phenoBMim  whkh  hate  been  here  deaonbed.  and  others 
^Uk  «Mr  luuli  eimipd  ns  to  omit^  aie  oonsidered  as  dhnng  a  high 
iHgn^  of  phjiinl  prabehililj  to  Hie  hjpotheae  of  SirW.  Henehel 
■Imdy  Dooeed,  mwUdi  the  ann  is  eonndered  to  be  a  eoUd,  opaqne, 
inoiis  i^dbe^  imeated  bj  two  ocmoentrio  strata  of  gueoos 
the  tral^  or  dwt  wUeh  rests  immediately  on  the  Barftee, 
wmineSmam^  and  tiie  oAm^  whidi  floats  ntpon  tfie  former 
hssfaioMi  gss  or  flame.  The  relation  and  arrangement  of 
t«o  inid  stnia  Wkj  be  illastrated  bj  oar  own  fUnospherei 
vpen  it  a  atretatt  of  doods.  If  sodi  elondswerelamei 
of  fliir  atsMisplkere  wonhi  represent  the  two  strata  on 


in  this  h jpothems  am  explained  by  ooosrional  openingi 
ions  siatuii  by  wlMi  psrts  of  the  opsoue  ind  non- 
anftiee  of  die  soHd  ^obe  are  disclosed.  Thess  partial 
_i  WKf  be  eompared  to  die  openings  in  the  donds  of  oar 
Vf  wUok  the  flnasment  is  rendered  partially  visible. 
^Rm  MjMsent  disflMter  of  the  son  is  not,  therefore^  the  diameter 
tf  tiw  aoM  i^oboi  bst  that  of  the  globe  bounded  by  the  sorikoe  of 
tta  gupetiut  or  Inodnoos  atmosphere;  and  this  oireamstance  may 
toavaome  lirikt  uon  the  snudl  oompated  mean  density  of  the  san| 
da«L  aoMidemg  the  h^^  d^;ree  of  rarefketion  whidi  most  be  sop- 
pasM  ta  diarsetarise  diese  atmospherie  strati^  and  espeeially  the  sa- 
r  mM^  the  denaily  of  die  sdid  globe  will  neoeoftrily  be  srach 
aonsAnUe  than  the  mesa  dmisity  of  the  volume  in  whioh 
nvafled  Bnlter  is  indoded. 
SiWO.  A  Mrd  goMemu  atmosphere  jnrobahU. '^TSMnj  dreom- 

^ ^"PAt  iDwations  of  the  ezistenoB  of  a  ffaseoos  atmosphere 

I  aitettt  above  the  laminoos  matter  which  fbrms  the  vinble 

of  the  son.    It  is  observed  dmt  die  brightness  of  the  solar 

ia  WBdhhr  Aninished  towards  its  bcvders.    This  effect  would 

kmsd  if  it  were  surrounded  by  an  imperfeody  transparent  at- 

mj  wheresa  If  no  snoh  aaseons  mecuum  surrounded  it,  the 

of  snA  an  eflbet  might  be  expected^  rinoe  then  die  thidcneis 

linuBoas  eoating  me«inred  in  die  direction  of  the  visual  ray 

be  jnereased  very  rapiAv  in  proceeding  from  the  centre 

Ifce  edgea.    This  gradnal  diminution  of  brightness  in  pro- 

^  towards  the  borden  of  the  solar  disk  has  Men  noticed  by 

aislrenomeis;  but  it  wu  most  dearly  manifested  in  the  series 

rvations  made  I7  Sir  J.  Hersehel  in  1887,  so  condusively, 

aa  to  leave  no  doubt  whatever  of  its  reality  on  the  mind  of 

mnt  obserter.    By  nrojeeting  the  imsge  of  tbe  sun's  HA 

«Ula  ftfet  by  OMBsaa  of  a  good  aehiomatie  tdesoope^  this  di- 


244  ASTBOHOIIT. 

mumtion  of  light  towards  tlw  boiden  wu  on  tihal 

■0  apparent,  tut  it  iq^peared  to  him  sorprifling  that  it  dMmU  ow 

]m¥6  been  qnestioQed. 

2651.  lu  exiitence  indicated  hy  §olar  ediptet, — Bat  tiho  WMC 
oondasiye  proofs  of  the  ezistenoe  of  sooh  an  external  atmns|ttini 
are  supplied  bj  certain  jphenomcna  observed  on  the  onwaion  of  tofed 
ediuKs  of  the  son,  whioh  will  be  fullj  explained  in  anottie  *^  " 
of  this  Yolnme. 

2552.  Sir  J.  BsnduiPi  hypotkeiu  to  tscpbnm  the  mbr 
The  immediate  oanse  of  the  spots  being  proved  to  be 
raptores  of  oontinui^  in  the  ooean  of  lummoos  fluid  wbieh 
the  visible  sor&oe  or  the  solar  globe,  it  remains  to  diaoovw 
physioal  ngincj  oan  be  imagined  to  prodnoe  djnamieal  phenc 
on  a  scale  so  vast  as  that  which  the  changes  of  appeanMO  of  dH 
spots  indicate. 

The  regions  of  the  spots  being  two  lones  paiillel  to  the  Mkr 
eqiuatoTi  manifests  a  connection  between  these  phenomena  and  lb 
son's  rotation.  The  like  reoions  on  the  esrth  are  the  theatmef 
the  trade-winds  and  anti-tradBS,  and  of  hnrricanes,  toniadooi^ 


2 outs,  and  other  violent  atmospherio  distorbances.  On  tlM  ptmrtb 
e  same  regions  are  marked  by  belts,  appearances  which  are  tnM 
bj  analogy  to  the  same  physicid  causes  as  those  which  produce  tfca 
tndes  and  other  atmospherio  perturbations  prevailing  in  the  trc^iiod 
and  ultra-tropical  zones.  Analogy,  therefore,  suggests  the  inqoij, 
whether  any  physical  agencies  can  exist  upon  the  sun  similar  ta 
those  which  produce  these  phenomena  on  the  earth  and  planets. 

So  far  as  relates  to  the  earth  it  is  certain,  and  so  fu  as  relates  to 
the  planets  probable,  that  the  immediate  physical  cause  of 
phenomena  is  the  inequality  of  the  exposure  of  the  earth's 
to  solar  radiation,  and  the  consequent  inequality  of  tempentm 
produced  in  different  atmospheric  zones,  either  by  the  direct  or  n» 
fleeted  calorific  rays  of  the  sun,  combined  with  the  earth's  rotatet 
(2528).  But  since  the  sun  is  itself  the  common  fountain  of  hea%- 
supplyiog  to  all,  and  receiving  from  none,  no  similar  agenej  eaa 
prevail  upon  it.  It  remains,  therefore,  to  consider  whether  the  plswf 
of  the  physical  principles  which  are  in  operation  on  the  son  mm^' 
irrespective  of  any  other  bodies  of  the  system,  can  supply  an  SK 
planation  of  such  a  local  difference  of  temperature  as,  oombined 
with  the  sun's  rotation,  would  produce  any  special  physical  eflbfllr 
on  the  macular  zones  by  which  the  phenomena  of  the  spots  taa^Ut. 
be  explicable.  ** 

The  heat  generated  by  some  undiscovered  agency  upon  the  aim  im 
dispersed  through  the  surrounding  space  by  radiation.  If,  as  nukj'C' 
be  assumed,  the  rate  at  which  this  heat  is  generated  be  the  same  oitf 
all  parts  of  the  sun,  and  if,  moreover,  the  radiation  be  equally  frai^ 
and  unobstructed  from  all  parts  of  its  surface,  it  is  evident  that  atf 


•nk 


fits 


i^IomI 


Biiik  \m  emjwlMra  mamtehtd*    Bat  if,  from 

^  the  nditlUNi  be  more  obetmoted  in  fome  remoa 

9Am,  heel  will  eoemmilate  in  the  former,  end  the  looel 

Witt  be  SMm  eletiled  then  thaniriiefe  the  lediation  b 


!■!  the  only  ubetiuelkn  to  ftee  lediatioQ  from  the  ean  nraeteriee 

th»  etnwephePi  with  wUeh  to  an  hei^t  eo  enormone  it  ie  eni^ 

It,  howewv  tiUe  atewwiliere  heiFe  ereiTwhera  the  eune 

emd  tihe  nme  deneitf ,  il  wm  pment  the  eame  obetroetion  to 

i;  and  the  efleetrre  ndhtion  whieh  takes  idaee  throng  il^ 

Mn  fMble  than  thai  whioh  wooU  be  piodnood  in  ita  ab> 

ia  atiU  nnifbtau 

the  eon  haa  n  aMition  of  rotation  on  ita  nma  in 
VFI^tSP-,  ito  almoipheBa,  like  thai  of  the  earthy  moat  partieipeto 
k  ttaft  iMlion  nd  ^  efleota  of  eentriftigal  force  npon  matter  ae 
:  tti  eqoatotial  sma  being  carried  imind  with  a  idodtv 
thai  MM  milee  per  aeeond,  while  the  poUr  aonee  are  moM 
Annto  indoSnitdy  dower,  all  the  eiliMla  to  whieh  the  qiheroidai 
nf  thn  earth  ia  doe  wiU  afied  thia  fluid  with  an  eneray  wo- 
to  ito  tonnb^  and  aMbiUty,  the  conaeqnence  ofwhiflh 
il  il  wiU  aannw  the  Ibrm  of  an  oblate  apheroidy  whoee 
«ia  wOI  be  thai  of  the  aon'a  rotation.  It  wiU  flow  from  the  polea 
ti  ttn  tqaatar,  and  ito  height  o?«r  the  aonee  oontignoaa  to  the 
i|aaiar  wiU  be  gyealer  than  ofer  thoae  oontignowi  to  the  poleo, 
il  n  iiiffm  proportionato  to  the  elliptioi^  Sf  the  atmospheric 


■bv,  if  thia  rcaaoning  be  admitted^  it  will  follow  that  the  ob- 
lien  to  radiation  prodneed  fay  the  aolar  atmosphere  is  greatest 
mp  ttn  eqinatori  and  gradually  deoreasee  in  proceeding  towuda 
;#ar  poln.  The  aecnmolation  of  heaty  and  consequent  ele?ation 
LJiSMpiiiBliini,  k,  therelbrey  greateat  at  the  equator,  and  gradually 
npaaasa  tawaida  the  polea,  eiaotly  aa  happeoa  on  the  earth  frDm 

^      Ifaeto  of  tkli  ineqmdi^  of  temperature,  combined  with  the 

IjMisay  upon  the  solar  atmoqihere,  will  of  conrae  be  similar  in 

|f|ir|naBal  dmracter,  and  diffinent  only  in  degree  from  the  phe* 

jinenn  psndneed  fay  the  like  cauae  on  the  earth.    Inforior  curreote 

Iw^flswpcn  the  earth,  pretail  towarda  the  equator,  and  superior 

lBBi«arrento  towards  the  poke  r2628).    The  spoto  of  the  sun 

,  therefore,  be  sssimilated  to  tooee  tropical  reffions  of  the  earth 

wUehy  for  the  moment,  hurrioanea  and  tomadoea  prevail,  the 

ainftum  whieh  has  come  from  the  equator  being  temporarily 

"  downwaida,  displacing  by  ite  force  the  strata  of  luminoob 

beneath  it  (whioh  may  be  conceived  as  forming  an  habitnallj 

"  fimil  between  the  oppoeite  upper  and  under  currents),  the 

of  oonrae  to  a  greater  extent  thiui  the  lower,  and  thus  wholly 

«1* 


S46  ASTBONOICT. 

or  pirlaall J  denuding  the  q»qiie  lar&oe  of  the  wan  bolair.  flbek 
prooeeees  cannot  be  onaooompuiied  faj  vortioooe  motumii  irfiiflli,  left 
to  themselves,  die  away  by  degrees,  and  dissipate,  inth  iStm  f&m^^ 
Itarity,  that  their  lower  portions  ootfie  to  rest  man  speedily  thn 
their  upper,  by  reason  of  the  greater  distance  betow,  as  wdl  as  d» 
remoteness  firom  the  point  of  action,  whidi  lies  in  a  higher  nffpOf 
so  that  their  centre  (as  seen  in  our  waterqioots,  whieh  an  nowBg 
but  small  tornadoes)  appears  to  retreat  upwards.* 
.  Sir  J.  Herschd  maintains  that  all  this  agrees  peiftefl/ with  whst 
is  observed  during  the  obliteration  of  tiie  solar  spots,  whieh  sfpssr 
u  if  filed  in  by  the  ooUap«  oflJieir  o^  the  pennafan  doivk 
Upon  the  spot  and  disappeanng  afterwards. 

It  would  have  rendered  this  ingmious  hypothesis  still 
fikctory,  if  Sir  J.  Hersohel  had  assigned  a  reason  wh^  the 
and  subjacent  non-luminous  atmosphere,  both  of  whioh  an 
to  be  gaseous  fluids,  do  not  affect^  in  consequence  of  the 
the  same  spheroidal  form  which  he  ascribes  to  the  superior 
atmosphere. 

.  2558.  (hhnjh  power  of  iolarrti^s.  —  IthasbeenalraadTd 
(2217)  that  the  intensity  of  heat  <m  the  sun's  snrftee  mnsl  bei 
times  as  ereat  as  that  of  the  vivid  ignition  of  the  fuel  in  the  si 
est  blast-furnace.  This  power  of  solar  light  is  also  proved  by  ths 
fadlity  with  which  the  calorific  rays  pass  through  glass.  Henebii 
found,  by  experiments  made  with  an  actinometer,  that  81-6  par  east 
of  the  calorific  rajs  of  the  sun  penetrate  a  sheet  of  plate-glass  O-U 
inch  thick,  and  that  85 -9  per  cent,  of  the  rays  which  have  passed 
through  one  such  plate  will  pass  through  another.f 

2554.  Probable  physical  cause  of  solar  heat,  —  One  of  the  iMMt 
cUffioult  questions  connected  with  the  physical  condition  of  the  ssn, 
is  the  discovery  of  the  agency  to  which  its  heat  is  due.  To  tki 
hypothesis  of  combustion,  or  any  other  which  involves  the  soppos* 
tion  of  extensive  chemical  change  in  the  constituento  of  the  surhoBi 
there  are  insuperable  difficulties.  Conjecture  is  all  tiiat  eaa  be 
offered,  in  the  absence  of  all  date  upon  which  reasoning  eaa  bi 
based.  Without  any  chemical  change,  heat  may  be  indefiaildy 
generated  either  by  friction  or  by  electric  currento,  and  each  of  these 
causes  have  accordingly  been  suggested  as  a  possible  source  of  solar 
heat  and  light.  According  to  the  latter  hypothesis,  the  sun  wosM 
be  a  great  electric  uqht  in  the  centre  of  the  system. 

*■  .       .  .1 

*  Herschers  Cape  Obsenrations,  p.  434.  f  Ibid.  p.  183. 


THE  SOLAR  SYSTEM.  247 


CHAP.  xn. 

THE  SOLAR  SYSTEM. 

2555.  Perception  of  the  motion  and  position  of  surrounding 
obJectB  depends  upon   the  station  of  the  observer.  —  The  facility, 
dflaniesBy  and  certainty  with  which  the  motions,  distances,  magni- 
tudes, and  relative  position  and  arrangement  of  any  surronnding 
otyjects  can  be  ascertained,  depends,  in  a  great  degree,  upon  the 
itatioa  of  the  observer.    The  form  and  relative  disposition  of  the 
bdldiogB,  streets,  squares,  and  limits  of  a  great  city,  are  perceived, 
for  example,  with  more  clearness  and  certainty  if  the  station  of  the 
obterver  oe  selected  at  the  summit  of  a  lofty  building,  than  if  it 
were  at  any  station  level  with  the  general  piano  of  the  city  itself. 
Hus  advantage  attending  an  elevated  place  of  observation  is  much 
logmented  if  the  objects  observed  are  affected  by  various  and  com- 
plicated motions  inter  se.     A  general,  who  directs  the  evolutions  of 
a  battle,  seeks  an  elevated  position  from  which  he  can  obtain,  as  far 
as  it  is  practicable  to  do  so,  a  hird*s-eye  view  of  the  field ;  and  it 
was  at  one  time  proposed  to  employ  captive  balloons  by  which  ob- 
nrvers  could  be  raised  to  a  sufficient  elevation  above  the  plane  of 
the  military  manoeuvres. 

All  these  difficulties,  which  arise  from  the  station  of  the  observer 
being  in  the  general  plane  of  the  motions  observed,  are,  however, 
infinitely  aggravated  when  the  station  has  itself  motions  of  which 
the  observer  is  unconscious ;  in  such  case  the  effects  of  these  motions 
are  optically  transferred  to  surrounding  objects,  giving  them  apparent 
motions  in  directions  contrary  to  that  of  the  observer,  and  apparent 
veloeitics,  which  vary  with  their  distance  from  the  observer,  in- 
creasing as  that  dbtance  diminishes,  and  diminishing  as  that  distance 
increaaes. 

All  such  effects  are  imputed  by  the  unconscious  observer  to  so 
many  real  motions  in  the  objects  observed ;  and,  being  mixed  up 
with  the  motions  by  which  such  objects  themselves  are  actually  af- 
fected, an  inextricable  confusion  of  changes  of  position,  apparent  and 
real,  results,  which  involves  the  observer  in  obscurity  and  difficulty, 
if  his  purpose  be  to  ascertain  the  actual  motions  and  relative  dis- 
tances and  arrangement  of  the  objects  around  him. 

2556.   Peculiar  difficulties  presented  hy  tJie  solar  system.  —  All 
fcese  difficulties  are  presented  in  their  most  aggravated  form  to  the 
observer,  who,  being  placed  upon  the  earth,  desires  to  asccttam  iVx^ 
n>otioas  Mttd  poBJtions  of  the  bodieu  composing  the  Bolar  B^^ftl^xa 


ttt  4«ntO»OIIT. 

TiMW  bodiM  all  mo^  natrlj^  in  ooe  fbuM.  tad  froa  ttuft  |lat  Ai 
obseoer  never  departs :  he  isi  theroron^  ae^yed  dtogBflwr  rf  fc 
iMNlitiee  and  advantages  which  a  hird's-eja  tmw  of  ll»  ajstaoi  voril 
afford.  He  is  like  the  oommander  who  oan  find  no  alatioa  ftai 
which  to  view  the  evolutions  of  the  anny  againal  whieh  ha  haifl 
eontendy  except  one  upon  a  dead  level  with  it^  hot  wMi  this  nal 
addition  to  his  embarnssment^  that  his  own  stalioa  is  ilMlf  wS^d 
to  varioos  changes  of  position,  of  which  he  is  altogether  rniniwh^ 
and  which  he  oan  only  ascertain  by  the  ap|Mnnt  dMnagea  ctjatM 
which  they  produce  among  the  objects  of  hisobserviatMO  ■riiiiM|& 
The  diimlties  arimng  oat  of  these  drmnBataneea  ohatawM  W 
agas  the  progress  of  astronomical  science.  The  fWiiiBshm  si  itf 
versally  entwtained  of  the  abeolnto  immobility  of  the  6sia,«itfrii 
odIt  a  vast  ttror  itselfi  bat  the  cause  of  nameraaa  other  effiM;  S 
misled  inqnirers  by  compelling  them  to  aseribe  notkii  to  MM 
which  are  atationaryi  and  to  ascribe  to  bodies  not  statioMijtosiili 
altoffether  different  from  those  vrith  which  they  are  nafly  sMJC 

2557.  Two  methods  of  expoMcn,  —  There  are  two  meHiods  If 
which  a  knowledge  of  die  motions  and  anrangement  of  the  ioir 
system  may  be  imparted.  We  may  first  explain  its  apparent  BMtfaas 
ttui  changes  as  actually  seen  from  the  earth,  and  deduce  from  thm^ 
combined  with  our  knowledge  of  the  motions  which  affect  the  eflAf 
itself,  the  real  motions  of  the  other  bodies  of  the  system ;  or  we  mtj^ 
on  the  contrary,  first  explain  the  real  motions  of  the  entire  sjatsmiB 
they  are  now  known,  and  then  show  how  they,  combined  with  As 
motion  of  the  earth,  produce  the  apparent  motions. 

The  former  method  would  perhaps  be  more  strictly  lo^cal,  dm 
it  would  proceed  from  observed  facts  as  data  to  the  concloaions  to  b 
deduced  from  them ;  while  the  other  method  first  assumes,  as  knov% 
that  which  we  desire  to  ascertain,  and  then  shows  that  it  is  earn* 
patible  with  all  the  obaerved  phenomena.  Nevertheless,  fer  dwiai 
tary  purposes,  such  as  those  to  which  this  volume  is  direetsdjy  Ai 
latter  method  is  preferable ;  we  shall,  therefore,  explain  the  motal 
and  relative  arrangement  of  the  bodies  of  the  system,  showing  n 
we  proceed,  how  their  motions  cause  the  phenomena  whidi  are  ob- 
served in  the  heavens. 

2558.  General  arrangement  of  hodtea  compoeing  Ac  9ohr  m» 
tern.  —  The  solar  system  is  an  assembhige  of  great  bodies,  (^obuhr 
in  their  form,  and  analogous  in  many  respects  to  the  earth.  Lib 
the  earth,  they  revolve  round  the  sun  as  a  common  centre  in  orbiii 
which  do  not  differ  much  from  circles :  all  these  orbite  are  rmj 
nearly,  though  not  exactly,  in  the  same  plane  with  the  annual  oAl 
of  the  earth,  and  the  orbital  motions  all  take  place  in  the  some  £- 
rection  as  that  of  the  earth. 

Several  of  these  bodies  are  the  centres  of  secondaiy  svsteBi^ 
another  order  of  smaller  globes  revolving  round  them  reapectnJyh 


THE  SOLAR  SYSTEM.  249 

tlie  same  manner  and  according  to  the  Bame  dynamical  laws  as 
govern  their  own  motion  round  the  sun. 

2559.  Planets  primary  and  scconclary.  —  This  assemblage  of 
globes  which  thus  revolve  round  the  sun  as  a  common  centre,  of 
vhich  the  earth  itself  is  one,  are  called  planets  ;  and  the  secondary 
globes,  which  revolve  round  several  of  them,  are  called  secondary 
PLANETS,  SATELLITES,  or  MOONS,  One  of  them  being  our  moon, 
which  revolves  round  the  earth  as  the  earth  itself  revolves  round 
the  sun. 

2560.  Primary  carry  with  them  the  secondary  round  the  sun.  — 
The  primary  planets  which  are  thus  attended  by  satellites,  carry  the 
latellites  with  them  in  their  orbital  course;  the  common  orbital 
motion,  thos  shared  by  the  primary  planet  with  its  secondaries,  not 
preventing  the  harmonious  motion  of  the  secondaries  round  the  pri- 
mary as  a  common  centre. 

25G1.  Planetary  motions  to  he  first  regarded  as  ciradar,  uniform, 
and  in  a  common  plane.  —  It  will  be  conducive  to  the  more  easy 
and  clear  comprehension  of  the  phenomena  to  consider,  in  the  first 
instance,  the  planets  as  moving  round  the  sun  as  their  common 
oeotre  in  exactly  the  same  plane,  in  exactly  circular  orbits,  and  with 
motions  exactly  uniform.  None  of  these  suppositions  correspond 
precisely  with  their  actual  motions ;  but  they  represent  them  so  very 
nearly,  that  nothing  short  of  very  precise  means  of  observation  and 
meaanrement  is  capable  of  detecting  their  departure  from  them.  The 
motions  of  the  system  thus  understood  will  form  a  first  and  very 
close  approximation  to  the  truth.  The  modifications  to  which  the 
conclusions  thus  established  must  be  submitted,  so  as  to  allow  for 
the  departure  of  the  several  planets  from  the  plane  of  the  ecliptic, 
of  their  orbits  from  exact  circles,  and  of  their  motions  from  perfect 
nniformity,  will  be  easily  introduced  and  comprehended.  But  even 
these  will  supply  only  a  second  approximation.  Further  investiga- 
tion will  show  series  after  series  of  corrections  more  and  more  minute 
in  their  quantities,  and  requiring  longer  and  longer  periods  of  time 
to  manifest  the  eflfects  to  which  they  arc  directed. 

2562.  This  method  folhncs  the  order  of  discovery.  —  As  to  the 
re^t,  in  following  thb  order,  proceeding  from  first  suppositions, 
which  are  only  rough  approximations  to  the  truth,  to  others  in  more 

I     exact  accordance  with  it,  we,  in  fact,  only  follow  the  order  of  dis- 
I     coverj  itself,  by  which  the  laws  of  nature  were  thus  gradually, 
-     klowly,  and  laboriously  evolved  from  masses  of  obscure  and  inexact 
hyp<#theses. 

2563.  Inferior  and  superior  planets.  — The  concentric  orbits  of 
the  planets  then  are  included  one  within  another,  augmenting  suc- 
eessivcly  in  their  distances  from  the  centre,  so  as  in  general  to  leave 
a  great  space  between  orbit  and  orbit.  The  third  planet,  proceeding 
fitim  the  san  outwards,  is  the  earth.      Two  orbits,  those  of  the 


i 

t 

1 


i 


SM  JdBlMtfOaftt' 

pimeli  oaUed  Merontj  and  Tmm,  m  flfaidbif  IvMriUf  fHili 
the  earth'i  orbit,  which  itself  is  indoded  widdil  dM  «Attlro^dlii 
other  planets. 
Those  planets  whieh  are  bolnded  irhUik  Hm  oitft  of  tte  mttk 

an  oaUed  INFEBIOB  FiAKns.  and  all  the  oftffia  an  odbl  sotttm 

_____  ^ 

KiANlTS. 

2564.  PertbA,— ThoFERiDinofnnorailaMtbibel^^ 
between  two  siiooessive  rstoms  to  the  aame  pouH  of  Ha  oMt^  MA 
ahorti  Uie  time  it  takes  to  make  a  oomplete  vsvohtiM  loiriftlli 
ann.    It  is  fimnd  by  obaernrtioni  aa  m^^  hb  ilff$aaJllf 
Oat  the  periodio  time  inereaaea  idth  Oe  oiUt^  being  aiieh 
fbr  the  more  distent  planets;  bnt^  aa  will  appear  toMftar,  tftt 
crease  of  the  periodio  time  is  not  in  the  aame  pwfiqiliaa  afe! 
Inerease  of  the  orbit  '^ 

2565.  Synodic  moHon. — The  motion  of  a  planel 
merely  in  reuition  to  that  of  the  earth|  without  refersDee  t0  Hs 
position  in  its  orbit,  is  called  its  8Tnodio  Monoar. 

2506.  OeoceiUnc  and  hdioeaUHc  maHom.  —  The 
iDOtion  of  a  pUuet  aa  they  appear  to  an  obaerm  on 
ealled  GKOGENTBio*;  and  as  they  wodd  appear  if  the 
transferred  to  the  son,  are  called  hxuooentbio  *. 

2567.  ffeliocentnc  motion  dedueihle /rom  geooeniric.^-^  iJ&ao^  \ 
the  apparent  motions  cannot  be  directly  observed  from  the  son  Ml)  i 
station,  it  is  a  simple  problem  of  elementary  f^metry  to  dedMl  r 
tiiem  from  the  geocentric  motions,  combined  with  the  relatife  dfe  ' 
tances  of  the  earth  and  planet  from  the  son ;  so  that  we  are  faj 
condition  to  state  with  perfect  clearness,  precision,  and  eerteinty|lii 
the  phenomena  which  the  motions  of  the  planetary  system  woji| 
present,  if,  instead  of  being  seen  from  the  moyeabb  station  of  til 
earth,  tbej  were  witnessed  from  the  fixed  central  station  of  the 

2568.  Relation  between  the  daily  heliocentric  motion  and  M 
period,  — If  the  mean  daily  heliocentric  motion  of  a  planet  bed|j 
pressed  by  a,  and  the  periodic  time  in  days  by  P,  it  is  evident  thtfj 
a  X  P  will  express  860^,  providing  that  a  is  expressed  in 
Thus  we  shall  have 

a**  X  P  =  860**; 

and  hence  it  follows,  that  if  either  the  period  P  or  the  dailfj 
centric  motion  be  given,  the  other  maybe  computed;  fbr  «( 
have 

^      360^  860« 

p    '  tt^ 

It  is  usual  to  express  a,  not  in  degrees,  but  in  seoonda.    In 

*  From  the  Greek  words  yn  (ge)  and  (Xiof  (helios),  iignityinf  Ik  .^_.. 
and  ih$  nm.  ^i*. 


ii.^ 


THB  SOLAB  8T0TB1L  S61 

mH  be  BgcewMj  to  ledaoe  800^  tko  to  Moonds.    We  diall 
]iav«(2292) 

^      1296000  1296000 

0.  Ikiify  t^nodic  mcium.  —  The  daily  synodic  motion  is  the 
by  which  the  planet  derarts  from  or  approaches  to  the  earth 
oofOTBe  Toand  the  san.  Thos  if  A  express  in  degrees  the  aoele 
1  by  two  lines  drawn  from  the  sun,  one  to  the  planet  and  ue 
to  the  earth|  the  daily  synodic  motion  will  be  the  daily  in- 
er  decrease  of  A  prodnced  by  the  motions  of  the  earth  and 
;.  Now,  since  the  earth  and  planet  both  move  in  the  same 
km  ronnd  the  snn  with  different  anralar  motions,  the  increase 
ireaeo  of  a  wXL  be  the  difference  of  their  motions.  Thus,  H 
anet  move  thronffh  S^  while  the  earth  moves  through  1^  per 
t  is  evident  that  uie  daily  increase  or  decrease  of  a  will  be  2^ ; 
f  while  the  earth  moves  thronffh  1^,  the  planet  move  through 
e  daily  increase  or  decrea9e  of  A  will  be  t^.' 
we  express,  therefbro,  the  daily  synodic  motion  of  a  planet  by 
daily  heliocentric  motion  by  a>  and  that  of  the  earth  by  t ,  we 
have,  for  an  inferior  planet,  whose  angular  motion  exceeds 
i  the  earth, 

a  =  tt  —  t; 

r  a  superior  planet,  whose  angular  motion  is  slower, 

*  =  t  —  a. 

rO.  JSUatum  between  Ae  synodic  moHon  and  the  period.'-^ 
tbe  daily  heliooentrio  motions  are  found  by  dividing  860^  by 
siods,  we  shall  have  for  an  inferior  planet 

^      860O        860<>      „      1296000       1296000 
p  «   '  p  I       ' 

w  a  saperior  pkaet 
^      860«       860«  1296000       1296000 

X  P     '  K  P 

ri.  Elongation, — The  geocentric  position  of  a  planet  in  re- 
to  the  sun,  or  the  anffle  formed  by  lines  drawn  from  the  earth 
son  and  planet,  is  cdled  the  slonoation  of  the  planet,  and 

IT  or  WX8T,  aooording  as  the  planet  is  at  the  one  side  or  the 

of  the  snn. 

r2.  Oonjunction.  —  When  the  elongation  of  a  planet  is  no- 
it  is  sud  to  be  in  confunctum^  being  then  in  the  same  direo- 

■  the  sun  when  seen  from  the  earth. 

rS.   Oppontum. — When  the  elongation  of  a  planet  is  180^, 

said  to  be  in  opposition,  being  then  in  the  quarter  of  the 

DS  directly  opposite  to  the  sun. 


888  AsnoHOiir, 

It  b  erident  thtt  s  pknet  wUoh  is  in  wnJmelioB  pmtm  IktM^ 
ridian  at  or  very  near  noon,  and  la  therrfora  abova  Hm  haam 
daring  the  day,  and  below  it  dorins  the  nigiit 

On  the  other  hand,  a  planet  mioh  ia  in  opposition  panes  Ik 
meridian  at  or  Tory  near  midnight,  and  therefore  is  aboie  As 
horison  during  the  night,  and  below  it  daring  the  day. 

2574.  Quadrature.  —  A  planet  b  said  to  be  in  quadratme  ifai 
its  dionffation  b  90^. 

Li  this  position  it  passes  the  meridian  at  about  six  o'olodc  m  lb 
morning,  when  it  has  western  qoadratnre,  and  aix  o'eloek  b  As' 
evening,  when  it  has  eastern  qoadratnre.  It  is^  therefore,  aboit 
the  horbcfn  on  the  eastern  side  of  the  firmament  daring  the  kttv 
part  of  the  night  in  the  former  ease,  and  on  the  western  side  damg 
the  first  part  of  the  night  in  the  lifter  oaae.  It  b  a  movniog  Hv 
in  the  one  ease,  and  an  OToning  atar  in  the  other. 

2575.  Synodic  period, — The  interval  which  eb^aea  hetisa 
two  similar  elongations  of  a  planet  b  called  the  stnodio  fbns 
of  the  planet  Thus,  the  interval  between  two  successive  oppos* 
tioDS,  or  two  successive  eastern  or  western  qnadratores,  is  tb 
synodic  period. 

2576.  Inferior  and  superior  conjunction, — A  sopeiior  pkaek 
can  never  be  in  conjunction  except  when  it  b  placed  on  the  sids  d 
the  sun  opposite  to  the  earth,  so  that  a  line  drawn  from  the  esiA 
throueb  the  sun  would,  if  continued  beyond  the  sun,  be  directed  it 
the  planet.  An  inferior  planet  b,  however,  also  in  oonjnndioH 
when  it  crosses  the  line  drawn  from  the  earth  to  the  snn,  betVMS 
the  earth  and  the  sun.  The  former  b  dbtingubhed  aa  aunuoi 
and  the  latter  as  inferior  conjunction. 

As  inferior  conjunction  necessarily  supposes  the  planet  to  k 
nearer  to  the  sun  than  the  earth,  and  opposition  supposes  it  to  b 
more  distant,  it  follows  that  inferior  pknets  alone  can  be  in  infinor 
conjunction,  and  superior  planets  alone  in  opposition. 

2577.  Relation  bettceen  the  periodic  time  and  ^fnodie  period.'^ 
Since  the  synodic  period  b  the  interval  between  two  similar  por- 
tions of  the  earth  and  planet,  the  one  must  gain  upon  the  other 
860^  in  such  interval.  To  perceive  thb,  let  s,  J!^,  733,  be  the  son, 
p'  the  earth,  and  P  an  inferior  planet  when  in  inferior  conjonettoo, 
the  common  direction  of  the  motions  of  both  beine  indicated  by  the 
arrows.  Leaving  this  position,  the  angular  motion  of  the  plsoet 
round  s  being  the  more  rapid,  it  gains  upon  the  earth  as  the  mmnte- 
hand  of  a  watch  gains  upon  the  hour-hand ;  and  when,  aftw  makisc 
a  complete  revolution,  the  planet  returns  to  the  point  p,  the  esrts 
will  have  advanced  from  p^  in  the  direction  of  the  arrow,  so  ibt 
before  the  next  inferior  conjunction  can  take  place  the  planet  most 

pass  beyond  p,  and  overtake  tVi^  esx\.\i.    \j&i  ^ '  be  the  position  d 
ibe  e&rib  when  this  takes  place,  tVie  ^Wl^^  >D««i%^«^  ^  <^«  VJ% 


THB  SOLAR  STBTEM. 


253 


fridtni,  therefbre,  that  in  the  ioterval  between  two  successive  in- 
fiarior  ooDJnnotkms  the  planet  describes  roand  the  sun  360^,  together 


Fig.  7SS. 

with  the  angle  pBV,  which  the  earth  has  described  in  the  same 
fnterral.  If  this  angle^  described  by  the  earth  in  the  synodic 
period,  be  called  A,  the  angle  described  by  the  planet  in  the  same 
mterral  will  be  360''  +  a. 

If  P  represent  the  place  of  the  earth,  and  p'  that  of  a  superior 
planet  in  opposition,  the  earth  leaviDg  p,  and  having  a  more  rapid 
aogolar  motion  round  s,  will  get  be^re  the  planet  as  the  minute- 
luuid  gets  before  the  hour-hand,  and  when  it  returns  to  p  the  planet 
win  have  advanced  in  its  orbit,  so  that  before  another  opposition  can 
take  place  the  earth  must  overtake  it.  If  this  happen  when  the 
planet  is  at  j/y  the  earth  in  the  synodic  period  will  have  made  an 
entire  revolution,  and  have  in  addition  described  the  angle  ^  s  p,  or 
A,  wldeh  the  planet  has  described.  Thus,  while  A  expresses  the 
angle  which  the  superior  planet  describes  in  the  syncniic  period, 
8€iO^  +  A  expresses  the  angle  described  by  the  earth  in  the  same 
time. 

If  tf,  as  before,  express  the  daily  synodic  motion  of  the  planet, 
we  shall  have 

360°     ,,       1296000 

a    =  — • 


5°  = 


and  consequently 


T  = 


360°      1296000 


Thus,  when  the  dailf  synodic  motion  is  given,  the  synodAQ  ^m^ 
cu*  if^  oompated,  and  m'ce  versd. 


III. 


.)•> 


Ii  inferior  or  nperior,  wo  ilull  Iuto  for  tn  itt&rfar  |lMHt 
860"      880"      860O 


Ibr  in  inferior  ^anel>  utd 


860"      860O      860° 


fer  »  niperin  planet,  ihowing  in  euk  cue  llto  trithmo&i 
Iwtween  t,  P,  ud  B. 

2578.   The  aj^artnt  motion  <^  an  infiinor  plmttt.  •^'. 
»'_.  the  aitpuent  from  toe  rekl  moi 

inferior  pknet,  let  i,  fy.  78' 
plaoe  of  the  earth,  t  that  of 
and  ebi^e  the  orbit  of  the  pi 
direction  of  tbe  planet's  mot 
.  shown  by  the  arrows,  tlie 
//  whioh  it  assumes  sacoeflmTel] 
cated  at  tf,  a!,  e,  a,  c,  b,  ^,  and  i 
the  earth  moves  round  Oia  i 
same  direction  sa  the  planet, 
rent  motion  of  the  ean  t  wil 
the  left  to  the  right  of  an 
looking  from  x  at  «  ;  and  nno 
tion  is  always  from  west  to 
planet  will  ba  west  of  tbe  sn: 
IB  any  whera  in  the  semicnrol 
and  east  of  it  when  it  is  any 
the  Bemicirole  <fa'eae. 

Tbe  elongation  (2571)  of  tl 
being  the  anrle  formed  by  lii 
to  tbe  son  and  planet  from  the  earth,  will  always  be  eaat 
planet  is  in  the  semioirole  c*  e  c,  and  west  when  in  the 
c'e'c. 

The  planet  will  have  its  greatest  elongation  eaat  whei 

B«  directed  to  it  from  the  earth  is  a  tangent  to  its  orbit,  a: 

maoner  its  greatest  elongation  west  when  the  line  X^  ia 

to  the  orbit. 

In  these  poutiona  the  angle  i  e  k,  or «  ^  K,  at  the  plam 


Pig.  m. 


tte  ilongrtiiNi  and  die  ngle  6  «  Sy  or  /  « ly  tl  the 
talMi  togtAfBTf  make  op  9<M^ 
b  «|^»enL  theielbrey  thai  tiie  greatest  elongation  of  an  inferior 
pkaet  aiast  be  leea  than  90^ 

If  the  earth  wwe  atationaiy,  the  real  orUtal  motion  of  Ae  planet 
VQold  give  it  aa  apparent  motion  idtemately  east  and  west  of  the 
■B,  extending  to  a  oerlain  limited  diirtiaseey  resembling  the  oaeOla- 
lion  of  a  pendalvn*  While  the  pbmet  moves  ftom  ?  to  0^  it  will 
qfssr  to  depMi  ftom  the  snn  eartwaid,  and  when  it  moves  from  e 
tB  c^  it  will  appear  to  retnm  to  the  sm;  the  elongatioii  in  the 
famer  ease  eoostaatlj  inereasing  tili  h  attain  its  maximnm  easi- 
wrd,  and  in  the  latter  eoostantlj  deoreasing  till  it  beoome  nothing. 
It  is  to  be  ofaservedi  howeveri  tliat  the  orbital  are  de  being  greater 
tkm  €Cf  the  time  of  attaining  the  greatest  esstem  elon|p£on  after 
■peiior  eonjonetion  is  greater  than  the  time  of  returning  to  the 
asi  frem  the  greatsit  ekmjption  to  inferior  oonjnnotion. 

After  inferior  eoi^nnotiony  while  the  plmet  passes  from  e  to  ^, 
ilB  ehngarion  eonstantly  ineresses  from  nothing  at  e  to  its  mazi- 
Bim  west  at  ^;  and  when  the  planet  moves  from  «^  to  </,  it  a^pun 
Ineases  imtil  it  beoomes  nothmg  at  superior  conjunction.  Smoe 
Iks  oriiitsl  area,  ctf  and  fl  d^vn  respectivelj  equal  to  ce  and  </e^  it 
Ailow%  that  the  interval  from  inteior  coigunction  to  the  greatest 
shnyliim  west^  is  equal  to  the  interval  from  the  greatest  elongation 
to  inferior  oonjnnotion.  In  }Sk»  manner,  the  interval  from 
eoojnnotioa  to  the  neatest  elongation  east,  is  equal  to  the 
ftom  the  greatest  elongation  west  to  superior  conjunction. 
The  eerillation  of  the  phnet  alternately  east  and  west  is  there- 
in made  through  the  same  anfde  —  that  is,  the  angle  es^,  in- 
\rf  tangents  drawn  to  the  Janet's  orbit  from  the  esrth ;  but 
motion  from  the  greatest  elongation  west  to  tlie  greatest 
esst  is  slower  than  the  apparent  motion  from  the  greatest 
dawatioii  esst  to  the  greatest  elongation  west^  in  the  ratio  of  the 
IhA  of  the  orUtnal  arcs  e </ ^  to  ec^. 

The  planet  being  induded  within  the  orbit  of  the  earth,  the  or- 
lU  flMMien  of  the  earth  will  |^ve  it  an  i^parent  motion  in  the 
n^tie  in  the  same  direction  as  the  apparent  motion  of  the  sun ; 
kt  sinee  the  apparent  motion  of  a  visible  object  increases  as  its 
ftlBMe  deenasesi  and  eiioe  vend^  and  since  the  planet  beinz  at  a 
WsHewWe  distance  from  the  centre  of  the  earth's  orbit,  the  dis- 
tmea  of  the  earth  from  it  is  subject  to  variation,  the  apj^rent 
aotkm  imparted  to  tilie  pbmet  hj  the  earth's  orbital  motion  will  be 
to  a  proportionate  variation,  being  greatest  when  the  planet 


iihi  inferior  eonjvnetion,  and  least  when  in  superior  conjunction. 
Iha  apparent  motion  of  the  planet,  as  it  is  projected  upon  the 


bj  the  visual  ray,  arises  from  the  combined  effrat  of  its 
sn  eribMsl  motion  aasd  thai  of  the  eaiih.    Now  it  is  endent  from 


8M  A8TB0V0IIT. 

ipbii  hu  been  jost  explainedi  HuiX  Hm  eflbol  df  lh»  fiMiiniiM 

motion  is  to  give  it  an  apparent  motion  from  met  to  oatl  vUi 
passing  firom  its  greatest  elongation  west  thzoo^  ■apennr  vmjm^ 
tion  to  its  greatest  elongation  east,  and  a  eontiwy  vpfmnoi  matim 
from  east  to  west  while  passing  from  its  jpieaieBt  elmigation  Mil  to 
its  greatest  elongation  west  throngh  inferior  oopjanotiqe. 

Bat  since,  in  all  poeitionS|  the  eflfoot  of  tiie  orinial  motion  of  At 
earth  is  to  ffive  the  planet  an  apparent  motion  direoted  fitMs  mt 
to  east,  both  causes  combine  to  impart  to  it  this  apparait  motioi 
while  passing  from  its  western  to  its  eastern  elongatioo  throogl 
superior  oonjnnotion.  On  the  other  hand,  the  effect  of  the  orbM 
motion  of  the  planet  being  an  apparent  motion  from  east  to  west  k 
passing  from  its  eastern  to  its  western  elongation  tiiroogh  inieikr 
conjunction,  whUe,  on  the  contrary,  the  earth  s  motion  imparls  to  it 
an  apparent  motion  from  west  to  east,  the  actual  apparent  motios 
of  the  planet,  resultiug  from  the  difference  of  these  effects,  will  bi 
westward  or  eastward  according  as  the  efiect  of  the  <me  or  the 
other  predominates,  and  the  pluiet  will  be  stationary  when  thaw 
opposite  effects  are  equaL 

In  leaving  the  greatest  eastern  elongation  the  efkd  of  the  eirth'i 
motion  predominates,  and  the  apparent  motion  of  the  planet  oon- 
tinues  to  be,  as  before,  eastward.  As,  in  approaching  inferior  ooa- 
junction,  the  direction  of  the  planet's  motion  becomes  more  and 
more  transverse  to  the  visual  line,  and  the  distance  of  the  pknet 
decreases^  the  effect  of  the  planet's  motion  increasiug  becomes,  it 
leugth,  equal  to  the  effect  of  the  earth's  motion,  and  the  plaset 
then  becomes  stationary.  This  takes  place  at  a  certain  elongation 
east.  After  this,  the  effect  of  the  planet's  motion  predominstiDg, 
the  apparent  motion  becomes  westward,  and  this  westward  moSiaa 
continues  through  iuferior  conjunction,  until  the  planet  acquires  i 
certain  elongation  west,  equal  to  that  at  which  it  becamo  previduh 
stationary.  Here  the  effects  becoming  again  equal,  the  planet  v 
again  stationary,  after  which,  the  effect  of  the  earth's  motion  pit* 
dominating,  the  apparent  motion  becomes  eastward,  and  oontiiraM 
so  to  the  greatest  elongation  west,  after  which,  as  before,  both  oamM 
combine  in  rendering  it  eastward. 

2579.  Direct  and  retrograde  motion.  —  When  a  planet  appsui 
to  move  in  the  direction  in  which  the  sun  appears  to  move,  its  sp- 
parent  motion  is  said  to  be  direct  ;  and  when  it  appemra  to  mofi 
in  the  contrary  direction,  it  is  said  to  be  retroorads. 

From  what  has  been  explained  above,  it  appears  that  the  appip 
rent  motion  of  an  inferior  planet  is  always  direct,  except  withm  a 
certain  elongation  east  and  west  of  inferior  conjunction,  when  U  v 
retrograde. 

The  extent  of  this  arc  of  retrogression  depends  on  the  relaftifO 


267 


wmnfatmi  nkArt  orlitel  ydooitiei^of  &•  Mrth  and 


mioiiim  as  prqfeded  <m  Ik  eeJtjp^— From 
kite  ispIiiiieditM  spputnt  motioii  of  the  |4aiiet  on 
wSk  b»  iMQy  uidanrtood.    Let  abmwk^ Jig.  785, 


npntent  the  aoBptio  in  which  the  pknet  is  st  present  eopposed  to 
■iVBL  While  pennff  from  iti  western  to  its  eastern  elongation  it 
ifpean  to  more  in  the  same  direction  as  the  son,  from  A  towards 
I.  As  it  appnabhes  B,  its  apparent  motion  eastwud  becomes  gra- 
Uly  slower  nnlil  it  stops  altogether  at  b,  and  becomes,  for  a  short 
iMsrm,  itstionaiy ;  it  then  moves  westward,  returning  npon  its 
Mnie  to  0|  where  it  again  becomes  stationary;  affcer  which  it  a^n 
aefss  eaatwaidi  and  continues  to  move  in  that  direction  till  it  arrives 
at  a  oerlain  pmnt  d,  where  it  again  becomes  stationary ;  and  then, 
Fitaming  npon  its  coorscy  it  again  moves  westward  to  x,  where  it 
i|aiB  beeomes  stationary ;  after  which  it  again  changes  its  direction 
aad  moves  eastward  to  r,  where,  after  being  stationary,  it  turns 
veatwaidy  and  so  on. 

The  middle  points  of  the  arcs  bo,  dk,  fq,  &c.,  of  retrogression 
sm  those  at  which  the  phmet  is  in  inferior  conjunction ;  and  the 
■iddle  points  of  the  arcs  od,  sr,  o  h, &c.,  of  progression  are  those 
il  wUen  the  phmet  is  in  snperifflr  conjunction. 

22* 


^tpuantlr  imvahr  momDeirt^  1^  whiek  tlw  ilaMli  w»  tUt^ 
gauhed  ftom  all  otlwr  edeilid  obgeoli,  nggnM  to  the  laria^ 
whoM  knowledge  of  Mtnnomj  wu  too  impnfcet  to  «mHo  Aart 
tnoe  sach  motiona  to  ftxad  uu  iwnkr  lawa,  tho  naao  fkai^'lik 
the  Greek  wotd  lOar^tig  (pluwtee),  wmdenr. 

2682.  J;]^ren/  mofioit  o/*  a  atq>erior  fbauL  — Tb  daAMl  fc 
■pparent  motion  of  •  enperuv  pluiet  bom  tlio  twl  4)riitol  HtiB 
of  the  eaUh  and  the  plane^  let  t,fy.  786,  bo  ihn  phee  of  Oia^ 


J>  that  of  the  planet,  and  E  ^  s"'  s"  the  orbit  of  tiie  earth  luiaUi 
within  that  of  the  planet,  the  direction  of  the  motions  of  the  eailk 
and  planet  being  indicated  bj  the  arrows. 

When  the  eanh  is  at  x"',  the  sun  B  and  planet  p  are  in  the  nw 
visnal  line,  and  the  planet  is  consequeutlj  in  coajanetioD.  Whn 
the  earth  moves  to  ^,  the  elongation  of  the  planet  west  of  the  m 
u  8  /  P.  This  elongation  increasing  aa  the  earth  movea  in  ita  ortil, 
becomes  90°  at  e',  when  the  visual  direction  e'  f  of  the  plaaet  a  a 
tangent  to  the  earth's  orbit,  and  the  planet  ia  then  in  ita  werttft 
quadrature. 

While  the  earth  eontinuea  its  orhitAl  motion  to  e"',  the  elonplioa 
west  of  the  snn  continues  to  increase,  and  at  length,  when  the  entb 
oomea  to  the  position  e,  it  becomes  180°,  and  the  planet  is  in  i^ipo- 
uuon. 

After  passing  E,  when  the  earth  moves  towards  e",  the  elooptioa 
of  the  planet  ia  east  of  the  sun,  and  is  less  than  180°,  but  graafci 
than  90°.  Aa  the  earth  cootinacs  to  advance  in  its  orbit,  the  eloi- 
gation  decreasing,  becomes  90°  when  at  e",  the  Tisoal  diieetioB  of 


THE  80LAB  SYSTEM.  259 

ke  pkaet  ii  a  tangent  to  the  earth's  orbit    The  planet  is  then  in 
liCBSteni  qnadratore. 

Aa  the  earth  moyes  from  sf'  to  s^',  the  elongation,  being  still 
mAf  constantly  decreases  until  it  becomes  nothing  at  e"',  where  the 
fluiet  is  in  conjunction. 

2583.  Direct  and  retrograde  motion.  —  If  the  planet  were  im- 
soTeaUei  the  effect  of  the  earth's  motion  would  be  to  give  it  an 
QKiUatory  motion  alternately  eastward  and  westward  through  the 
ngle  if  p  nf'y  which  the  earth's  orbit  subtends  at  the  planet.  While 
the  earth  moves  from  if'  through  E^'  to  e',  the  planet  would  appear 
to  move  cattvcard  through  the  angle  e'  p  e",  and  while  the  earth 
1D0VC8  from  if  through  S  to  E^,  it  would  appear  to  move  tccsitcard 
through  the  same  angle. 

Thus  the  effect  of  the  earth's  motion  alone  is  to  make  the  planet 
appear  to  move  from  east  to  west  and  from  west  to  east  alternately 
through  a  certain  arc  of  the  ecliptic,  the  length  of  which  will  de- 
pend CD  the  relation  between  the  distances  of  the  earth  and  planet 
6om  the  sun,  the  arc  being  in  fact  measured  by  the  angle  which 
the  earth's  orbit  subtends  at  the  planet,  and,  consequently,  this 
%DgIe  of  apparent  oscillation  will  decrease  in  the  same  ratio  as  the 
distance  of  the  planet  increases. 

The  times  in  which  the  two  oscillations  eastward  and  westward 
would  be  made  are  not  equal;  the  time  from  the  western  to  the 
eastern  quadrature  beinip  less  than  the  time  from  the  eastern  to  the 
western  quadrature  in  the  ratio  of  the  orbital  arc  e'  £  e"  to  the  arc 

It  is  evident  that  the  more  distant  the  planet  p  is  the  less  unequal 
these  arcs,  and,  consequently,  the  less  unequal  the  intervals  between 
qoadrature  and  quadrature  will  be. 

But,  meanwhile,  the  earth  being  included  within  the  orbit  of  the 
planet,  the  effect  of  the  planet's  orbital  motion  will  be  to  give  it  an 
apparent  motion  in  the  ecliptic  always  in  the  same  direction  in  which 
the  sun  would  move  when  in  the  same  place,  and  therefore  always 
eastward  or  direct. 

This  apparent  motion,  though  always  direct,  is  not  uniform,  since 
it  increases  in  the  same  ratio  as  the  distance  of  the  earth  from  the 
planet  decreases,  and  vice  versd.  This  apparent  motion  thus  due  to 
the  planet's  own  orbital  motion  is,  therefore,  greater  from  western 
to  eastern  quadrature  than  from  eastern  to  western  quadrature. 

From  eastern  to  western  quadrature,  through  conjunction,  the 
apparent  motion  of  the  planet  is  direct,  because  both  its  own  orbital 
motion  and  that  of  the  earth  combine  to  render  it  so.  From  western 
quadrature,  as  the  planet  approaches  opposition,  the  effect  of  the 
earth's  motion  is  to  render  the  planet  retrograde,  while  the  effect  of 
iti  own  motion  is  to  render  it  direct  On  leaving  quadrature  the 
latter  effect  predominates,  and  the  apparent  motion  is  direct;  but  at 


>  — <Ma  ^loDgnlioDy  heton  amviog  wi 

eutVn  motion  ioereamns  booomei  eqoil  to  thaft  «f  IM 

Beatimlinoff  it^  rendoTB  toe  planal  Btetionur;  wt 

of  the  GAws  motioQ  predominaliiigy  the  puMl 

and  oontmoes  ao  uotal  it  aomiires  an  equal  eloagiiMM 

again  beoomea  atationaiyi  and  ia  afterwaida  diieeti  and  eanlii 

2684.  JfpeureiU  motion  pn^ecied  am  A€^claiie^^ 
lepreaent  toe  jdaoe  of  a  anpeiior  ptaaet  men  mumog  mm  i|p 
wealern  qnadn^oie  towaida  eoigiine(ieO|  ito  appawat  motion  kii| 


Fig.  TIT. 

then  direct.  Let  b  be  the  point  where  it  beoomea  atationaiy  ate 
ite  eastern  quadrature;  its  apparent  motion  then  beooming  nbe* 
grade,  it  appears  to  return  upon  its  course  and  moves  weatwaid  to  0^ 
where  it  again  becomes  stationary ;  afier  which  it  again  retonii  M 
its  course  and  moves  direct  or  eastward,  and  continues  so  until  it  «- 
rives  at  a  certain  point  D  after  its  western  quadrature,  when  it  agua 
becomes  stationary,  and  then  again  retrogrades,  moving  throogh  tbft 
arc  D  £,  which  will  be  equal  to  b  o ;  after  which  it  will  again  beaoatf 
direct,  and  so  oo. 

The  places  of  the  planet's  opposition  are  the  middle  pointB  of  te 

arcs  of  retrogression  b  c,  D  £,  f  o,  &o. ;  and  the  plaoea  of  ooB^jaa^ 

Hon  Mie  the  middle  points  of  the  aioa  of  pTo^ssion  o  D,  x  r,  a  H,  fe 

li  k  evident,  therefore,  ihal  il^  vg(igm«nl  T&K^ass^  t^  ^ 


?UH.  —  It  is  evident  that  to  be  visible;  ia  tljc  absence  of  the 

(.■Icstiul  object  must  be  so  far  clongalcd  from  tint  lumicjary 

;  above  the  horizon  before  the  comineocemcut  of  the  moroiDE  ,i  . .. 

t  or  after  the  end  of  the  eveoiog  twilight.     One  or  two  of  'jj-^jj 

inets  have,  neverthelega,  an  apparent  maguitniie  so  oonoder- 

[id  a  loBlre  so  intense,  that  they  are  sometimea  seen  with  the 

eye,  even  before  saoset  or  after  sunrise,  and  may,  in  some 

«  seen  with  a  telescope  when  the  sno  has  a  conuderable  &lti- 

In  general,  however,  to  be  visible  without  a  telesoope,  a 
mast  have  an  elongation  greater  than  S0°  to  35°. 
i,  Eitning  and  moming  ttar.  —  Since  the  inferior  planets 
ver  attain  so  great  an  elongation  as  90°,  they  must  always 
le  meridian  at  an  interval  oonsiderably  less  dian  ux  honra 
or  after  the  sua.  If  they  have  eastern  elongation  they  pass 
ridina  in  the  aftemoon,  and  are  visible  above  the  horizon  after 

and  are  then  called  kvxnimq  btaas.  If  they  have  western 
ion  they  pass  the  meridian  in  the  forenoon, .and  are  viuhle 
he  eastern  horiion  before  sunrise,  and  are  then  called  Mobn- 

'.  Appearance  of  tuperior  planelt  at  varuna  dongalimu.  — 
rior  planet,  having  every  degree  of  elongation  east  and  west 
I  from  0"  to  \W,  passes  the  meridian  during  its  synodic 


s  tiie  meridian  ekrlier  than  six  o'clock  in  the  u'ternoon  in  the 
okM,  and  Ikter  than  six  o'clock  in  the  forenoon  in  the  latter 
teinj^  like  an  inferior  planet,  an  evening  etar  in  the  former 


Ml  ARROHomr. 

90^  irest  of  the  son,  the  planet  nmrt  MMOe  muUSmt  A\ 
between  midnight  and  rix  (/oloolc  in  the  mornings  and  it  k  flMnlm 
Tirible  from  some  hoars  after  sonaet  nntQ  aonriee. 

At  opposition  the  planet  passes  the  meiidiaa  aft  mUd^f^  nl  k 
therefore  Tisible  firom  sonset  to  sonrise. 

2&88.  To  find  the  periods  time  of  Ae  pbmeL'^Thmt  m 
several  solutions  of  this  problem,  whidi  me  rssolts  Inifiiig  dUnMl 
domes  of  approximation  to  the  exact  woe  of  the  quanftf^r  lO^lhfc 

2589.  P.  By  meatu  of  the  ^nodic  period — If  the  wjmk 
period  t  be  asoertained  bj  obaemSMm,  we  ahall  haifo  ftr  an  hdhriflr 
phmet  0577). 

1      i— 1 

T  **   P  ■' 

and  oontcqnentlT  i 

111  t 

7  =  7  +  7? 

and  for  a  superior  planet 

111  " 

^»     ^S    ^^  ^^mm  a^M* 

T  «  P' 

and  therefore 


PET 

In  each  case,  therefore,  p  may  be  found,  B  and  T  being  known. 

This  method  gives  a  oertain  approximation  to  the  value  of  ilM 
period ;  but  the  sjDodio  time  not  being  eapable  of  very  exact  appro- 
oiation  by  observation,  the  method  does  not  supply  extremely  aooo- 
rate  results. 

2590.  2°.  By  observing  the  transit  through  the  nodes, — TIm 
periodic  time  may  also  be  determined  by  observiuff  the  interval  b^ 
tween  two  suooessive  passages  of  the  planet  through  the  plane  efdM 
ecliptic.  , 

It  has  been  already  stated  that,  although  the  planets  move  neat^  !^ 
in  the  plane  of  the  ecliptic,  they  do  not  exacdy  do  so.  Thar  pattl  * 
are  inclined  at  very  email  angles  to  the  ecliptic,  and  they  eoasi*  * 
quently  must  pass  from  one  side  to  the  other  of  the  plane  of  Ihl  ^ 
earth's  orbit  twice  in  each  revolution.  If  the  momenta  of  thsi  ^ 
passing  through  the  plane  of  the  earth's  orbit  on  the  same  ttde  cf  * 
the  sun  be  observed  twice  in  immediate  suooession,  the  interval  w3l  ^ 
be  the  periodic  time.  i- 

Owing  to  the  very  small  inclination  of  the  orbits  in  genenl,  il  i^  /< 
impossible  to  ascertain  with  great  precision  the  time  <n  the  oeaM  ^1 
of  the  planet  passing  through  the  ecliptic,  and  therefore  this  voNrthol  N 
is  only  approximation.  ^  »8 

2591.  8^  By  comparing  oppositions  or  conjtmctume  AovAy  M^ 


THB  BOLAR  STSTEM.  2SS 

wUknal  place. — The  periodio  tune  of  a  i»lanet  being  approzi- 
■atolj  found  by  eidier  of  the  preceding  methods^  it  may  be  rendered 
BMHe  enot  bv  the  following. 

When  a  pLuiet  ia  in  anperior  oonjanotion  or  in  oppoaition,  its  phuse 
h  the  firmament  ia  the  nme,  whether  viewed  from  the  earth  or 
ftoB  the  son.  Now,  if  two  oppodtions  or  conjunctions  separated 
by  a  loog  interval  of  time  be  foondi  at  which  the  apparent  plaoe  of 
toe  planet  in  the  firmament  is  the  same,  it  may  be  inferred  that  a 
eooiplete  number  of  revolutions  must  have  taken  place  in  the  inter- 
val. Now  the  periodic  time  bein^  found  approximately  by  either 
of  the  methods  already  explained,  it  will  be  easy  to  find  by  it  how 
Buny  revolutions  of  the  planet  must  have  taken  place  between  the 
two  distant  oppositions.  If  the  periodio  time  were  known  with  pre- 
cifion,  it  would  divide  the  interval  in  question  without  a  remainder; 
bat  being  only  approximate,  it  divides  it  with  a  remainder.  Now 
tbe  nearest  multiple  of  the  approximate  period. to  the  interval  be- 
tween the  two  oppositions  will  be  that  multiple  of  the  true  period 
which  ia  exactly  equal  to  tho  interval.  The  division  of  the  interval 
bj  the  number  thus  determined  will  give  the  more  exact  value  of 
the  period. 

2592.  4^.  By  the  daily  angular  motion.  —  The  daily  angular 
nocentric  motion  may  be  observed,  and  the  heliocentric  motion 
uence  computed.  If  the  mean  heliocentric  daily  motion  a"  can  be 
obtained  by  means  of  a  sufficient  number  of  observations,  the  period 
will  be  given  by  the  formula  (2568), 

1296000 

a" 

2593.  To  find  the  distances  of  the  Janets  from,  the  sun,  —  One 
of  the  most  obvious  methods  of  solving  this  problem  is  by  observing 
the  elomgation  of  the  planet,  and  computing,  as  always  may  be  done, 
the  angle  at  the  sun.  Two  angles  of  the  triangle  formed  by  the 
Mrth,  son,  and  planet,  will  thus  be  known,  and  a  triangle  may  be 
inwn  of  which  the  sides  will  be  in  the  same  proportion  as  those  of 
Ae  triangle  in  question.  The  ratio  of  the  earth's  distance  firom  the 
mn  to  the  planet's  distance  from  the  sun  will  thus  become  known 
(229Q ;  and  as  tho  earth's  distance  has  been  already  ascertained, 
the  planet's  distance  may  be  immediately  computed. 

Other  methods  of  determining  the  distances  will  be  explained 
kieafter. 

2594.  Phases  of  a  planet. — While  a  planet  revolves,  that  hemi- 
iphere  which  is  presented  to  the  sun  is  illuminated,  and  the  other 
oiIl  But  since  the  same  hemisphere  is  not  presented  generally  to 
At  earth,  it  follows  that  the  visible  hemisphere  of  the  planet  will 

of  a  part  of  the  dark  and  a  part  of  the  enlightened  hemi- 
I,  and,  oonsequenlly,  the  planet  will  exhibit  phases,  the  vane- 


11,.  "•■  ,1,.  l.l»'-    ,  ^?„  I,  tb.  !»■?•'  J'e  A» 

„,a.l  to  "  "  •   ,  dn.«  <<'"  •'■    ' 


Bis.  i>'-  t.  «  ao". M '*" ■'^^-'^  v« 


THB  80IJLR  STSXflL 


265 


than  90^,  and  the  planet  appears  gibbouS;  as  the  moon  does  when 
between  opposition  and  qnaoratores. 

Whan  the  angle  s^i  is  ffreater  than  90^,  as  in  fig,  739,  the 
bnadth  i/  /  of  tl^  enlightened  part  of  the.  visible  hemisphere  is  less 
tkaa  90*^,  and  the  planet  appears  as  a  crescent,  like  the  moon  be- 
tween oonjnnetion  and  qnadratore. 

When  the  angle  s p  i  =  0,  which  happens  when  the  earth  is 
between  the  sun  and  planet,  as  in  fig,  740,  the  centre  m'  of  the 
caligfatened  hemisphere  is  presented  to  the  earth,  and  the  planet 
ippeara  with  a  full  phase,  as  the  moon  does  in  opposition.  This 
Jwaja  happens  when  the  planet  is  in  opposition. 

When  the  angle  sps  becomes  ==  180^,  as  in^.  741,  the  centre 
M  of  the  dark  hemisphere  is  presented  to  the  earth,  and  therefore 
the  entire  hemisphere  tamed  in  that  direction  is  dark.  This  takes 
ikee  when  the  planet  is  between  the  earth  and  sun,  which  can  only 
Mfipen  when  an  inferior  planet  is  in  inferior  conjunction. 

2595.  Phases  of  an  inferior  planet.  —  It  will  bo  evident  from 
■specting  the  diagram,  fig.  734,  representing  the  relative  positions 
tf  an  inferior  planet  with  respect  to  the  sun  and  earth,  that  the  angle 
fcrmed  by  lines  drawn  from  the  planet  to  the  sun  and  earth  passes 
tboogh  all  magnitudes  from  0^  to  180^,  and  consequently  such  a 
fknet  exhibits  every  variety  of  phase.  Passing  from  c  towards  ^y 
the  angle  <  6  e  gradually  decreases  from  180^  to  90^,  and  therefore 
the  phase,  at  first  a  thin  crescent,  increases  in  breadth  until  it  is 
lalved  like  the  moon  in  quadrature.  From  ef  to  cf  the  angle  s  2/  e 
pidually  decreases  from  90^  to  0%  and  the  planet  beginning  by 
king  gibbous,  the  breadth  of  the  enlightened  part  gradually  in- 
creases until  it  becomes  full  at  </.     From  c'  to  e,  and  thence  to  c, 

these  phases  are  reproduced  for  like 
reasons  in  the  opposite  order. 

2506.  Phases  of  a  superior  planet. 
—  It  will  be  evident  on  inspecting 
fig.  742,  that  in  all  positions  what- 
ever of  a  superior  planet,  the  lines 
drawn  from  it  to  the  earth  are  in- 
clined at  an  angle  less  than  90^ ;  and 
this  angle  is  so  much  the  smaller  the 
greater  the  orbit  of  the  planet  is 
comparatively  with  that  of  the  earth. 
The  angle  saE  being  nothing  at  o 
increases  until  the  planet  is  in  qua- 
drature at  ^y  where  it  is  greatest; 
and  then  the  breadth  of  the  enlight- 
ened part  is  least,  and  is  equal  to 
k  difference  between  the  angle  s  ^e  and  180^.  From  ^'  to  c  the 
f^  sVe  decreases,  and  b^mes  nothing  at  c.     The  planet  in 


Fig.  742. 


«vr 


206  ABIRQHQMr. 

therefore  full  at  q>po8iii(m  and  eoBJunetioii,  and  it  moit  fpUbons  at 

quadrature. 

It  will  appear  hereafter  that,  with  one  ezoeptioo,  all  the  mmnar 
planeta  are  at  dbtancea  from  the  aim  ao  much  greater  than  tnt  <f 
the  earth,  that  even  at  quadrature  the  aoglo  a  j^a  ia  ao  amall,  thil 
the  departure  of  the  phase  from  fulneaa  ia  not  aenaible. 

2587.   The  planeUt  are  mbjed  to  cetUral  atiraeiitm,  —  If  m  hoij 
in  motion  be  not  subject  to  the  attraction  of  any  eztenud  foiee^  ift  . 
must  move  in  a  straight  line.     If,  therefore,  it  be  obaenred  to  laafa 
in  any  curvilinear  path,  it  may  be  inferred  that  it  ia  acted  upoa  hj 
some  force  or  forces  exterior  to  it,  which  constantly  deflect  it  fnm    i 
the  straight  course  which,  in  Tirtue  of  its  inertia,  it  moal  foUaw  if    - 
Idft  to  itself  (220).    This  force  must,  moreover,  be  inceaaant  ia  te 
operation,  since,  if  its  action  were  suspended  for  a  moment,  the  bodj 
during  such  suspension  would  move  in  the  direction  of  the  stnigy 
line,  which  would  be  a  tangent  to  the  curve  at  the  point  where  tfai 
action  of  the  force  was  suspended. 

Now,  since  the  orbits  of  the  planets,  including  the  earth,  are  iD 
curved,  it  follows  that  they  are  all  under  the  luceaaant  operation  of 
aome  force  or  forces,  and  it  becomes  an  impcMiamt  problem  to  d»> 
termine  what  is  the  direction  of  these  forces,  whether  they  are  one 
or  several,  and,  in  fine,  whether  they  are  of  invariable  intensity,  or, 
if  variable,  what  is  the  law  and  conditions  of  their  variation. 

2598.  What  is  the  centre  to  which  this  attraction  is  directed  f^'    -. 
We  are  aided  in  this  inquiry  by  a  principle  of  the  highest  generaliij  ;' 
and  the  greatest  simplicity,  established  by  Newton,  the  demonstntioB  J^ 
of  which  forms  the  subject  of  the  first  two  propositions  of  his  oela'  ; 
brated  work,  entitled  "  Principia." 

2599.  General  principle  of  the  centre  of  equal  arecu  demoh 
strated.  —  If  from  any  point  taken  as  fixed,  a  straight  line  be  dram 
to  a  body  which  moves  in  a  curvilinear  path,  such  line  is  called  the 
radius  vector  of  the  moving  body  with  relation  to  that  point  Mft 
centre  of  motion.  As  the  body  moves  along  its  curviliuear  path, 
the  radius  vector  sweeps  over  a  certain  superficial  area,  greater  or 
less,  according  to  the  velocity  and  direction  of  the  motion  and  the 
length  of  the  radius  vector.  This  superficial  space  is  called  the 
''area  described  by  the  radius  vector,"  or,  sometimes,  the  ''ares 
described  by  the  moving  body." 

Thus,  for  example,  if  c,  fig.  743,  be  the  point  taken  as  the  centie 
of  motion,  and  bb"  be  a  part  of  the  path  of  the  moving  body,  CB 
and  c  b'  will  be  two  positions  of  the  ^^  radius  vector,"  and  in  paasiog 
from  one  of  these  positions  to  the  other,  it  will  sweep  over  or  "d^ 
scribe  "  the  superficial  space  or  "  area  "  included  between  the  lines 
0  B  and  0  b',  and  the  body  is  said  shortly  to  "  describe  this  arei 
round  the  point  o  as  a  centre." 

Now,  according  to  the  principle  established  by  Newtoo,  it  if 


L 


IBS  SOUK  8TBTSM. 


afft 


peus  that  whenever  a  body  inov«B  in  &  cnrrili- 
near  orbit,  ooder  the  attnction  of  a  force  di- 
rected to  a  fixed  centre,  such  a  bod;  vill 
deecribe  round  aoch  centre  equal  areaa  in 
equal  timee;  and  it  is  proved  also  convereelr, 
that  if  a  point  can  be  found  vithin  the  cnrvili- 
iiear  orlnt  of  a  revolving  body,  round  which 
Buoh  body  describes  equal  areas  in  equal  times, 
inch  body  is  in  that  case  subject  to  the  action 
of  a  single  force,  always  directed  towards  that 
pdnt  as  a  centre.  It  follows,  in  short,  that 
"  lh«  centre  of  equable  area*  it  Ae  centre  iff 
Jbres,  and  that  the  centre  of  force  it  the  centre 
of  equable  area*." 

As  this  is  a  principle  of  high  generally  and 
capital  importaDce,  and  admits  of  demonstration 
by  the  moat  elementary  principles  of  mechanias 
and  geometry,  it  may  be  proper  to  explain  it 

If  a  body  b  move  independently  of  the  action 
of  any  force  npon  it,  its  motion  must  be  in  a 
■ttugat  line,  and  must  be  uniform.     It  must, 
tlierefore,  move  over  equal  spaces  per  second. 
?]£.  la.  I^t  its  velocity  be  such,  that  in  the  first  second 

it  would  move  from  b  to  b'.  In  the  next 
1,  if  no  force  acted  npon  it,  it  would  move  through  the  equal 
B*  b'  in  the  same  direction.  But  if  at  b'  it  receive  from  a 
directed  to  C,  an  impolse  which  in  a  second  would  carry  it 
b'  to  c',  it  will  then  be  affected  by  two  motions,  one  repre- 
1  by  B*  h',  and  the  other  by  b'  c*,  and  it  will  move  in  the  din- 
s' b"  of  the  parallelogram,  and  at  the  end  of  the  second  second 
«  at  b". 

w,  in  the  first  second,  the  radtux  vector  described  the  area 
,  and  in  the  next  second  it  described  the  area  b'ob".     It  ■■ 

0  show  that  these  areas  are  eqaal.  For  since  B  b*  =  b'&',  the 
BCB*  and  b'c&' are  equal;  and  since  A' b"  is  parallel  to  b'o, 
reas  b'gI^  and  b'ob"  are  equal  by  the  welt-known  property 
angles.  Therefore  the  areas  bgb'  and  b'ob",  described  by 
idius  vector  in  the  first  and  second  seconds,  are  equal. 

the  body  received  no  impulse  from  the  central  force  at  b",  it 

1  move  over  &"&"=  b'b"  in  the  third  second,  but  receiving 
the  central  force  another  impulse  sofficient  to  carry  it  from  ir 

it  again  moves  over  the  diagonal  b"  b'"  of  the  next  parallelo- 
,  and  at  the  end  of  the  third  second  is  found  at  b"'.  It  is 
I  in  the  same  manner  that  the  area  of  the  triangle  b"  0  B^  ii 


268  ASTBOHOMT. 

equal  toB^OB^and  toBOBf;  ao  tluit  in  eifwy  ■niwtwwfiag 
the  radius  vector  deseribes  round  o  an  equal  area. 

In  this  case  it  has  been  supposed  that  the  force,  instead  of  aeiiM 
eoDtinuously,  acts  by  a  succession  of  impulses  at  the  end  of  cm 
scooody  and  the  body  desoribeS|  not  a  curve,  but  a  polygon.  If  tb 
sucoession  of  impulses  were  by  tenths,  hundredths,  or  thoosand^ 
or  any  smaller  fhustion  of  a  second,  the  areas  would  still  be  in  Ai 
ratio  of  the  times,  but  the  polygon  would  have  more  numeroos  nl 
smaller  sides.  In  fine,  if  the  intervals  of  the  action  of  the  fim 
be  infinitely  small,  the  sides  of  the  polygon  would  be  inimld^ 
small  in  magnitude  and  great  in  number.  The  fc»rce  woiddl,in  ImI^ 
be  continuous,  instead  of  being  intermitting,  and  the  path  of  tb 
body  would  be  a  curve,  instead  of  being  a  polygon.  Tk  anM^ 
however,  described  by  the  radius  vector  round  uio  centn  of  im 
0,  would  still  be  proportional  to  the  time. 

The  converse  of  the  principle  is  easily  inferred  bj  loamiM 
altogether  rimilar.  If  o,  fig,  748,  be  the  centre  of  equal  arsM^  * 
will  be  the  centre  of  attraction ;  for  let  b'  6^  be  taken  equal  to  Bl^. 
The  triangular  area  b'  c  6^  will  then  be  equal  to  the  area  BOI^  by 
the  common  properties  of  triangles,  and  since  the  areas  desoribed 
round  o  in  successive  seconds  are  equal,  we  have  the  area  B^Oi^s 
bob', and  therefore  =  b' c V,  Hence  we  infer  that  ji o 'bT^t^qV^ 
and  therefore  that  the  line  1/  b"  is  parallel  to  b'  c.  The  force  then- 
fore  expressed  by  the  diagonal  b'  b"  of  the  parallelogram  is  equifa- 
Icnt  to  the  forces  expressed  by  the  sides.  The  body  at  b',  tberfr- 
fore,  besides  the  projectile  force  B  b'  or  b'  h\  is  urged  by  a  cental 
force  directed  to  c. 

2600.  Linear,  angular,  and  areal  velocity.  —  In  the  descriptioB 
and  analysis  of  the  planetary  motions,  there  are  three  quantitiei 
which  there  is  frequent  occasion  to  express  in  reference  to  the  onit 
of  time,  and  to  which  the  common  name  of  '^  velocity"  is  oonie- 
quently  applied. 

1^.  The  linear  velocity  of  a  planet  is  the  actual  space  over  wUeh 
it  moves  in  its  orbit  in  the  unit  of  time.  We  shall  invariably  ex- 
press this  velocity  by  v. 

2^.  The  angular  velocity  is  the  angle  (bos'  mfig.  743)  whidi 
the  radius  vector  from  the  sun  to  the  planet  moves  over  in  the  onit 
of  time.     We  shall  invariably  express  this  by  the  Qreek  letter  ». 

3®.  The  areal  velocity  is  the  area  (bob'  mfig,  743)  which  the 
radius  vector  from  the  sun  to  the  planet  sweeps  over  in  the  unit  of 
time.     We  shall  express  this  by  a. 

2601.  Relation  heticeen  angular  and  areal  velocities, -^  It  jf^} 
fig.  743,  be  supposed  to  be  perpendicular  to  b'  o,  the  area  of  the 
triangle  b'  c  b''  will  be  ^  b'  o  x  b"  d.    But  since  in  this  case  iPi 


THE  BOLAR  ST8TSM .  269 

maj  be  eonudered  ai  the  arc  of  a  drcle,  of  which  o  ia  the  centre 
and  B^  o  the  nuiiua,  we  ahall  have  (2292), 


206265' 


where  the  diatance  j/*  0  of  the  planet  from  the  sun,  or  the  radius 
feetor^  u  expressed  hj  r.     Hence  we  havo 

the  areal  velocity  is  always  proportional  to  the  product  of  the 
galar  Telocity  and  the  square  of  the  radius  vector  or  distance. 
To  aaoertain,  therefore,  whether  any  point  within  the  orbit  of  a 
(Janet  be  the  '^  centre  of  equal  areas/'  and  therefore  the  centre  of 
attraction,  it  is  only  necessary  to  compare  the  angular  velocity 
found  aach  point  with  the  square  of  the  distance ',  and  if  their  pro- 
dttct  be  always  the  same,  or,  in  other  words,  if  the  angular  velocity 
inerease  in  the  same  ratio  as  the  square  of  the  distance  or  radius 
Tsctor  decreases,  and  vxct  versd,  then  the  point  in  question  must  be 
Ibe  oentre  of  equal  areas,  and  therefore  the  centre  of  attraction. 

2602.  Cote  of  the  motion  of  the  earth.  —  In  the  case  of  the 
earth,  the  variation  of  its  distance  from  the  sun  is  inversely  as  the 
Tariation  of  the  sun's  apparent  diameter,  which  may  be  accurately 
obaerved,  as  may  also  be  the  sun's  apparent  motion  in  the  firma^ 
■ent  Now,  it  is  found  that  the  apparent  motion  of  the  sun  in- 
ereasea  exactly  in  the  same  ratio  as  the  square  of  its  apparent 
diameter,  and  therefore  inversely  as  the  square  of  its  distance; 
from  which  it  follows  that  its  centre  is  the  centre  of  equal  areas  for 
tbe  earth's  motion,  and  therefore  the  centre  of  attraction. 

2603.  Case  of  the  planets.  —  In  the  same  manner,  by  calculating 
from  observation  the  angular  motions  of  the  planets,  and  their  dis- 
tances from  the  sun,  it  may  be  shown  that  their  angular  motions 
are  inversely  as  the  squares  of  their  distances,  and  consequently 
that  the  oentre  of  the  sun  is  the  centre  of  the  attraction  which 
moves  them. 

2604.  Orbits  of  the  planets  ellipses.  —  By  comparing  the  varia- 
tion of  the  distance  of  any  planet  from  the  sun  with  the  change  of 
direction  of  its  radius  vector,  it  may  be  ascertained  that  its  orbit  is 
an  ellipse ;  the  centre  of  the  sun  being  at  one  of  the  foci,  in  the 
same  manner  as  has  been  already  explained  in  the  case  of  the 
earth. 

2605.  Perihelion^  aphelion^  mean  distance. — That  point  of  the 
elliptic  orbit  at  which  a  planet  is  nearest  to  the  sun  is  called  peri- 
HKLiON|  and  that  point  at  which  it  is  most  remote  is  called  aphx- 

UOM. 

23* 


i 


270 


ASTRONOMT. 


Fig.  744. 


The  MSAN  DISTANCE  of  a  pknct  from  tlie  ran  is  half  the  anm 

of  its  greatest  and  least  distanoes. 

2606.  Major  and  minor  ax€s,  and  ecceniricttjf  of  the  orWt  — 
The  Jig.  744  represents  an  ellipse,  of  whioh  r  la  the  focoa  and  o  the 
eentre.    The  line  or  continaed  to  p  and  A  is  the  major  axis, 

sometimes  called  the  tfanarerae  azit. 
Of  all  the  diameters  which  can  be 
drawn  through  the  centre  o,  ter- 
minadng  in  the  curve,  it  ia  the 
longest,  while  mom', drawn  at rij^t 
angles  to  it,  called  the  minor  axis, 
'  is  the  shortest  The  line  v  yf, 
whioh  is  eqnal  to  p  o,  half  the  major 
axis,  and  Uierefore  to  half  the  ram 
of  the  greatest  and  least  distances  of  the  ellipse  from  its  fixms,  is 
the  MJBAN  distance. 

A  planet  is,  therefore,  at  its  mean  distance  from  the  sun  when  it 
is  at  the  extremities  of  the  minor  axis  of  its  orbit. 

There  is  another  point  r^  on  the  major  axis,  at  a  diatanoe  /o 
from  the  centre,  equal  to  F  c,  which  has  also  the  geometrio  pfop»- 
ties  of  the  focus.  It  is  sometimes  distinguished  as  the  xmptt 
rocus  of  the  planet's  orbit. 

Ellipses  may  be  more  or  less  eccentric,  that  is  to  say,  more  or 
less  oval.  The  less  eccentric  they  are,  the  less  they  differ  in  form 
from  a  circle.  The  degree  in  which  they  have  the  oval  form  de- 
pends on  the  ratio  which  the  distance  FC  of  the  focus  from  the 
centre  bears  to  p  c,  the  semi-axis  major.  Two  ellipses  of  difiereot 
magnitudes  in  which  this  ratio  is  the  same,  have  a  like  form,  and 
are  equally  eccentric.  The  less  the  ratio  of  c  F  to  c  p  is,  the  more 
nearly  docs  the  ellipse  resemble  a  circle.  This  ratio  is,  therefore, 
called  the  eccentricity. 

The  eccentricity  of  a  planet's  orbit  will,  therefore,  be  that  num- 
ber which  expresses  the  distance  of  the  sun  from  the  centre  of  the 
ellipse,  the  semi-axis  major  of  the  orbit  being  taken  as  the  unit. 

2607.  ApsideSy  anomali/.  —  The  points  of  perihelion  and 
APIIELION,  are  called  by  the  common  name  of  apsides. 

If  an  eye  placed  at  the  sun  F  look  in  the  direction  of  P,  that 
point  will  be  projected  upon  a  certain  point  on  the  firmament.  This 
is  called  the  place  op  perihelion. 

The  angle  formed  by  a  line  drawn  from  the  sun  to  the  place  p  of 
a  planet,  and  the  major  axis  of  its  orbit,  or,  what  is  the  same,  the 
angular  distance  of  the  planet  from  its  perihelion,  as  seen  from  the 
eun,  IS  called  its  anomaly. 

If  an  imaginary  planet  be  supposed  to  movo  from  perihelion  to 
aphelion  with  any  uniform  angular  motion  round  the  sun  in  the 
same  time  that  the  real  planet  moves  between  the  same  point*  with 


THB  SOLAB  SYSTEM.  271 

a  Tftriable  angaUr  motion^  iho  anomaly  of  this  imaginary  planet  is 
oallcd  the  mean  anomaly  of  the  planet. 

2608.  Place  of  perihelion,  —  The  place  op  perihelion  is  ex- 
pressed hy  indicating  the  particolar  fixed  star  at  or  near  which  the 
planet  at  P  is  seen  from  F,  or,  what  is  the  same,  the  distance  of 
that  point  from  some  fixed  and  known  point  in  the  heavens.  The 
point  selected  for  this  purpose  is  the  vernal  equinoxial  point,  or  the 
jirti  point  of  Aries  (2435).  The  distance  of  perihelion  from  this 
point,  as  seen  from  the  sun,  is  called  the  longitude  of  perihe- 
lion, and  is  an  important  condition  affecting  the  position  of  the 
planet's  orhit  in  spaoe. 

2609.  Eccentricities  of  orbits  small, — The  planets'  orbits,  like 
that  of  the  earth,  though  elliptical,  are  very  slightly  so.  The  ec- 
centricities are  so  minute,  that  if  the  form  of  the  orbit  were  de- 
lineated on  paper,  it  could  not  be  distinguished  from  a  circle  except 
by  very  exactly  measuring  its  breadth  in  different  directions. 

2610.  Law  of  attraction  deduced  from  elliptic  orhit.  —  As  the 
equable  description  of  areas  round  the  centre  of  the  sun  proves  that 
point  to  be  the  centre  of  attraction,  the  elliptic  form  of  the  orbit 
and  the  position  of  the  sun  in  the  focus  indicate  the  law  according 
to  which  this  attraction  varies  as  the  distance  of  the  planet  from  the 
sun  varies.  Newf^n  has  demonstrated,  in  his  Puincipia,  that  such 
a  motion  necessarily  involves  the  condition  that  the  intensity  of  the 
attractive  force,  at  different  points  of  the  orbit,  varies  inversely  as 
the  square  of  the  distance,  increasing  as  the  square  of  the  distance 
decreases,  and  vice  versa. 

2611.  T/ie  orhit  mif/ht  he  a  parahola  or  ht/perholai — Newton 
also  proved  that  the  converse  is  not  necessarily  true,  and  that  a 
body  may  move  in  an  orbit  which  is  not  elliptical  round  a  centre  of 
fircc  which  varies  according  to  this  law.  But  he  showed  that  the 
orbit,  if  not  an  ellipse,  must  be  one  or  other  of  two  curves,  a  para- 
coiJL  or  HYPERBOLA,  baviog  a  close  geometric  relation  to  the  el- 
lipse, and  that  in  all  cases  the  centre  of  force  would  be  the  focus  of 
tlie  curve. 

These  three  sorts  of  curves,  the  ellipse,  the  parabola,  and  hyper- 
Lola,  are  those  which  would  be  produced  by  cutting  a  cone  in  differ- 
c'ut  directions  by  a  plane,  and  they  are  hence  called  the   conic 

.MICTIONS. 

201 2.  Conditions  which  determine  the  species  of  the  orhit. —  The 
(Venditions  under  which  the  orbit  of  a  planet  might  bo  a  parabola  or 
hyperbola,  depend  on  the  relation  which  the  velocity  of  the  motion 
of  the  planet,  at. any  given  point  of  the  orbit,  bears  to  the  intensity 
of  the  attractive  force  at  that  point.  It  is  jlcmonstrable  that,  if 
the  Telocity  with  which  a  planet  moves  at  any  given  point  of  its 
orbit  were  suddenly  augmented  in  a  certain  proportion,  its  orbit 


272 


ABTBOVOMT. 


wimld  become  m  parabola,  aod  if  it  were  alill 
would  become  an  hyperbola. 

The  ellipee  is  a  cunre  vhichy  like  the  eurete,  rofiirM  mto  AaKa 
that  a  body  movlDg  in  it  moat  neceenrilj  retraee  the  aame  ftikk 
an  CDdlesa  Buoceasion  of  revolutioDa.  Thia  ia  not  the  charwIiK  rf 
the  parabola  or  hyperbola.  They  are  not  doaed  ourfea^  bul  naM 
of  two  branches  which  oontinae  to  diTove  from  eadi  odwr  wilM 
OTor  meeting.  A  planet^  thereforoi  whidi  would  thoa  movBi  ladl 
pasa  near  the  sun  oncC;  followbg  a  curved  path,  bat  weald  An 
depart  never  to  return. 

2618.  Law  of  gravitation  general  —  The  elliptio  fimn  cf  Ai 
orbit  of  a  planet  indicates  the  law  which  govema  the  varialioB  rf 
the  sun's  attraction  from  point  to  point  of  such  orbit ;  but  (mjobI 
this  orbit  it  proves  nothing.  It  remainSi  thereforoi  to  abow  fiw 
the  planetary  motions  round  the  sun,  and  firom  the  motiona  cf  Al 
satellites  round  their  primaries,  that  the  same  law  of  attnetioi  If 
which  the  intensity  decreases  as  the  square  of  the  dutanee  fiea  wk 
oentre  of  attraction  increases,  and  vice  versdf  is  imiTeraal. 

The  attraction  exerted  upon  any  body  may  be  measured,  in  gene- 
ral, as  that  of  the  earth  on  bodies  near  its  sur&oe  is  measurra,  hj 
the  spaces  through  which  the  attracted  body  would  be  drawn  in  t 
given  time.  It  has  been  shown,  that  the  attraction  which  the  etrtk 
exerts  at  its  surface,  is  such  as  to  draw  a  body  towards  it  throngk 
193  inches  in  a  second.  Now  if  the  space  through  which  the  saa 
would,  by  its  attraction  at  any  proposed  distance,  draw  a  body  ia 
one  second  could  be  found,  the  attraction  of  the  sun  at  that  dislaDM 
could  be  exactly  compared  with  and  measured  by  the  attractioii  of 
the  earth,  just  as  the  length  of  any  line  or  distance  is  ascertainei 
by  applying  to  it  and  comparing  it  with  a  standard-yard  measare. 
2614.  Method  of  calailating  the  central  force  by  the  tdodbf 

and  curvature,  —  Now  the  space  through 
which  any  central  attraction  would  draw  a 
body  in  a  given  time  can  be  easily  calculated,  if 
the  body  in  question  moves  in  a  circular  or 
nearly  circular  orbit  round  such  a  centre,  u 
all  the  planets  and  satellites  do. 

Let  £,  fig.  745,  be  the  centre  of  attraction, 
and  E  m  the  distance  or  radius  vector.  Let 
mw!  zzzYj  the  linear  velocity.  Let  m  n  aod 
m'  vl  be  drawn  at  right  angles  to  B  m,  and  ther^ 
fore  parallel  to  each  other.  The  velocity  m  W 
may  be  considered  as  compounded  of  two  (17S), 
one  in  the  direction  m  n!  of  the  tangent,  and 
the  other  m  n  directed  towards  the  centre  d 
attraction  E.  Now  if  the  body  were  deprived  of 
Pig*  U5.  its  tangential  motion  m  n',  it  would  be  attncted 


El 


TBM  SOLAR  BTBTSX.  278 

lovaidi  tha  eentre  m,  through  the  space  m  »,  in  the  unit  of  time. 
By  means  of  this  qpaoe,  therefore,  the  force  which  the  central  at- 
tnetkn  exerts  at  m  can  be  brought  into  direct  comparison  with  the 
foioe  which  terrestrial  grayily  exerts  at  the  surfiice  of  the  earth. 

It  foUowSy  therefore,  that  if  /  express  the  space  throngh  which 
soeh  a  body  wonld  be  drawn  in  the  nnit  of  time,  falling  freely  to- 
wards the  centre  of  attraction,  we  shall  haye/  =  mn.  %ut  by  ^e 
efanentaiy  principles  of  geometry, 

mil  X  2Efit=r  mm^. 
Therefiovey 

that  is,  the  space  throngh  which  a  body  would  be  drawn  towards  the 
eentre  of  attaction,  if  depriyed  of  its  orbital  motion,  in  the  nnit 
if  time,  is  fbnnd  by  dividing  the  square  of  the  linear  orbital  yelocity 
hj  twice  its  distance  from  the  centre  of  attraction. 


Snee  y  =  oo^aH?  (2601),  we  shall  also  haye 


2x206265' 


The  attractiye  force,  or,  what  is  the  same,  the  space  ihroneh 

wUeh  the  revohing  body  would  be  drawn  towards  the  centre  in  the 

mil  of  time,  can,  therefore,  be  always  computed  by  these  formulsD, 

when  its  distance  from  the  centre  of  attraction  and  its  linear  or  an- 

gokr  yelocity  are  known. 

•  Once  (2668) 

1296000 

•  = 

p 

ttisy  being  snbstitnted  for  »  in  the  preceding  formnla,  will  giye 

/=  412541X^5 

by  which  the  attractiye  force  may  always  be  calculated  when  the 
distanee  and  period  of  the  reyolyiug  body  are  known. 

2615.  Law  of  aravitation  ihawn  in  the  ccue  of  the  moon,  —  The 
sttraetion  exerted  by  the  earth,  at  its  sur&ce,  may  be  compared  with 
the  attraction  it  exerts  on  the  moon,  by  these  formula). 

In  the  case  of  the  moon,  v  =  0.6356  miles,  and  r  =  239,000 
ttilca;  and  by  calculation  from  these  data,  we  find 

/  =  00000008459  -"-•  =  00536  "^ 

Ike  nttnolion  exerted  by  the  earth  at  the  moon's  distance  wonldt 


ASTHOKOMY. 

re,  canse  a  body  to  fall  ihrongh  536  tcD-thonnndtlig  of  m 

mcu,  while  at  the  earth's  surfuce  it  waulil  fall  through  193  iochn 
(247). 

The  intensity  of  [he  earl.h's  attrnotion  on  the  moon  is,  thprefare, 
less  than  its  attraction  on  a  body  at  the  Biirfaee,  in  the  ratio  of 
1,930,000  to  536,  or  3600  to  1,  or,  what  is  the  same,  as  the  sqtura 
of  60  to  1. 

But  it  has  been  ebown  that  the  mooD'a  diBtanco  from  the  earth't 
centre  is  60  times  the  earth's  rudioB.  It  appears,  therefore,  that  ia 
this  case  the  attraction  of  the  earth  decrcasca  as  the  square  of  Ihs 
distance  from  the  attract! og  centre  increase?  ;  and  that,  cinsequeDtlj, 
the  same  law  of  gravilatioD  ptCTails  as  in  the  elliptic  orbit  of  ■ 
jJunet. 

2616.  iSiin's  artra<-tioJt  on  planttM  Kxmparcd — laic  of  ffravilO' 
tion  /ulJiJkJ.  —  In  (he  Hame  manner,  esnctly,  the  atlractions  which 
the  sun  cscrls  at  different  distances  may  he  computed  by  the  mo- 
tions and  distances  of  the  planets.  The  distance  of  a  planet  gives 
the  circumference  of  its  orbit,  and  this,  compared  with  its  periodic 
time,  will  give  the  arc  through  which  it  moves  in  a  day,  an  boar,  at 
&  minate.  This,  represented  by  m  m',  Jiff.  745,  being  known,  tb« 
space  m  n  through  which  the  planet  would  fall  towards  the  sun  in 
^c  some  time  may  be  calculated ;  and  this  being  done  for  any  two 
planets,  it  will  bo  found  that  these  spaces  arc  in  the  inverse  ratio 
of  the  squares  of  their  distances. 

Thus,  for  example,  lot  the  earth  and  Jupitor  be  compared  in  thii 
manner.  IS  D  express  the  distance  from  the  sun  in  miles,  p  the 
period  in  days,  A  the  arc  of  the  orbit  in  miles  described  by  the 
planet  in  an  hour,  and  u  the  space  m  n  in  miles,  through  which  the 
planet  would  full  towanis  the  sun  in  an  hour  if  the  tangential  forcq 
were  destroyed,  we  shall  then  hwfe 


•> 

A 

B 

E«lh 

»:= 

aai-m 

Siwo 

si'4oa) 

Now,  on  comparing  the  numhere  in  the  Inst  column  with  tb 
squares  of  those  in  the  first  column,  we  find  them  in  almost  exaet 
accordance.     Thus, 

(95)"  :  (494)'  : :  24-402  :  0  8024. 
The  difference,  small  as  it  is,  would  disappear,  if  exact  valoea  « 
taken  instead  of  round  numbera. 

2617.    Th€  law  of  gravitation  HniVwso?.  —  Thus  is  ertaUii 

the  great  natural  law,  known  as  the  law  of  gravitation,  at  least 

>  the  action  of  tbe  sun  upon  the  planets,  and  the  planela 


THE  SOLAE  STSTEM.  275 

their  satelliCes,  is  ooncerned.  Bat  this  law  docs  not  alone  affect  the 
ceDtral  attracting  bodies.  It  belongs  equally  to  the  revolving  bodies 
themselves.  Each  planet  attracts  the  sun,  and  each  satellite  attracts 
its  priaiaiy  as  well  as  being  attracted  bj  it ;  and  this  reciprocal  at- 
traction depends  on  the  mass  of  the  revolving  as  well  as  on  the  mass 
of  the  central  body  and  their  mutual  distance. 

The  planets,  moreover,  as  well  as  the  satellites,  attract  each  other, 
and  thus  modify,  to  some  small  extent,  the  effects  of  the  predorai- 
nant  central  attraction. 

2618.  lu  analogy  to  the  general  Jaw  of  radxatwg  influences.  — 
It  will  be  observed  that  this  law  is  similar  to  that  which  governs 
light,  heat,  sound,  and  other  physical  principles  which  are  propa- 
gated by  radiation ;  and  it  might  (bus  be  inferred  that  gravitation 
is  an  agency  of  which  the  scat  is  the  sun,  or  other  gravitating  body, 
and  that  it  emanates  from  it  as  other  physical  principles  obeying  the 
Mme  law  are  supposed  to  do. 

2619.  Not  J  however y  to  he  identified  with  them,  —  No  such  hy- 
pothesis as  this,  however,  is  either  assumed  or  required  in  astro- 
nomy. The  law  of  gravitation  is  taken  as  a  general  fact  established 
by  observation),  without  reference  to  any  modus  operandi  of  the 
force.  The  planets  may  be  drawn  towards  the  sun  by  an  agency 
vhose  scat  b  established  in  the  sun,  or  they  may  bo  driven  towardh 
it  by  an  agency  whose  seat  is  outside  and  around  the  system,  or  they 
may  be  pressed  towards  it  by  an  agency  which  appertains  to  the 
ipace  in  which  they  move.  Nothing  is  assumed  in  astronomy  which 
vould  be  incompatible  with  any  one  of  these  modes  of  action.  The 
law  of  gravitation  assumes  nothing  more  than  that  the  planets  are 
nbject  to  the  agency  of  a  force  which  is  every  where  directed  to 
the  sun,  and  whose  intensity  increases  as  the  square  of  the  distance 
from  the  sun  decreases,  and  vice  versd  ;  and  this,  as  has  been  shown, 
ii  proved  as  a  matter  of  fact  independent  of  all  theory  or  hypo- 
liiesis. 

2620.  The  harmonic  law.  —  A  remarkable  numerical  relation 
thus  denominated  prevails  between  the  periodic  times  of  the  planets 
lod  their  mean  distances,  or  major  axes  of  their  orbits.  If  the 
iqaarea  of  the  numbers  expressing  their  periods  be  compared  with 
tile  cubes  of  those  which  express  their  mean  distances,  they  will  be 
fnand  to  be  very  nearly  in  the  same  ratio.  They  would  be  exactly 
^  if  the  masses  or  weights  of  the  planets  were  absolutely  insigni- 
ficant compared  with  that  of  the  sun.  But  although  these  nmssos, 
u  will  appear,  are  comparatively  very  small,  they  are  sufficiently 

Iecia&idcrablu  to  affect,  in  a  slight  degree,  this  remarkable  and  im- 
portant law. 
Omitting  for  the  present,  then,  this  cause  of  deviation,  the  har- 
Booir  law  may  be  thus  expressed.     If  P^  p', p',  &o.y  be  a  series  of 


A8THON0MT. 


here  which  express  or  aro  proportional  to  the  periodic  thocs,  anl 

,  r"',  &c.,  to  the  mean  distances  of  the  planets,  wo  Ehali  have  | 


that  is,  the  qunticuts  found  by  dividing  the  numhers  eipiessiDg  tli 
cubes  of  the  distances  h;  the  DUmbcrs  which  express  the  s(uani 
of  the  periods  are  equal,  subject  nevertheleas  to  such  deviatiori 
from  the  lav  as  may  be  due  to  the  cause  above  mentionnd-  ' 

2621.  Fulfilled  III/  iheplanels,  —  Mttliod  of  eomyvHng  the  Ji^ 
lavce  of  a  planet  from  tlie  nm  tchen  ilt  periodic  lime  im  knotm.- 
To  show  the  new  approach  to  numerical  accuracy  wilh  which  H 
remarkable  law  is  fulfilled  by  the  morons  of  the  planets  compoaini 
the  solar  eyslem,  we  have  exbibiled  id  the  followiog  bible  the  re! 
tive  approiimate  numerical  values  of  iheir  eeveral  distances  a 
periods,  and  have  shown  that  the  quotients  found  t^  dividing  li 
cubes  of  the  distances  by  the  squares  of  the  periods  a  '" 


Period.       Cnbt  or  DbUDca.     e^-orPslad. 


In  general,  the  distance  of  a  phnct  from  the  snn  can  be 
puted  by  means  of  this  bw,  when  the  distance  of  the  earth  ai 
periodic  times  of  the  earth  and  planet  are  known. 

For  this  purpose  find  the  number  which  expresses  the  f 
time  p  of  the  planet,  that  of  the  earth  being  expressed  by 
let  D  be  the  number  vhich  expresses  the  mean  dbtance  of  tiu 
from  the  snn,  that  of  the  earth  being  also  expressed  by  ' 
shall  then,  according  to  the  harmonic  law,  have 


1»  :  p*  : 


But  since 


To  find  the  distance  l>,  therefore,  it  is  only  Deceasaiy  i 


THB  SOLAR  STSTEM.  277 

■nber  whose  enbe  is  the  square  of  the  number  expressing  the 
fniod,  or,  what  is  the  same,  to  extract  the  cube  root  of  the  square 
«f  the  period. 

2622.  Harmonic  law  deduced  from  the  law  of  gravitation.  — 
II  it  not  difficult  to  show  that  this  remarkable  law  is  a  necessary 
^BBnquenoe  of  the  law  of  gravitation. 

^  Soppoeiog  the  orbits  of  3ie  planets  to  be  circular,  which  for  this 
^vpose  they  may  be  taken  to  be,  let  the  distance,  period;  and  an- 
.pbr  Telocity  of  any  one  planet  be  expressed  by  r,  p,  and  a,  and 
Aon  oi  any  other  by  /,  p^,  and  »',  and  let  the  forces  with  which 
Aenm  attracts  them  respectively  be  expressed  by /and/'.  We 
Adl  then,  according  to  what  has  been  proved  (2614),  have 


X»"  ^  /  X  » 


/a 


2  X  206265  -^    ""  2  X  206265' 

Md  therefoie 

f  if  i\r  X  a^if'  X  fj!^. 
Bat  by  the  law  of  gravitation 

/:/'::>^:r«, 
fterefore 

r"  :  r* : :  r  X  »■ :  /  X  o'*, 
iiid  ccmsequently 

r^  X  o'*  =  r»  X  o«. 

fiat  the  angles  described  in  the  unit  of  time  arc  found  by  dividing 
160^  by  the  periodic  times.     Therefore, 


360^  ,       360^ 

O    =  r- 


aiid  consequently 


p2  — p«l' 


which  is,  in  fact,  the  harmonic  law. 

It  is  easy,  by  pursuing  this  reasoning  in  an  inverse  order,  to  show 
tkit  if  the  harmonic  law  be  taken,  as  it  may  be,  as  an  observed  fact, 
the  law  of  gravitation  may  be  deduced  from  it. 

2623.  Keriler'i  laws, — The  three  great  planetary  laws  explained 
in  the  preceding  paragraphs — 1.  The  equable  description  of  areas; 
2.  The  elliptic  form  of  the  orbits;  and  3,  the  harmonic  law  — 
were  discovered  by  Kepler,  whose  name  they  bear.  Kepler  deduced 
them  as  matter-of-fact  from  the  recorded  observations  of  himself 
tnd  other  astronomers,  but  failed  to  show  the  principle  by  which 
they  were  connected  with  each  other.  Newton  gave  their  interpre- 
tation, and  showed  their  connexion  as  already  explained. 

III.  24 


278  ASTEOHOICT. 

2624.  IndituOion  of  Ae  orhiti — tiacfet. — In  wkai  kai  beta 
stated j  the  planets  are  regarded  as  moTing  in  tlie  idaiie  of  the  auth'a 
orbit  If  this  were  strictly  true,  no  planet  woiud  e?er  be  eeeB  oo 
the  heavens  out  of  the  eoliptio.  The  infisrior  planetii  when  m  ni- 
ferior  conjonotion,  woold  altoa^  ^PP^i'  ^  *P<^  <n  ^  MBf  Hid 
when  in  superior  oonjunotioni  thej^  as  w^as  the  wperior 

BtUieoaa 


would  always  be  behind  the  sun's  disk.  This  is  not  ue  oaaa.  Ibe 
planets  generally,  superior  and  inferioTi  are  seldom  seen  aetnaBj 
upon  the  ecliptic^  although  they  are  never  fiur  remonrod  tnm.  it 
Tne  centre  of  the  planet,  twice  in  each  revolutiony  is  observed  upon 
the  ecliptic.  The  points  at  which  it  is  thus  found  upon  the  plane 
of  the  earth's  orbit  are  at  opposite  sides  of  the  sun,  180^  asunder, 
as  seen  from  that  luminary.  At  one  of  them  the  pluiet  pasMs  frna 
the  south  to  the  north  of  the  ecliptic,  and  at  the  other  from  tbe 
north  to  the  south. 

2625.  ITodes,  ascending  and  descending. — Those  potntSi  wh«8 
the  centre  of  a  planet  crosses  the  ecliptic,  are  called  its  MODXs;  that 
at  which  it  passes  from  south  to  north  being  called  the  Ascxvnne 
MODE,  and  the  other  the  descendinq  node. 

While  the  planet  passes  from  the  ascending  to  the  desoendiag 
node,  it  is  north  of  the  ecliptic ;  and  while  it  passes  from  the  d^ 
scendiDe  to  the  ascending  node,  it  is  south  of  it. 

All  these  phenomeDa  indicate  that  the  planet  does  not  move  in 
the  plane  of  the  ecliptic,  but  in  a  plane  inclined  to  it  at  a  certain 
angle.  This  angle  cannot  be  great,  since  the  planet  is  never  ob- 
served to  depart  far  from  the  ecliptic.  With  a  few  exceptioosi 
which  will  be  noticed  hereafter,  the  obliquity  of  the  planets'  orbits 
do  not  amount  to  more  than  7^. 

2626.  The  zodiac. — The  planets,  therefore,  not  departing  vom 
than  about  8^  from  the  ecliptic,  north  or  south,  their  motions  m 
limited  to  a  zone  of  the  heavens  bounded  by  two  parallels  to  tbo 
ecliptic  at  this  distance,  north  and  south  of  it. 

2627.  Method  of  determining  a  planefs  distance  from  the  nm. 
—  This  problem  may  be  solved  with  more  or  less  approximation  by 
a  great  variety  of  different  methods.  In  all  it  is  assumed  that  the 
earth's  distaoce  from  the  sun  is  previously  ascertained,  the  iome- 
diate  result  beiog  in  every  case  the  determination  of  the  ratio  which 
the  planet's  distance  from  the  sun  bears  to  the  earth's  distance. 

2628.  1®.  By  the  elongation  and  synodic  mo/wm.  —  This  methoi 
has  been  already  explained  (2592). 

2629.  2°.  By  the  greatest  elongation  for  an  inferior  pianeL'^ 
When  an  inferior  planet  is  at  its  greatest  elongation,  the  angle  ?» 
included  by  lines  drawn  from  it  to  the  sun  and  earth,  will  he  90^ 
(2576),  and  conseouently  the  two  angles  at  e  and  s  taken  together 
will  be  90^.     If  the  elongation  E  be  observed,  the  angle  al  s  will 


i 


^ 
b 


i- 


THB  SOLAR  ST8TEM.  279 

be  90^— -Sy  and  iriU  therefore  be  known,  and  thus  the  distances 
8P  and  xp  may  be  eompnted  as  in  the  first  method. 

2630.  8®.  Bff  the  greatest  and  least  apparent  magnitudes.  —  If 
m  and  nt'  be  the  apparent  magnitades  of  an  inferior  planet  when  at 
inferior  and  superior  conjunction,  and  e  and  p  be  the  distances  of 
the  earth  and  planet  from  the  son,  e — p  will  be  the  distance  of  the 
planet  from  the  earth  at  inferior,  and  e  -f  p  at  superior  conjunction 
(2577) ;  and  ainee  the  apparent  magnitudes  are  in  the  inverse  ratio 
of  thc»  diatanoee  (1118)|  we  shall  have 

m  ^  e+p 

m'  ""  e — p' 

tad  oonaequentlj 

m — ni 

^       m  +  m 

If  m  +  m'  be  the  apparent  magnitudes  of  a  superior  planet  in  op- 
position and  conjunction,  its  distances  at  these  points  will  be  p  —  e 
andp  +  e,  and  we  shall  have  as  before 

m  ^p  +  e 
ind  therefore 


mf      p — e' 


m  +  m' 
p  = .    X  e. 

2631.  4<*.  By  the  harmonic  law,  —  This  law  (2614)  being  de- 
duced from  the  law  of  gravitation  (2616),  independently  of  the 
observation  and  comparison  of  times  and  distances,  it  may  be  used 
fer  the  determination  of  the  distances,  the  times  being  known.  Let 
I  and  P  be  the  periodic  time  of  the  earth  and  planet,  and  e  and  p 
their  distances  from  the  sun.  We  shall  then,  by  the  harmonic  law, 
have 

p«       p» 


and  thexefore 


i^=Sx«^» 


and  thus  the  distance  p  may  be  found. 

2632.  To  determine  the  real  diameters  and  volumes  of  the  bodies 
of  the  system.  — The  apparent  diameter  at  a  known  distance  being 
observed,  the  real  diameter  may  be  computed  by  the  principle  ex- 
plained in  2299.  The  linear  value  of  1''  at  the  distance  being 
known,  the  real  diameter  will  be  obtained  by  multiplying  such  value 
by  ike  apparent  diametei^  expressed  in  seconds. 


880  ASTBOHOMT. 

The  disks  of  the  inferior  pLaneti  not  beiog  iririUa  wk  ialiKior 
jaDction  when  tbeir  dark  hemispheres  are  presented  to  the  enthy 
and  being  lost  in  the  effulgence  of  the  son  at  sopezior  eODJiowlioDi 
oan  only  be  observed  between  their  greatest  elongatioo  and  aupmor 
oonjunctionj  when  they  appear  ffibbons.  ^  The  distanee  of  the  plant 
from  the  earth  is  computed  in  wis  position  by  knowing  the  diateiMas 
of  the  phuet  and  the  earth  from'the  son,  and  the  an^  vador  dN 
lines  drawn  from  the  son  to  the  earth  and  phnet^  whwh  oan  alvaji 
be  computed  ^2587).  This  distanee  being  obtained,  tho  linear  vdni 
of  1"  at  the  planet  will  be  found  (2298),  which,  bdng  mvdt^lied 
by  the  p;reatest  breadth  of  its  ^bbbus  &k,  the  real  £ameter  will 
be  obtained. 

In  the  case  of  the  superior  plsnetSi  their  diameters  may  be  bat 
obtained  when  in  opposition,  because  then  they  appear  with  a  foO 
disk,  and,  being  nearer  to  the  earth  than  at  any  other  elongato, 
have  the  greatest  possible  magnitude.  Their  distance  from  the  eartb 
in  this  position  is  always  the  difference  between  the  distances  of  the 
earth  and  planet  from  the  sun. 

When  the  real  diameters  are  found  the  volumes  will  be  obtained, 
rince  they  are  as  the  cubes  of  the  real  diameters. 

2683.  Methods  of  determining  the  masses  of  the  bodies  of  the 
solar  system.  —  The  work  of  the  astronomer  is  but  imperfectly  pe^ 
formed  when  he  has  only  mentioned  the  distances  and  magnitades, 
and  ascertained  the  motions  and  velocities,  of  the  great  bodies  of 
the  universe.  He  must  not  only  measure,  but  weigh  these  sta- 
pendens  masses. 

The  masses  or  quantities  of  matter  in  bodies  upon  the  surface  of 
the  earth  are  estimated  and  compared  by  their  weights — that  is,  by 
the  intensity  of  the  attraction  which  the  earth  exerts  upon  them. 
It  is  inferred  that  equal  quantities  of  matter  at  equal  dbtanoes  from 
the  centre  of  the  earth  are  attracted  by  equal  forces,  inasmuch  as 
all  masses,  great  and  small,  fall  with  the  same  velocity  (234). 

The  intensity  of  the  attraction  with  which  the  earth  thus  acti 
upon  a  body  at  auy  given  distance  from  its  centre  depends  on  tbs 
mass  or  quantity  of  matter  composing  the  earth.     If  the  mass  of 
the  earth  were  suddenly  increased  in  any  proposed  ratio,  the  weights 
of  all  bodies  on  its  surface,  or  at  any  given  distance  from  its  centre, 
would  be  increased  in  the  same  ratio,  and,  in  like  manner,  if  its 
mass  were  diminished,  the  weights  would  be  decreased  in  the  same 
ratio.     In  fine,  the  weights  of  bodies  at  any  given  distance  from  the 
earth's  centre  would  vary  with,  and  be  exactly  proportional  to^  eveiy 
variation  in  the  mass  of  the  earth. 

This  principle  is  general.  If  M  aud  m'  be  any  two  masses  of 
matter,  the  attractions  which  they  will  exert  upon  any  bodieS| 
placed  at  equal  distances  from  their  centres  of  gravity^  will  be  in 


THB  BOLAR  STSTBH.  281 

Ae  eanel  proportion  of  the  quantities  of  ponderable  matter  com- 
ponng  them. 

Bat  it  will  be  convenient  to  obtain  the  relation  between  the 
manes  and  the  attractions  they  exert  at  unequal  distances.  For 
this  purpose,  let  the  attractions  which  they  exert  at  equal  distances 
be  expressed  by/and/',  and  let  the  common  distance  at  which 
liioee  attractions  are  exerted  be  expressed  by  x,  and  let  v  and  f' 
cxptcao  the  attractions  which  they  respectively  exert  at  any  other 
manoesy  r  and  /,  and  we  shall  have^  according  to  the  general  law 
of  ^vitatioD, 


ad  eolueqaenily 


/  1  /  1 


from  which  it  follows  that 

/  ~  r'    X     r«' 

But  since  the  masses  M  and  m'  are  proportional  to  the  attractions 
ftLdff  we  have 

tod  therefore 

M         F     X     r* 


a^ 


M'       r'    X     / 

that  isy  the  attracting  masses  are  proportional  to  the  products  ob- 
tiioedy  by  multiplying  any  two  forces  exerted  by  them  by  the 
Kiuares  of  the  distances  at  which  such  forces  are  exerted. 

Hence  in  all  cases  in  which  the  attractive  forces  exerted  by  any 
eentiml  masses  at  given  distances  can  bo  measured  by  any  known  or 
observable  motions,  or  other  mechanical  effects,  the  proportion  of 
the  attracting  masses  can  be  determined. 

2634.  Method  of  estimating  central  masses  round  which  bodies 
rtt/olve,  —  If  bodies  revolve  round  central  attracting  masses  as  the 
planets  revolve  round  the  sun,  and  the  satellites  round  their  prima- 
ries, the  ratio  of  the  attracting  forces,  and  therefore  that  of  the  cen- 
tral masses,  can  be  deduced  from  the  periods  and  distances  of  the 
Kfolving  bodies  by  the  principles  and  method  explained  in  2614. 

Thus  if  P  and  P^  be  the  periods  of  two  bodies  revolving  round 

24  • 


2tt  A8TB0H01IT. 

diieraiit  aitaoting  musm  u  and  m'  ai  the  diiNmeM  r  nl  if^m 
shall  have 

and  sabfitiinting  this  for  -^  in  the  formnla  found  in  208$,  vs  km 

?L  — !!.  V  !!! 

By  this  principle  the  ratio  of  the  attracting  masses  can  alwqi  b 
ascertained  when  the  periods  of  any  bodies  reyolving  ronnd  them  aft 
known  dbtances  are  known. 

2685.  Method  of  determining  the  ratio  of  the  fnoMSt  ff  oS 
planeU  whu^  have  satellitesy  to  the  moM  of  the  ran. — ^Thia  OfoUeB 
IS  nothing  more  than  a  particular  application  of  the  prinaple  efr 
plained  above. 

To  solve  it,  it  is  only  necessary  to  ascertain  the  period  and  & 
tance  of  the  planet  and  the  satellite,  and  substitute  them  in  the 
formula  determined  in  2634.  The  arithmetical  operaliMia  lMi*g 
executed,  the  ratio  of  the  masses  will  be  determined. 

2636.  To  deterrtitne  the  rath  of  the  mass  of  the  earth  to  that  of 
the  sun. — Since  the  earth  has  a  satellite,  this  problem  will  be  scdm 
by  the  method  given  in  2635. 

If  r  and  /  express  the  distances  of  the  earth  from  the  sun  tnd 
moon,  and  P  and  p'  the  periods  of  the  sun  and  moon,  we  shall  hiTt 

!;^4oo    ^=^''''       ^ 


/  p        365-25       13-38 

r*  p"  1 

-r.  =  64000000 


r"  ~~  --— —       j;i  -  179  024' 
which  being  substituted,  and  the  operations  executed^  gives 

-,  =  357500. 

2637.  To  determine  the  masses  of  planets  whirh  have  no  saleUiit* 
—  According  to  what  has  been  explained,  the  masses  of  the  bodiei 
composing  the  solar  system  are  measured,  and  compared  one  with 
another,  by  ascertaining,  with  the  necessary  precieioD,  any  similar 
effects  of  their  attractions,  and  allowing  for  the  effects  of  the  dif- 
ference of  distances.  The  effects  which  are  thus  taken  to  measme 
the  masses  and  to  exhibit  their  ratio  to  the  mass  of  the  sun  in  the 
case  of  planets  attended  by  satellites,  is  the  space  through  which  a 
satellite  would  be  drawn  by  its  primary,  and  the  space  through 
which  a  planet  would  be  drawn  in  the  same  time  by  the  sun.  Thsee 
spaces  indicate  the  actual  forces  of  attraction  of  the  planet  upon  the 


THE  BOLAE  ST8TEM.  288 

•itellite,  and  of  the  sun  npon  the  plaoet,  and  when  the  effect  of  the 
difference  of  distance  is  allowed  for,  the  ratio  of  the  mass  of  tho 
pUnct  to  the  mass  of  the  san  is  found. 

In  the  case  of  planets  not  attended  by  satellites,  the  effect  of 
their  gravitation  is  not  manifested  in  this  way,  and  there  is  no  body 
mailer  than  themselves,  and  sufficiently  near  them  to  exhibit  the 
nme  easily  measured  and  very  sensible  effects  of  their  attraction, 
and  hence  there  is  considerable  difficulty,  and  some  uncertainty,  as 
to  their  exact  masses. 

2638.  Mass  of  Mars  estimated  hy  its  attraction  upon  the  earth, — 
The  nearest  body  of  the  system  to  which  Mars  approaches  is  tho 
earth,  its  distance  from  which  in  opposition  is  nearly  fifty  millions 
of  miles,  or  half  the  distance  of  the  earth  from  the  sun.  Now, 
anoe  the  volume  of  Mars  is  only  the  eighth  part  of  that  of  the 
cuth,  it  may  be  presumed,  that  whatever  be  its  density  its  mass 
must  be  bo  small,  that  the  effect  of  its  attraction  on  the  earth  at  a 
distance  so  great  must  be  very  minute,  and  therefore  difficult  to  as- 
certain by  observaUon.  Nevertheless,  small  as  the  effect  thus  pro- 
duced is,  it  is  not  imperceptible,  and  a  certain  deviation  from  the 
path  it  would  follow,  if  the  mass  of  Mars  were  not  thus  present, 
has  been  observed.  To  infer,  from  this  deviation,  the  mass  of  Mars 
is,  however,  a  problem  of  much  greater  complexity  than  the  deter- 
mination of  the  mass  of  a  planet  by  observing  its  attraction  upon 
its  satellite.  The  method  adopted  for  the  solution  of  the  problem 
it  a  sort  of  ''  trial  and  error.''  A  conjectural  mass  is  first  imputed 
to  Mars,  and  the  deviation  from  its  course  which  such  a  mass  would 
canse  in  the  orbital  motion  of  the  earth  is  computed.  If  such  de- 
Tiation  is  greater  or  less  than  the  actual  deviation  observed,  another 
conjectural  mass,  greater  or  less  than  the  former,  is  imputed  to  the 
planet,  and  another  computation  made  of  the  consequent  deviation, 
which  will  come  nearer  to  the  true  deviation  than  the  former.  By 
repeating  this  approximative  and  tentative  process,  a  mass  is  at  length 
found,  which,  being  imputed  to  Mars,  would  produce  the  observed 
deviation ;  and  this  is  accordingly  assumed  to  be  the  true  mass  of 
the  planet. 

In  this  way  the  mass  of  Mars  has  been  approximatively  estimated 
at  the  seventh  part  of  the  mass  of  the  earth. 

The  smallness  of  this  mass  compared  with  its  distance  from  the 
only  body  on  which  it  can  exert  a  sensible  attraction  will  explain 
the  difficulty  of  ascertaining  it,  and  the  uncertainty  which  attends 
its  value. 

2689.  Masses  of  Venus  and  Mercury. — The  same  causes  of  diffi- 
eolty  and  uncertainty  do  not  affect  in  so  great  a  degree  the  planet 
Venus,  whose  mass  is  somewhat  greater  than  that  of  the  earth,  and 
which  moreover  comes^  when  in  inferior  conjunction,  w*\t\uTi  ;x\^c^w\. 
durijr  milUoDa  of  milca  of  tbo  earth.     The  effects  of  t\ie  «AtoL<i^i«iii 


284  ASTBOHOirr. 

of  the  mass  of  this  planet  npon  the  earth's  orbital  molioii  are  4fln- 
fbre  much  moro  decided.  The  deviation  prodooed  bj  it  ia  not  onl^ 
easily  observed  and  measured,  bat  it  affeeta  in  a  aenmble  mannar 
the  position  of  the  plane  of  the  earthi'a  orbit  By  the  aauM  ijaleBi 
of  ''trial  and  error,"  the  mass  di  this  planet  ia  aaoertainod  to  be 
greater  by  a  twentieth  than  that  of  the  earth. 

The  difficnltiea  attendinff  the  determination  of  the  hhmb  of  Hc^ 
onry  are  atill  greater  than  woae  whidi  alfeet  Ifan^  and  its  tma  lAm 
ia  still  very  uncertain.  Attempts  have  lately  been  made  to  mrat* 
imate  to  its  yalno;  by  obserying  the  effisots  t/t  ita  attnetioa  ob  cm 
of  the  comets. 

2640.  Metkodi  of  determining  the  nuui  of  the  moon.— Owiu 
to  its  proximity  and  close  relation  to  the  earth,  and  the  maiiy  aaa 
striking  phenomena  connected  with  it,  the  determinatioQ  of  the  nnai 
of  the  moon  l^ecomes  a  problem  of  considerable  importaiiee.'  Umib 
are  varioos  ol^rvable  ^ects  of  its  attraction  by  wnieh  die  latio  of 
its  mass  to  those  of  the  sun  or  earth  may  be  compnted. 

2641.  l"".  By  nutation.— It  will  be  ahown  hereafter  that  tha  it- 
tractions  of  the  masses  of  the  sun  and  moon  npon  the  protdbsnat 
matter  surrounding  the  equator  of  the  terrestrial  spheroid  prodaes 
a  regular  and  periodic  change  in  the  direction  of  the  axis  of  the 
earth,  and  consequently  a  corresponding  change  in  the  apparent 
place  of  the  celestial  pole.  The  share  which  each  mass  hss  ia. 
these  effects  being  ascertained,  their  relative  attractions  exerted 
upon  the  redundant  matter  at  the  terrestrial  eauator  ia  fonnd,  tod 
the  effect  of  the  difference  of  distance  being  allowed  for,  the  nUio 
of  the  attracting  masses  is  obtained. 

2642.  2"".  By  the  tides,— It  has  been  shown  (Chap.  X.),  thil, 
by  the  attractions  of  the  masses  of  the  son  and  moon,  the  tides  of 
the  ocean  arc  produced.  The  share  which  each  mass  has  in  the  pro* 
duction  of  these  effects  being  ascertained,  and  the  effect  of  the  dif* 
ference  of  distance  being  allowed  for,  the  ratio  of  the  masses  of  the 
sun  and  moon  is  obtained. 

2643.  3°.  By  the  common  centre  of  gravity  of  the  moon  owJ 
the  earth.  —  It  has  been  stated  that  the  centre  of  attraction  roasd 
which  the  moon  moves  in  her  monthly  course  is  the  centre  of  tlie 
earth.  This  is  nearly,  but  not  exactly  true.  By  the  law  of  gnvi- 
tation,  the  centre  of  attraction  is  not  the  centre  of  the  earth,  bat  the 
centre  of  gravity  of  the  earth  and  moon,  that  is,  a  point  whose  ^ 
tance  from  the  centre  of  the  earth  has  to  its  distance  from  the  oentre 
of  the  moon  the  same  ratio  as  the  mass  of  the  moon  has  to  the 
mass  of  the  earth  (309).  Around  this  point,  which  is  within  the 
surface  of  the  earth,  both  the  earth  and  moon  revolve  in  a  month, 
the  point  in  question  being  always  between  their  centres.  If,  the% 
the  position  of  this  point  can  be  found,  the  ratio  of  its  dialaneef 


THB  SOLAE  ST8TE1C.  286 

from  the  centres  o£  the  earth  and  moon  will  give  the  ratio  of  their 
masses. 

Now,  the  monthly  motion  of  the  earth  round  such  a  centre  would 
necessarilj  produce  a  corresponding  apparent  monthly  displacement 
cf  the  sun.  Such  displacement,  though  small  (not  amounting  to 
more  than  a  few  seconds),  is  nevertheless  capable  of  observation  and 
measurement.  The  exact  place  of  the  sun's  centre  being  therefore 
eompnted  on  the  supposition  of  the  absence  of  the  moon,  and  com- 
pmd  with  ita  observed  place,  the  motion  of  the  earth's  centre  and 
the  position  of  the  point  round  which  it  revolves  has  been  deter- 
nnedy  and  the  rektiYe  masses  of  the  earth  and  moon  thus  found. 

2644.  4**.  By  terrestrial  gravtfy.  —  By  what  has  been  already 
ophuned,  the  space  through  which  the  moon  would  bo  drawn  to- 
vuds  the  earth  in  a  given  time  by  the  earth's  attraction  can  be  de- 
termined. Let  this  space  be  expressed  by  s.  The'ttnear  velocity 
T  ol  the  moon  in  its  orbit  can  also  be  determined.  Now^  if  r  bs 
the  radius  of  the  orbit^  we  shall  have  (2614) 

2  r  X  8  =  v', 
ud  consequently 

We  find,  therefore,  the  radius  vector  of  the  moon's  orbit  by  divi- 
£Dg  the  square  of  its  linear  velocity  by  twice  the  space  through 
vfaich  it  would  taXL  towards  the  earth  in  the  unit  of  time.  But  this 
adias  vector  is  the  distance  of  the  moon's  centre  from  the  common 
eratre  of  gravity  of  the  earth  and  moon.  The  distance  of  that 
point,  therefore,  from  the  centre  of  the  earth,  and  consequently  the 
iitio  of  the  masses  of  tho  earth  and  moon,  will  be  thus  found. 

An  these  methods  give  results  in  very  near  accordance,  from 
lUch  it  is  inferred  that  the  mass  of  the  moon  is  not  less  than  the 
ttfenty-fifth,  nor  greater  than  the  eightieth,  part  of  tho  mass  of  the 
etrth,  and  it  is  consequently  the  twenty-eighth  millionth  part  of  the 
■isB  of  the  sun. 

2645.  To  determine  the  masses  of  the  satellites.  —  The  same  dif- 
ficulties which  attend  the  determination  of  the  masses  of  the  planets 
not  accompanied  by  sateUites  also  attend  the  determination  of  the 
mtSBCfl  of  satellites  themselves,  and  the  same  methods  are  applicable 
to  the  solution  of  the  problem.  The  masses  of  the  satellites  of  Ju- 
pHer  and  the  other  superior  planets  are  ascertained  in  relation  to 
diOBe  oi  their  primaries  by  the  disturbing  effects  which  they  produce 
spon  the  motions  of  each  other. 

2646.  To  determine  the  densities  of  (he  bodies  of  the  system.  — 
The  mmaaes  and  volumes  being  ascertained,  the  densities  are  found 
by  difidiDg  the  masses  by  the  volumes.     Thus^  if  d  and  i/  be  the 


S88  AsnuRloiiT. 

dMuities  of  the  eaiih  and  a  planet^  K  and  m'  Oair  mmm,  aai  T 

aad  y'  their  Yolames^  we  shall  have 

M       M^ 

D  :  D  : :  — :  -7- 
V     V 

2647.  The  method  of  determining  Ae  ng^Jieial  gravi^mM 
body. — When  it  is  considered  how  important  an  demant  io  all  lb 
mecbanioal  and  physical  phenomena  on  the  aorfiMM  of  the  oarthf  lb 
intensity  of  gravity  at  the  snr&oe  i%  it  will  be  mntj  uaknlkid 
that  in  the  inyestigationof  the  aaperfioial  oonditHm  and  local  eeoaoBf 
of  the  other  bodies  of  the  solar  STstem,  the  dotermhiatioD  of  ths» 
tensities  of  the  forces  with  which  they  attract  bodiea  pheed  m  « 
near  their  snrftcesy  is  a  problem  of  consideiable  intarat 

H  the  mass  of  the  euth  be  expressed  bj  M^  its  aemidiaBMkrlf 
r,  and  the  fofoe  of  gravity  on  its  sorfikce  dy  g,  while  u',  t^ftaii  , 
express  the  (fame  physical  quantities  in  relation  to  any  odMr  hodj  j 
having  the  form  of  a  globe,  we  shall  have 

M         M^ 


because,  by  the  general  law  of  gravitadon,  the  force  is  in  the 

ratio  of  the  masses  and  the  inverse  ratio  of  the  square  of  the  atUastai 
body  from  their  centre;  and  in  this  case  the  attracted  body  hfOf 
supposed  to  be  at  their  surfacesi  those  distances  wiU  be  their  seal* 
diameters. 

From  the  preceding  proportion  may  be  inferred  the  formula 

or         M  r" 

?  ~    M*     "^     /«'  j 

by  which  the  superficial  gravity  may  always  be  computed  when  lb  % 
ratios  of  the  masses  and  the  diameters  are  known.  | 

2648.  Superficial  gravity  on  the  mn,  —  The  mass  of  the  itt  ^ 
being  855,000  times  that  of  the  earth,  while  its  diameter  if  HI  / 
times  that  of  the  earth,  we  shall  have 

..y  ..1.365^  _  28.9 

It  appears,  therefore,  that  the  weight  of  a  body  placed  at  the  snrfM 
of  the  sun  is  twenty-nine  times  its  weight  on  the  surface  of  the  ear^ 

A  man,  whose  average  weight  would  bo  1}  cwt.  on  the  earth, 
would  weigh  2  tons  and  l-8d  if  transferred  to  the  surface  of  the  sod* 
The  human  frame,  organised  as  it  is,  would  be  crushed  under  itt 
own  weight  if  removed  there. 

Muscular  force  is  therefore  29  times  more  efficacious  upon  tho 
earth  than  it  would  be  upon  the  sun. 

2649.  Superficial  gravity  on  the  moon.  — The  mass  of  the  inofli 
has  been  ascertained  to  be  the  80th  part  of  that  of  the  earth,  wh3» 


TBI  fiOLAE  8T8TSM.  287 

of  th«  moon  ib  aboat  the  fourth  part  of  that  of  the 
have,  therefore,  in  the  oaae  of  the  mooOy 

9  'ff  ''  ^   '   80""  5' 

nperfioial  gravity  on  the  moon  is  five  times  less  than  on 
I  man  weighing  1*5  owt  on  the  earth  woold  only  weigh 
33}  lbs.,  if  transferred  to  the  moon. 
autfication  of  the  planets  in  three  groups. -^  Fini 
i  terrestrial  planets.  —  Of  the  planets  hitherto  discov- 
rhich  present  in  several  respects  remarkable  analogies 
,  and  whose  orbits  are  included  within  a  circle  which 
earth's  distance  from  the  san  by  no  more  than  one-half| 
from  these  circumstances  denominated  terrestrial 
Fwo  of  these,  Mercury  and  Venus,  revolve  within  the 
earth ;  and  the  third,  Mars,  revolves  in  an  orbit  outside 
earth,  its  distance  from  the  earth  when  in  opposition 
lalf  the  earth's  distance  from  the  sun. 
dcond  group  —  the  planetoids,  —  A  chasm  having  a 
oring  little  less  than  four  times  the  earth's  distance, 
or  many  ages  after  astronomy  had  made  considerable 
9  terrestrial  planets  from  the  more  remote  members  of 

The  labours  of  observers  during  the  last  half  centary, 
luring  the  last  seven  years,  have  filled  this  chasm  with 
1  twenty-three  planets,  distinguished  from  all  the  other 
e  system  by  their  extremely  minute  magnitudes,  and  by 
tance  of  revolving  in  orbits  very  nearly  equal.  These 
been  distinguished  by  the  name  of  asteroids  or  plan- 

latter  being  preferable  as  the  most  characteristio  and 

iird  group — the  major  planets, — Outside  the  planetoids, 
nous  distances  from  the  sun  and  from  each  other,  revolve 
of  stupendous  magnitude  —  named  Jupiter,  Saturn, 
id  Neptune  :  the  two  former  being  visible  to  the  naked 
Qown  to  the  ancients ;  the  two  latter  are  telescopic,  and 
3red  in  modem  times. 


CHAP.  xm. 

the  terrestrial  planets. 
I.  Mercury. 

eriod,  —  The  nearest  of  the  planets  to  the  sun,  and  that 
»letes  its  revolution  in  the  shortest  time,  is  Mercury. 


^^ 


Hie  ijnocUo  period  of  thiapbne^  deterralMd  liy  immBitt  ob- 
Brarstion,  ie  115'88  days.  Henee  m  ihkll  ban  by  tha  fisnoli 
(258S) 

1  1        J.   _1_  1    . 

p  ""  116-88   "^   866-26        8758 

Tke  period  of  Mereoi;  ia,  therefins,  87-98,  or  my  aoulj  88  iap. 

Bj  methods  of  cmlimlation  nuoeptibla  of  stiU  poKtor  pwMiB^ 
the  period  is  fboDd  to  be  87-97  dsji. 

If  die  earth's  period  be  espreMed  b;  1,  that  of  Hatnny  wSl, 
tha-efore,  be  0-2408. 

2%&i.  MdiocetUric  and  ^nodie  motwiu. — Tha  netB  duly  hdiK 
Mnbrio  molioD  is,  therefbre  (2568), 

.  =  }^^  =  14782'-5  =  246-5  =  4»-092. 
The  moan  duly  synodic  motion  is  (! 
•  =  ft  —  t  =  14732"5  - 8548"-2  - 11184" 3  =  186'-4  =  r-ll. 
2655.  DiUaiux  determined  ly  gmUat  eloagatian.  —  Owju  to 
tbe  ellipdeity  of  the  planet's  orbit,  its  greatest  elongaUm  isa^sst 
to  some  variation,  I(a  mean  amouot  is,  however,  about  22°-8.  If 
the  radius  r  of  the  planet's  orbit,  drawn  frciui  tbc  eun  to  the  pbstl 
at  the  point  of  its  greatest  elongation,  were  the  arc  of  a  circle,  lunig 
the  earth's  distance  from  the  sun  as  radios,  wo  should  Lava  (2294) 
_  95,000,000 

*■ 5^3       ^ 

Bnt  the  radius  r  being,  in  fact,  the  wne  of  22°-5,  and  not  Uufin 
itself,  the  value  of  r  is  a  little  less,  being  about  36]  millions  of  nibi' 
265G.  By  the  harmonic  late.  —  If  r  express  the  distance  of  ft' 
plaaet,  that  of  the  earth  bciog  1,  we  shall  have  (2621) 

r*=  0-2408*=  0-387'. 
The  distance  of  the  planet  is,  therefore,  0-^87.     But  the  meim  i» 
tance  of  the  earth  being  05  millions  of  milc.q,  we  Bhull  buvo  for  llx  --' 
mean  distance  of  the  pkact  ' 

r'  =  95,000,000  x  0-387  =  36,770,000  miles. 
2657.  Mfan  and  eztrfmedittanca/rom  Ae  earth.  —  The  etwa-  ^ 
tridty  of  the  orbit  of  Mercury  is  much  more  considerable  thsi  u- 
those  of  the  planets  generally,  being  a  little  more  than  0-2,  Cfr  '- 
pressed  in  parts  of  the  mean  distsnce.     The  distance  of  the  {daiMt  ^ 
from  the  sun  is,  therefore,  subject  to  a  variation,  Dmoanting  to  tf 
much  as  a  fifih  part  of  its  mean  value.     The  greatest  aod  least  dit- 
tances  from  the  sua  are,  therefore, 

36}  +  7J  =  433  millions  of  miles  in  aphelion. 
86J  -  "i  ^  29J         "  ■'  perihelioo. 


=  87;i03,000  miles. 


THE  TBKRESTRIAL  PLASETS.  289 

Tbo  distance  i^  therefore,  subject  to  a  varUtioa  in  tbo  ratio  of  5  to 
7  Tery  acarly. 

The  uesD  dist&QceB  of  the  planet  from  the  earth  are,  therefore, 
95  —  36f=    59i  mill,  of  miles  at  inf.  conj. 
95  +  S6J  =  181|         «         «         Bup.  conj. 
Ttiese distaDcei  are  anbjeot  to  an  iDorease  anddiniiDntion  of  aeren 
•ad  one-third  millions  of  miles  dne  to  the  eccentricity  of  the  ortnt 
cf  the  planet,  and  ooe  million  and  a  hnlf  of  miles  dne  to  the  eocen- 
trieiij  of  the  orbit  of  the  earth. 

•2658.  Scale  of  the  orbit  relaticrly  to  thai  of  tke  earth.  — The 
grbit  of  Mercury  and  a  part  of  that  of  the  earth  are  exhibited  on 
their  proper  scale  iajlg.  746,  where  fiR  ia  the  earth's  distance  from 

the  aun,  and  mm"m  the  orbit  of 

the  planet.  The  lines  E  m"  drawn 
from  the  earth  touching  the  orbit  of 
the  planet  dctemiino  the  positions 
of  the  planet  when  its  clongaUon  ia 
greatest  east  and  west  of  the  snn. 
The  points  m  are  the  positions  of 
the  pbnct  at  inferior  and  superior 
conj  n  notion. 

2659.  Apparent  motion  of  the 
plaitel.  —  'i'ho  effects  of  the  combi- 
nation of  the  orbital  motions  of  the 
planet  and  the  earih  upon  the  appa- 
rent place  of  the  plunct  will  now  he 
easily  comprehended. 

Since  the  nicau  value  of  the 
greatest  elongation  m"E8  =  '22J'', 
tbo  arc  m  tn"  =  67  i°,  and  therefore 
m"  m  m"=  07}°  x  2  =  135".  The 
times  of  the  greatest  clongation.s 
raet  and  west  therefore  divide  the  whole  synodic  period  iulo  two 
uncigual  parts,  in  one  of  which,  that  from  the  greatest  elongation 
rtht  through  inferior  conjunction  to  the  grealcat  elongation  we!<t,  the 
planet  gains  upon  the  earth  135"  ;  and  in  the  other,  that  from  the 
{.Tcatest  elongatiiin  west,  through  superior  conjunction  to  the  greatest 
elongation  cast,  it  gains  360"  —  1^5°  =  225°.  Since  the  parts 
into  which  the  synnlic  period  is  thus  divided  are  proportional  to 
these  angles,  they  will  be  (taking  tl>o  synodic  period  in  round  num- 


rif.  MB. 


bcrsss  116  days), 


135 


X  116  =  43JdorB; 
^  X  116  =  721  days. 


290  ABTROvoinr. 

And  rinoe  tba  former  intenral  is  divided  eqiudly  hj  tlie  cpoeh  of 
inferior,  and  the  latter  by  the  epooh  of  eaperior,  oonjanclioii,  il  fot 
lowsi  that  the  intervals  between  inferior  ooDJoDOtioii  wd  pmtuA 
elongation  are  21  f  days,  and  the  intervals  between  anpenor  oqb- 
jnnction  and  neatest  elongation  are  86|>  days. 

The  interna  between  the  times  at  which  the  {danet  is  strtioMry, 
before  and  after  inferior  conjunction,  is  sabjeot  to  some  varialioBy 
owing  to  the  eccentricities  of  the  orbits  both  of  the  planet  and  the 
earth,  but  chiefly  to  that  of  the  planet's  orUt,  which  b  oonsider 
able.  If  its  mean  value  be  taken  at  22  days,  the  angle  gained  by 
the  planet  on  the  earth  in  that  interval  being 

8^11  X  22  =  68*>-4, 

the  angular  distances  of  the  points  at  which  the  phaeft  le  elslioeBiT 
from  inferior  conjunction  as  seen  from  the  sua  wonld  be  94t^% 
which  would  correspond  to  an  elongation  of  abont  21%  ae  aeea  tnm 
Uie  earth.  This  result,  however,  is  subjeet  to  very  met  lai'hBiij 
owing  to  the  eccentricity  of  the  planetTs  orbit  and  otaer  eenssi* 

2660.  CoRditums  tohich  favour  Ae  obtervaium  cf  om  iifiiitm 
pittnei. — These  conditions  are  threefold;  1.  The  megnitade d 
inat  portion  of  the  enlightened  hemisphere  which  is  presenlsd  to 
the  earth.  2.  The  elongation.  3.  The  proximity  of  the  pknet  to 
the  earth. 

Since  it  happens  that  the  positions  which  render  some  of  these 
conditions  most  favourable  render  others  less  so,  the  determinatioQ 
of  the  position  of  greatest  apparent  brightness  b  somewhat  oompl^ 
cated.  When  the  planet  is  nearest  to  the  earth,  its  dark  henii- 
sphere  is  presented  towards  us  (2595);  )i>e8ides  which,  being  in 
inferior  conjunction,  it  rises  and  sets  with  the  sun,  and  is  only  pM- 
sent  in  the  day-time.  At  small  elongations  in  the  inferior  part  of 
the  orbit,  its  distance  from  the  earth  is  not  much  augmented,  bat 
it  is  still  overpowered  by  the  sun's  light,  and  would  only  appear  si 
a  thin  crescent  when  it  would  be  possible  to  see  it  At  the  greateit 
elongation,  when  it  is  halved,  it  is  most  removed  from  the  inte^ 
ference  of  the  sun,  but  is  brightest  at  a  less  elongation,  even  thoogli 
it  moves  to  a  greater  distance  from  the  earth,  sinc£*it  gains  more  bj 
the  increase  of  its  phase  than  it  loses  by  increased  distance  and 
diminished  elongation. 

Owing  to  the  very  limited  elongation  of  Mercury,  that  planet, 
even  when  its  apparent  distance  from  the  sun  is  greateat,  sets  in  the 
evening  long  before  the  end  of  twilight ;  and  when  it  rises  befoie 
the  sun,  the  latter  luminary  rises  so  soon  after  it,  that  it  is  never 
free  from  the  presence  of  so  much  solar  light  as  to  render  it  ex- 
tremely difficult  to  see  the  planet  with  the  naked  eye. 

In  these  latitudes.  Mercury  is  therefore  rarely  seen  with  the 
naked  eye.     It  is  said  that  Copernicus  himself  never  saw  thii 


THE  TERRESTRIAL  PLANETS. 


291 


planet ;  a  drenmstaDoe  which,  however,  may  have  been  owing,  in  a 
great  degree,  to  the  nnfavourable  climate  in  which  he  resided.  In 
lifwer  latitadcs,  where  the  diurnal  parallels  are  more  nearly  vertical 
ind  tbo  atmosphere  less  clouded,  it  is  more  frequently  visible,  and 
there  it  is  more  conspicuouSi  owing  to  the  short  duration  of  twi- 
light. 

2661.  Apparent  diameter, — its  mean  and  extreme  values.-^ 
Owing  to  the  variation  of  the  planet's  distance  from  the  earth,  its 
apparent  diameter  is  subject  to  a  corresponding  change.  At  its 
greatest  distance  its  apparent  diameter  is  4}",  and  at  its  least  dis- 
tance 11}",  its  value  at  the  mean  distance  being  6}". 

The  apparent  diameter  of  the  moon  being  familiar  to  every  eye, 
sapplies  a  convenient  and  instructive  comparison  by  which  the  ap- 
parent magnitudes  of  other  objects  may  be  indicated,  and  we  shall 
refer  to  it  frequently  for  that  purpose.  The  disk  of  the  full  moon 
rabtenda  an  angle  of  1800"  to  the  eye.  It  follows,  therefore,  that 
the  apparent  diameter  of  Mercury,  when  it  appears  as  a  thin  crescent 
near  iDferior  conjunction,  is  about  the  150th  part,  near  the  greatest 
elonoatioD  it  is  the  280th  part,  and  near  superior  conjunction  the 
400u  part^  of  the  apparent  diameter  of  the  moon.  With  a  mag- 
mfying  power  of  140,  it  would  therefore,  at  its  greatest  elongation, 
appear  with  a  disk  half  the  apparent  diameter  of  the  moon. 

2662.  Re€U  diameter,  —  The  distance  of  Mercury  in  inferior  con- 
junction being  36}  millions  of  miles,  the  linear  value  of  1"  at  it 
then  18  (2298) 

69,250,000      ^^^  ^     ., 

At  tliia distance  its  apparent  diameter  is  IH" }  and  if  d'  express  its 
real  diameter,  we  shall  have 

1/  =  287-2  +  11-25  =  3231  miles. 

Other  observations  make  the  diameter  somewhat  less,  and  fix  it  at 
2950  miles. 

2663.  Volume,  —  If  v'  express  the  volume,  that  of  the  earth 
being  Y,  we  shall  have 


V  ~  D*  ""  ^7Jil2^  ""  14-6 


Fiff.  747. 


The  volume  is  therefore  less  than  the 
14th  part  of  that  of  the  earth.  If  the 
lesser  estimate  of  the  diameter  of  Mercury 
be  adopted,  it  will  follow  that  its  volume  is 
about  the  ITtb  part  of  that  of  the  earth. 
The  relative  volumes  are  represented  by  M 
and  E,  Ji(/.  747. 

2664.  Mau  and  dennty.  —  Some  uncer- 


299  AaTBXaiOKT.  , 

tuntjhaa  liitherto  attendod  tlio  taiaiJ^Stm  of  die  density  ati  mtm 
of  this  planet,  owing  to  the  kbrnnoe  of  ■  satellite.  The  di«tiirl'- 
UiCta  prodnceil  by  it  upon  the  molioD  of  Enoke'a  comet  (i  Wj 
whiob  will  be  desaribed  id  uiatliGr  ahiptor}  bitTe,  boweTer,  euppUM 
the  means  of  a  oloaer  kpprozimfltion  to  it.  B)-  this  means  it  W 
been  found  that  if  U*  eipreu  the  miw  of  the  placet  and  H  tbattf 
the  earth,  m  ahall  have  ^^ 

H*       100  ^^L 


M  that  the  man  ie  12)-  ^mes  len  than  that  of  tba  eMb. 

If  <P  and  d  expTMB  the  denaitiee  of  the  plmet  and  Ikt  walk,  n 
■ball  therefore  hare 

T 

'1226'^  ■lO~iM5" 
Other  estimates  make  it  112.  8o  that  it  may^  be  infbnad  that  A« 
dennlT  of  Merenrr  ezoeeda  that  of  the  earUi  bj  an  d|^th  lo  > 
fifth. 

2666.  Superfeial  ffravUy.  —  If  j/  expreaa  the  foroe  of  ffndj 
on  the  enrfaoe  of  Mcrcorj,  g  being  the  force  on  the  sorbee  of  IM 
earth,  we  shall  have  (2639) 

?         M         D» 

The  snperfioisl  gravity  is  therefore  only  half  the  same  foroe  oolht 
earth.  Masculu  and  other  forces  not  depending  on  weight  in 
therefore  twice  as  efficadous.  The  height  throogh  whioh  a  bo(^ 
would  fall  in  a  second  would  be  96}  inches,  or  a  little  man  tbu 
eight  feet. 

2666.  Solar  li-fht  ami  heal.  —  The  apparent  magnitude  of  Ibt 
BUD  is  greater  than  upon  the  earth,  in  the  game  ratio  as  the  diituM 
is  leas;  and  owing  to  the  considemble  dlipticityof  Mercnrj'i ocki^ 
it  has  apparent  mngnitudca  sensibly  different  in  different  parts  d 
Mercury 'a  year.  The  apparent  diameter  of  the  sun  as  seen  from  tht 
earth  being  30',  its  apparent  diameter  seen  from  Mercury  will  be 

in  perihelion       SCf  x  ^  =  92'-5, 
in  aphelion  SC  X  ^~  =  64'-2, 

at  mean  distance  30'  x  ■^— r-  =  78'. 

Thus  the  apparent  diameti^r  when  least  is  twice,  and  when  gnsleit 
three  times,  that  under  which  the  sun  appears  from  the  earth. 


lU  TXBBK8I1UAL  FLASSIfl. 


B  tg.  748,  B,  tlw  nUtiro  apptnnt  mignitadea  <X  the  ans,  u 
B  from  the  «uth  and  irom  MflKmry,  it  the  mean  diafauioe  and 


T(i.74a. 


Slf.T«. 


•xlniofl  diBtanoea,  ara  represeated  at  x,  u,  m*,  and  ii".  If  k  be 
■opposed  to  repreMDt  tbe  apparent  disk  of  tfae  aun  as  leen  from  the 
mtUi,  h  will  repreMnt  it  u  it  appeani  to  Mercury  at  tbe  mean  dii- 
tanoe,  h'  at  aphelion  sad  m"  at  perihelion. 

Since  tbe  iUumintting  and  heating  power  i>r  the  Bun's  rays,  what- 
enr  be  the  phyeical  condition  nf  the  surface  of  the  planet,  mutt 
TCiT  io  the  same  proportion  as  the  apparent  area  of  tbe  sun's  disk, 
it  nllowB,  that  the  light  and  warmth  pruduccd  b;  the  sun  on  the 
■nrfaee  of  the  planet  will  be  greater  in  perihelion  ihun  in  apbelion, 
in  the  ratio  of  9  to  4,  and,  consequently,  there  muat  be  a  succeasioD 
of  acaaons  on  this  planet,  depending  exclusiveiy  on  the  elUpticity 
of  the  orbit,  and  having  no  relation  to  the  direction  of  its  axis  of 
TotatioD  or  the  poeition  of  the  plane  of  ita  equator  with  relation  to 
that  of  its  orbit.  The  parage  of  the  planet  through  its  peribelion 
naat  prodnce  a  summer,  snd  its  passage  throngh  aphelion  a  winter, 
the  mean  temperature  of  the  former  ceterii  paribut  being  above 
twice  that  of  the  latter. 

If  the  axis  of  the  planet  be  inclined  to  the  plane  of  its  orbit, 
another  aaccession  of  seasons  will  be  produced,  aependent  on  such 
iDelinadon  and  the  position  of  the  equinoctial  points.  If  these 
pojnta  coincide  with  the  apsides  of  the  orbit,  the  summers  and  win- 
ten  ariaing  from  both  csases  will  either  respectively  coincide,  or  the 
■atntner  from  each  cause  will  ooincide  with  tho  winter  from  the 
other.  In  tbe  former  case,  tbe  intensities  of  tho  seasons  and  their 
extrenie  temperatures  will  be  augmented  by  the  coincidenoc,  and  in 
the  latter  they  will  bo  mitigated;  the  summer  heat  from  each  cause 
tempering  the  winter  cold  from  tbe  other. 

If,  on  the  other  hand,  the  line  of  apsides  he  at  right  angles  to 
the  direction  of  the  equinoxes,  the  summer  and  winter  from  each 
cause  will  correspond  with  tbe  spring  and  autumn  from  the  other, 
and  a  curious  snd  complicated  succession  of  sessons  must  ensue, 
depending  on  the  degree  of  obliquity  of  the  axis  of  the  planet, 
eompared  with  the  eficcts  of  the  eccentricity  of  its  orbit. 

In  oonparing  the  calorific  influence  of  the  sun  on  Metcary  and 
25" 


tha  Mitli,  it  must  be  Tcmcmberc^  Ibat  tbc  tctau  Te>iDp^^^^» 
dooed  by  tbe  Mlnr  rays  dupcnda  tin  the  lictmily  of  ihe  almtn-pbtra 
through  which  tlitj  pass,  hy  wliiuh  tho  tiisat  is  collected  ami 
diBind.  nie  densitj  of  ti>e  suo's  rays  above  tbe  snow-liae  in  tlM 
tnfSoa  fa  u  great  as  at  tbe  level  of  tbe  ecs,  but  the  tcmpenlniv 
of  tlw  air  lud  ^urroandiiig  objects  arc  cicrcmcl;  different  Not- 
withstanding, therefore,  tho  greuter  deasity  of  the  aolar  ny»,  (li« 
■iMmiihwIn  oonditJDDS  of  the  piaoet  may  be  mch  that  the  npciC- 
cU  I— pWMtiire  nay  not  be  different  fram  that  of  the  end. 

The  intensity  of  ilie  solar  light  naBt  Im  ^r^tor  thu  mt  (be  aartli 
in  the  ndo  of  loar  to  one  when  the  planet  la  in  xphdJOD,  and  ni 
to  one  when  in  perihelion.  Ita  efiecta  on  vinon,  howe««\  nay  h 
lendend  the  aame  by  the  meie  adaphtion  of  the  ocntraotile  jvtNt 
of  thejmpil  of  the  eye.    (1129.) 

2667.  MAod  of  amenaininff  At  diuntal  rdatio*  of  At 
plantta.  —  One  of  the  moot  IntOTOHing  objeota  of  tabnofie  b- 

Sojiy  r^aHiag  the  eondition  of  tha  planets  ia,  the  qaaatkai  at  ti 
leir  diimal  rotation.  In  genaral,  the  mannar  in  vbwh  «■  AtJH 
seek  to  aaoftrtain  thia  &et  would  be,  by  examining  with  powitfii 
tdeaoc^  the  marka  ohBDrrable  aptni  the  diak  of  the  |^aaeL  J/ 
the  planet  revolve  upon  an  axis,  these  marks,  being  earned  rand 
with  it,  would  appear  to  move  across  the  disk  from  one  fdde  to  &» 
other;  they  woutd  disappear  on  one  side,  and,  remaiaing  for  aeo^ 
tain  time  invisible,  would  reappear  on  the  other,  pasang,  as  belbn, 
across  the  visible  disk.  Let  any  one  stand  at  a  distance  from  ■ 
common  terrestrial  globe,  and  let  it  be  made  to  revolve  nprni  ill 
axil :  the  spectator  will  see  the  geographical  marks  delineated  on  it 
pass  across  tbe  hemisphere  which  b  turned  towards  him.  They  wiU 
Bucoesmvely  disappear  sod  reappear.  Tbe  same  effects  lnna^  of 
oourae,  be  expected  to  be  seen  upon  the  several  planets,  if  thty 
have  a  motion  of  rotAtion  resembling  the  diurnal  motion  of  ov 

2568.  Difficultj/  of  Ait  qualum  in  the  caw  of  Mercury.  —  lb 
is  a  species  of  observation  whieh  has  not  jct  been  BoeoeaafnOj 
made  in  the  case  of  Mercury.  Sir  John  Herschcl,  who  haa  so- 
joyed  more  than  common  advantages  for  telescopic  observatioa 
under  different  climates,  affirms,  that  little  more  can  be  cerUioIy 
affirmed  of  Mercury  than  that  it  is  globular  in  form,  and  exhitats 
phases,  and  that  it  ia  too  small  and  too  much  lost  in  the  constant 
and  close  effulgence  of  the  bud  to  allow  the  further  discovery  of  itt 
physical  condition.  Other  observers,  however,  claim  the  disoovery 
of  Indications  not  only  of  rotation  but'other  physical  cbaraoteiB. 
Schroter  says,  that  by  examining  daily  the  appearance  of  the  cons 
of  the  crescent  he  ascertained  that  it  haa  a  motion  of  rotation  id 
24».  5-.  28'.. 

2669.   AfJrged  dtKovery  of  mmrntain*. — Tbe   same   obserrer 


THE  TERRESTRIAL  PLANETS.  295 

cbims  the  diacoyerj  of  monDtuns  on  Mercury,  and  cTen  assigns 
their  height^  estimatiog  ono  at  2132  jards^  and  another  18;978 
juds. 

Tbeie  observBtioDfl,  Dot  having  heen  confirmed,  most  be  considered 
^oehryphaL 

II.  Venus. 

2670.  Period.  —  The  next  planet  proceeding  outwards  from  the 
ran  is  Venus,  which  revolves  in  an  orbit  within  that  of  the  earth, 
tnd  which,  afier  the  sun  and  moon,  is  the  most  splendid  object  in 
Uie  firmament. 

The  synodic  period,  ascertained  by  observation,  is  584  days.  Her 
period  deduced  from  this  (2589)  is,  therefore, 

2^_  _i 11 

-      p  ~  365-25      584  ""  225* 

By  the  other  methods  it  is  more  exactly  determined  to  be  224*7 
days. 

If  the  earth's  period  be  taken  as  the  unit,  that  of  Venus  will, 
tbereforCy  be  0-61. 

2671.  Ileliocentric  and  ^nodic  motions.  —  The  mean  daily 
heliocentric  motion  of  Venus  is,  therefore  (2568), 

.  =  lg6?00  =  5768"=96'13  =  l<».6, 

and  the  mean  daily  synodic  motion  is  (2569) 

tf  =  a  —  f  =  5768"  —  3548"  =  2220"  «=  87'. 

2672.  Distance,  by  tfreateU  elongation.  —  The  mean  amount  of 
greatest  elongation  of  Venus  being  found  by  observation  to  be  about 
45^  or  46^,  it  follows  that  in  that  position  lines  drawn  to  the  earth 
and  sun  from  the  planet  would  form  the  sides  of  a  square,  of  which 
the  earth's  distance  from  the  sun  is  the  diagonal.  If,  therefore,  tho 
earth's  distance  be  expressed  by  1*0000,  that  of  Venus  would  bo 
0  7071. 

3673.  Bjf  the  harmonic  law. — If  r  express  the  mean  distance  of 
the  planet  from  the  sun  (2621),  we  have 

r»=0-6P=  0-719'. 

Therefore  r  =  0-719 ;  and  since  the  mean  distance  of  the  earth  is 
95  millions  of  miles,  we  shall  have 

f/  =^5,000,000  X  0-719  =  68,300,000. 

By  more  exact  methods  the  distance  is  found  to  bo  08}  millions  of 
milee. 

2674.  Mean  and  extreme  diMances  from  the  earth — Its  distances 


296 


ABTHOSOXT. 


from  tbe  earth  at  iaferior  con  junction,  gratteat  «l 
p«nor  conjunction,  are  thercfora 

26,250,000  miles  at  inf.  con. 
65,000,000  milcB  at  greatest  elong. 
163,750,000  milea  at  super,  con. 
The  ccoentricity  of  tba  orbit  of  Venus  being  leas  than  1 
these  distances  ore  subject  to  very  little  variation  from  that 
The  extreme  distance  of  the  planet  from  the  ann  will  bo 
68}  —  ^i^  ^^i  millions  of  miles  in  perihelion, 
68i  +  01  =  691      "  "         aphelion. 

Theso  distances  of  the  planet  from  the  earth  are  anbject  tbi 
to  an  increase  and  diminution,  amounting  to  half  a  milLon  of 
dne  to  the  eocentricity  of  the  planet's  orbit,  and  one  and  s 
million  of  miles  due  to  that  of  tbe  earth's  orbit. 

2675.  Scah  of  the  orbit  relative  to  that  of  (A«  earlk. — Tb 

Uon  of  the  orbit  of  Venus 

eartb  is  represented  in  ^ 

where  sx  rapiesenta  the  i 

distance  from  the  son,  uu 

1  mean  diameter  of  the  pi 

orbit  on  tbe  same   scale. 

angles  s  e  v"  represent  the 

est  elongation  of  the  pknet, 

is  about  46°.     The  leraer 

gatioaa  u"'  e  g  are  those  at 

the  planet  appears  with  les 

a  full  disk,  or  gibbous,  aa 

or  as  a  crescent,  as  at  i/.  (i 

2676.    Aj>i>arenl    moti 

Since    tbe    mean   value    c 

greatest  elongation  is  ascei 

to  be  46°,  the  angle  at  th 

p"  8  K  ^  44°,  and  conseq 

Kg.  750.  tbe   angle   e"  b  i-",  includi 

tween    tbe   greatest  elooj 

east  and  west,  is  88°,     Since  tbe  lime  taken  bjr  the  planet  t 

this  angle  upoD  tbe  eartb  bears  the  same  ratio  to  the  sjnodie 

as  this  angle  bears  to  360°,  tbe  intervals  into  which  the  b, 

period  is  divided  bj  the  epochs  of  greatest  elongation,  are 


3li0 


:  581  = 


I  142  8  days.- 
441-2  days. 


THE  TERRESTRIAL  PLANETS.  297 

The  ioterrab  between  inferior  oonjnnction  and  greatest  elongation 
are  therefore  71 1  dajit,  and  the  intervals  hctween  superior  conjunc- 
tion and  greatest  elongation  are  220^  days. 

2677.  S(ation$  and  retrogression,  —  From  a  comparison  of  the 
orbital  motions  and  distances  of  the  earth  and  planet,  it  is  found 
that  the  epochs  at  which  it  is  stationary  are  about  twenty  days  bo- 
fore  and  after  inferior  conjunction.  Now,  since  the  planet  gains 
0^*61  per  day  upon  the  earth,  this  interral  corresponds  to  an  an^e  of 

20  X  0^-61  =  12<^-2, 

it  the  saOy  which  corresponds  to  an  elongation  of  25^. 
The  arc  of  retrogression  is  little  less  than  a  degree. 

2678.  Conditions  which  favour  the  observation  of  Venus, — This 
|»lanet  presents  itself  to  the  observer  under  conditions  in  many  re- 
spects more  &YOurable  for  telescopic  examination  than  Mercury. 
The  actual  diameter  of  Venus  is  more  than  twice  that  of  Mercury. 
It  approaches  nearer  to  the  earth  in  the  inferior  part  of  its  orbit  in 
the  ratio  of  13  to  30.  It  elongates  itself  from  the  sun  to  the  dis- 
tance of  46^y  while  the  elongation  of  Mercury  is  limited  to  22}^.' 
The  latter  is  never  seen,  except  in  strong  twilight.  Venus,  espe- 
ciallj  in  the  lower  latitudes,  is  seen  at  a  considerable  elevation  long 
after  the  cessation  of  evening  and  before  the  commencement  of 
nomiog  twilight,  and  when  she  has  a  gibbous  or  a  orescent  phase. 
The  planet  appears  brightest  when  its  elongation  is  about  40^  in  the 
nperior  part  of  her  orbit. 

2679.  Evening  and  morning  star,  —  Lucifer  and  Hesperus,  — 
This  planet  for  these  reasons  is,  next  to  the  sun  and  moon,  the  most 
eoDspieaoua  and  beautiful  object  in  the  firmament.  When  it  has 
western  elongation,  it  rises  before  the  sun,  and  is  called  the  morn- 
Dio  STAR.  When  it  has  eastern  elongation^  it  sets  afler  the  sun, 
Hid  is  called  the  eyrning  star. 

The  ancients  gave  it,  in  the  former  position,  the  name  LuoiFER 
(the  harbinger  of  day),  and  in  the  latter  Hesperus. 

2680.  Apparent  diameter, — Owing  to  the  great  difference  be- 
tween its  distance  from  the  earth  at  inferior  and  superior  conjunc- 
tions, the  apparent  diameter  of  this  planet  varies  in  magnitude 
within  wide  limits.  At  superior  conjunction  it  is  only  lOr,  from 
which  to  inferior  conjunction  it  gradually  enlarges  until  it  becomes 
62^,  and  in  some  positions  even  so  much  as  76".  At  its  greatest 
elongation  its  apparent  diameter  is  about  25"|  and  at  its  mean  dis- 
tance 161". 

Thus,  when  the  planet  appears  as  a  thin  crescent  immediately  be- 
fore or  after  inferior  conjunction,  the  magnitude  is  such  that  the 
line  joining  the  cusps  is  the  30th  part  of  the  line  joining  the  cusps 
of  the  crescent  moon,  and  a  telescope  having  a  magnifying  power 
no  greater  than  30  will  show  it  with  an  apparent  size  equal  to  that 
of  Uic  crescent  moon  to  the  naked  eye. 


let  at  whith  Um  olvsmlHU  m  giovMlIj  mmk 
diffioaltjr,  du  imgnlst  oAeli  of  nAHtioa  talip 


.  Aieir  hmt  tiie  gnateat  doogatfoB  H 

tt  70,  and  near  superior  eonjunotiaa  Ma  of  180,  lb 

dbet. 

2681.  Diffiaikia  atlaidiiig  (k  Jd^i 
— NotwithstandiDK  this,  tha  mataat  £knltiit  I 
telcaoopia  obsarrabon  of  thia  planefc     Iti  iatanaa 
^,  and  agffravatea  all  the  optieal  !■]     '   " 

The  lowaJdtadea   '    "'    ■*       * 
eonatitate  another 

Aring  materialljr  with  the  appearaoee. 
BBqoeotl;  oontended  that  the  Mat  poailion  for  olwmliaH  ^m  il 
ia  near  saperior  eoojanetioii,  when  its  |diaae  ia  fUl,  mod  vkn  If 
proper  asmdieoU  it  maj  be  obaemd  at  middaj  i^dhm  m  UmA. 
giuia  of  the  BDti'i  diak. 

£682,  Seal  diamHer. — The  linear  valiM  of  1"  at  Tasp^  «l« 
aha  appeaia  as  a  thin  crenent  near  hn  inferior  ootjuMtion,  k 
26,250,000       ,„^    ., 
-5gg^  =  m-2»dea. 

~      mpannt 
her  real  diameter,  we  enall  have 

i>'=127-2  X  61=7760  milM. 
The  magDitnde  of  Tenoa  is,  therefore,  nearly  eqnal  to  that  td  Aa 
earth. 

2683.  3fatM  and  dentity. — By  the  methoda  explained  ia  (S6B9), 
it  has  been  ascertained  that  the  mass  of  Yenos  Is  grealar  than  wt 
of  the  earth  in  the  ratio  of  113  to  100 :  and  as  the  nlomes  ara 
nearly  equal,  their  densitiea  are  also  nearly  eanal, 

2684.  Saper/icial  gravilj/.  —  All  the  oondiliona  which  mBui  As 
gravity  of  bodies  oa  the  Burfaoe  of  Tenns  being  the  same,  or  naailj 
BO,  as  those  which  aSect  bodies  on  the  earth,  the  snpeifioial  gfni^ 
is  nearly  the  same. 

2685.  Solar  light  and  heat.  —  The  density  of  the  aolar  lajt  k 
greater  than  upon  the  earth  in  the  invetae  ratio  of  the  aqjum  tf 
the  nnmbers  7  and  10,  which  express  their  distanoea  from  the  an. 
The  intenuty  is,  therefore,  greater  at  Veoas  in  the  ratio  of  2  to  1. 

The  relative  apparent  magaitodes  of  the  snn'a  disk  at  Tenna  avd 
the  earth  are  represented  at  T  and  x,  ^.  751.    Owing  to  the 
vei^   small   eooenttidty  of  Iha 
I  orbit,  this  magnitada  ia  not  soh- 
jeot  to  any  very  senaiblo  nria- 

-pnbaVi 

Fif.  TEl.  moantaini.  —  Although  there  ti 

very  little  doabt  of  tha  &et  that 

tma  planet  has  a  dittmal  rotation  analogous  to  that  of  tba  miU^  ik 


THE  TEBBSSTRUL  PLANETS.  290 

obserratioDS  which  XDight  have  been  expected  to  demonstrate  it  in  a 
ntisfactory  manner  have  been  obstructed  by  the  causes  already  no- 
ticed (2631).  Nevertheless,  Gassini,  in  tbc  17th  century,  and 
Schrdter,  towards  the  close  of  the  18th,  with  instruments  very  infe- 
lior  to  the  telescopes  of  the  present  day,  deduced  from  the  phases 
1  period  of  rotation  in  complete  accordance  with  the  results  of  the 
most  recent  observations. 

These  astronomers  found  that  the  points  of  the  horns  of  the 
crescent  observed  between  inferior  conjunction  and  greatest  elonga- 
tion appeared  at  certain  moments  to  lose  their  sharpness,  and  to 
become  as  it  were  blunted.  This  appearance  was,  however,  of  very 
short  doration,  the  horn  after  some  minutes  always  recovering  its 
sharpness.  Such  an  etfect  would  obviously  be  produced  by  a  local 
irregularity  of  surface  on  the  planet,  such  as  a  lofty  mountain,  which 
womd  throw  a  long  shadow  over  that  part  of  the  surface  which 
would  form  the  point  of  the  horn.  Now,  admitting  this  to  be  the 
cause  of  the  phenomenon,  it  ought  to  be  reproduced  by  the  same 
mountaio  at  equal  intervals,  this  interval  being  the  time  of  rotation 
of  the  planet.  Such  a  periodical  recurrence  was  accordingly  as- 
certained. 

2687.  Obiervatian$  of  Cassiniy  Herschel,  and  Schrdter.  —  From 
inch  observations  the  elder  Gassini,  so  early  as  1667,  inferred  the 
time  of  rotation  of  the  planet  to  be  23"*  16"^,  a  period  not  very  dif- 
ferent from  that  of  the  earth.  Soon  after  this,  Bianchini,  an  Italian 
aitroDomer,  published  a  series  of  observations  tending  to  call  in 
doubt  the  result  obtained  by  Gassini,  and  showing  a  period  of  576 
honn.  Sir  William  Herschel  resumed  the  subject,  aided  by  bis 
powerful  telescopes,  in  1780,  but  without  arriving  at  any  satisfactory 
result,  except  the  fact  that  the  planet  is  invested  with  a  very  dense 
atmosphere.  He  found  the  cusps  (contrary  to  the  observations  of 
Caaaini|  and,  as  we  shall  see,  of  more  recent  astronomers)  always 
sharp,  and  free  from  irregularities.  Schrdter  made  a  series  of  most 
eUborate  observations  on  this  planet,  with  a  view  to  the  dctcrmina- 
tioD  of  its  rotation.  He  considered  not  only  that  he  saw  periodical 
changes  in  the  form  of  the  points  of  the  horns,  but  also  spotj?,  which 
had  sufl&cicDt  permanency  to  supply  satisfactory  indications  of  rota- 
tion. From  such  observations  he  inferred  tbc  time  of  rotation  to  be 
23^  21*"  7'98''.  From  observations  upon  the  horns,  he  iuferred 
also  that  the  southern  hemisphere  of  the  planet  was  more  mountain- 
ous than  the  northern ;  and  he  attempted,  from  observations  on  tho 
biuntoess  periodically  produced  on  the  southern  point  of  tbc  crescent, 
to  estimate  the  height  of  some  of  the  mountains,  which  be  inferred 
to  amount  to  the  almost  incredible  altitude  of  twenty-two  miles. 

2688.  OlaervcUioM  of  MM.  Betr  and  Madler  —  time  of  rota- 
Htm,  —  Although  the  estimate  of  the  planet's  rotation  resulting  from 
the  obserrations  of  Schrdter,  corroborating  those  of  Gassini,  ha%  be^ix 


800 


ABTROHOXT. 


gcnernlly  accepted  by  the  BdentiSo  world,  the  question  wu  not  re- 
gardcil  as  dcfiulti^ly  Bcttlcd ;  lad  a  wrieB  of  o^ir&tioiiB  wbb  made 
by  M.'tl.  13ccr  and  Madlcr,  between  1833  &nd  1836,  vhioh  vent  tu 
to  conGrai  the  conclusiona  of  Caasim  and  Schroter;  nnd  the  Elill 
more  recent  obsenations  of  De  Vioo  at  Rome  may  be  eonaidercd  u 
removing  all  doubt  that  tbe  period  of  the  planet's  rotftUon  does  Dot 
vary  much  from  23i''', 

•2ii80.  Beer  and  MwUrr's  diagrams  of  Venvt.  — In  fig.  'th'l, 
are  represented  a.  series  of  eighteen  diagranis  of  the  planet,  selected 
from  a  much  greater  number  mndo  by  MM.  Beer  and  Madlerit 
the  dates  indicated  above.     These  drawings  were  taken  when  the 


<<<((IUlC 


(((<(«<( 


Fig.  7=2. 

plunel  was  nppn>;icliing  inferior  conjunction,  the  plunet  being  cb- 
suFTud  cither  before  BuiK^et  or  during  twiliglit. 

If  the  Kurfacc  of  the  jilnnet  were  exempt  frum  eonsidemble  is- 
cquulities,  (he  eonc&vc  f<\p:  of  the  crescent  would  be  a  sensible  cllipH', 
aulijcet  to  110  other  dctic;ii.nev  of  perfect  regularity  and  aharpni**. 
save  Rueb  as  might  be  exjiluiocd  by  the  grudual  fuiutness  of  illusii- 
nuticin  due  to  the  utniOFphere  nf  Venus.  The  mere  inspectinn  i<t' 
tbe  diugrunis  is  enough  to  ^hutv  that  such  is  not  ibc  appeuniaee  >'^ 
the  clisc.  Irregularities  of  curvature  and  of  the  forms  of  the  eusf-s 
are  apparent,  which  eitn  only  arise  from  corrcspnuding  irrceulariu<:9 
of  the  Kurfuec  of  IJie  planet.  If  ilic  want  of  stiarpness  in  the  ham' 
of  the  crescent  ar'ise  frutu  any  efl'ect  prrnluccd  by  the  terrestrial  a'- 
uiusphcro  ou  the  optical  image  of  the  disc,  it  would  equally  iS^i't 
both  cus)R(.  tiovci'al  of  the  diagrams,  for  example,  yfyn.  I,  2,  i!,  L 
8,  IT),  17,  are  at  vari:iuce  with  i<uch  an  hypothesis,  the  cusps  bdi^ 
obviously  dllT.'rcMr  itj  i;>rm. 


THB  TERRESTRIAL  PLANETS.  801 

In  oonobonition  of  the  obserrations  of  Sohrdter,  it  was  ascertained 
that  the  southern  cusp  was  subject  to  greater  and  more  frequent 
changes  of  form  than  the  northern,  from  which  it  was  inferred  that 
the  Boathem  hemisphere  of  the  planet  is  the  more  mountainous. 
It  18  remarkable  that  the  same  character  is  found  to  prevail  on  the 
moon. 

It  was  not  only  observed  that  the  irregularities  of  the  concave 
edge  of  the  crescent  were  subject  to  a  change  visible  from  5"^  to  5"^-, 
bat  that  the  same  forms  were  reproduced  after  an  interval  of  23  i***, 
■abject  to  an  error  not  exceeding  from  5  to  10  minutes. 

2690.  More  recent  observaiions  of  De  Vico.  —  In  fine,  De  Yico, 
observing  at  a  still  later  date  at  Rome,  favoured  by  the  clear  sky  of 
Italy,  made  several  thousand  measurements  of  the  planet  in  its 
piiaM8|  the  general  result  of  which  is  in  such  complete  accordance 
vith  thorn  of  MM.  Beer  and  Midler,  that  the  fact  of  the  planet's 
RMitifla  may  now  be  regarded  as  satisfustorily  demonstrated,  and 
Ihat  ita  period  does  not  difier  much  from  23^  15"*. 

2081.  Direction  of  the  axis  of  rotation  unascertained.  —  If  such 
have  attended  the  mere  determination  of  the  rotation,  it 
ba  auQy  conoeived  that  those  which  have  attended  the  attempts 
to  anertain  the  direction  of  the  axis  of  rotation  have  been  much 
■on  iaanrmoontable.  The  observations  above  described,  by  which 
Ik  rotation  has  been  established,  supply  no  ground  by  which  the 
BieeftBon  of  the  axis  could  be  ascertained.  No  spot  has  been  seen 
im  direction  of  whose  motion  could  indicate  that  of  the  axis.  It 
eoDJectnred,  with  little  probability,  by  some  observers,  that  the 
was  inclined  to  the  orbit  at  the  angle  of  75^.  This  conjecture, 
however,  has  not  been  confirmed. 

2692.  Twilight  on  Venus  and  Mercury.  —  The  existence  of  an 
extensive  twilight  in  these  planets  has  been  well  ascertained.  By 
>baerving  the  concave  edge  of  the  crescent  which  corrcpponds  to  the 
boundary  of  the  illuminated  and  dark  hemispheres,  it  is  found  that 
the  enlightened  portion  does  not  terminate  suddenly,  but  there  is  a 
mdual  fadine  away  of  the  light  into  the  darkncs<3,  produced  by  the 
nnd  of  atmosphere  illuminated  by  the  sun  which  overhangs  a  part 
of  tho  dark  hemisphere,  and  produces  upon  it  the  phenomena  of 
twilight. 

Some  observers  have  seen  on  tho  dark  hemisphere  of  the  planet 
Venus  a  faint  reddish  and  grayish  light,  vi.sible  on  parts  too  distant 
from  the  illuminated  hemisphere  to  be  produced  by  the  light  of  the 
Ban.  It  was  conjectured  that  these  effects  are  indications  of  the  pltiy 
of  some  atmospheric  phenomena  in  this  planet  similar  to  the  aurora 
horealis. 

In  fine,  it  may  be  stated  generally,  that  so  far  as  relates  to  the 
physical  condition  of  the  inferior  planets,  the  whole  extent  of  our 
certain  knowledge  of  them  is,  that  they  are  glubcs  like  the  earth, 

III.  !'(> 


Stt  iflZBOVOiar. 

Olumiiiated  and  winned  by  the  son;  tiwi  Aeran  hwtiJ  iridi 
Atmoq>heTe8  probably  more  denae  than  that  of  tiM  aarth;  and  mm 
obaervitiona  londer  probaUe  the  OTJitmioe  of  Taii  BMiaaa  of  daaii 
cm  Yenua,  if  not  on  Menmiyi  analogy  jvatUba  the  InfcnMa  llal 
liquids  euBt  on  theae  planets. 

2698.  Spheroidal  /arm  imoaosrtouux^-^fii^pBBfsil  mUdNk^^^ 
One  of  the  phenomena  from  whidi  the  rotatkm,  as  well  aa  Ifaa  Aee- 
lion  oi  the  axis,  might  be  in&nedy  is  the  spheraidBl  ftm  e(  thi 
planet  To  ascertain  tlus  by  obsenrations  of  the  diak,  ife  mijiid  bs 
neoesaaiT  to  see  the  planet  with  a  loll  phase.  Baft  whm  the  iaMsr 
pbmets  ha^  that  phasoy  they  aie  near  superior  cioiiJDiioiis>|  mrf 
therefore  lost  in  the  solar  light.  It  has  been  Be?Brthaleaa  eoBlaaM^ 
that  when  Yenns  is  most  remote  from  her  node,  she  ia  safioisalir 
removed  from  the  plane  of  the  eeliptio  to  be  obsenrad  with  aMl  I 
telescope  at  noon  when  in  superior  eoigunetiaiL  No  ohasMttos^ 
however,  of  this  kind  has  ever  yet  been  mado^  and*  tlia  sphaiaiid 
form  of  the  planet  is  unasoertaiiied. 

Several  observers  of  the  last  two  eentoiies  eoDeoirad  ia 
ing  that  they  had  seen  a  satellite  of  Yenna.  Cssaini,  the 
imagmed  he  saw  such  a  body  near  the  planet  on  the  SSth  of  Ai- 
uary,  1672,  and  again  on  27th  of  August,  1686 ;  Short,  the  weD- 
known  optical  iDstrument  maker,  on  8d  November,  1740;  Mon- 
taigne, the  French  astronomer,  in  May,  1761 ;  several  obaerfen  ia 
March,  1764,  all  agree  in  reporting  observations  of  snob  a  body.  Ii 
each  case  the  phase  was  similar  to  that  of  Yenus,  and  the  mpgn^ 
diameter  about  a  fourth  of  that  of  the  planet  By  oolleoting  then 
observations,  Lambert  computed  the  orbit  of  the  supposed  satellite. 

In  opposition  to  all  this,  it  may  be  stated  that  notwithatandiBg 
the  immense  improvement  in  optical  instruments,  and  espeoiaUy  ia 
the  construction  of  telescopes  of  power  frr  surpassing  any  of  whidi 
the  observers  before  the  present  century  were  in  possession,  no  tnos 
of  such  a  body  has  been  detected,  although  observers  have  inorssssl 
in  number,  activity,  and  vigilance,  in  a  proportion  mater  atiU  thsa 
that  of  the  improvement  of  telescopes.  It  must,  Uierefore^  be  eo^ 
eluded,  at  least  for  the  present,  that  the  supposed  appearanofli 
recorded  by  former  observers  were  illusive. 

III.  Mars. 

2694.  Position  in  the  system.  —  Proceeding  outwards  from  tiM 
sun,  the  third  planet  in  the  order  of  distance  is  the  Earth.  Tbt 
fourth  in  order,  whose  orbit  circumscribes  that  of  the  earth,  is  the 
planet  Mars. 

2695.  Period,  —  The  synodic  period  of  Mars  is  found  by  ober- 
vation  to  be  780  days.  It  follows  from  this  that  if  p  express  the 
periodic  time  of  the  planet  in  days,  we  shall  have 


THE  TERRB8TRIAL  PLANETS.  W8 

p  "  365       780  ""  687' 

The  periodio  time  of  M%rs  is  therefore  687  days,  or,  as  appears  by 
Bore  exact  methods  of  calculation  and  observatioD,  686'97d  days. 

The  earth's  period  being  taken  as  the  unit,  the  period  of  Mars 
will  therefore  be  1*881. 

2696.  DiMtance,  —  To  compute  by  the  Harmonic  Law  the  mean 
distance  of  Mars  firom  the  sun,  we  have  therefore 

l-88«  =  l-624fl». 

The  mean  distance  is  therefore  1*5246,  that  of  the  earth  being  the 
VBift,  and  the  mean  distance  in  miles  is 

95,000,000  X  1-624  =  144,780,000, 

or  about  144}  millions  of  miles. 

2697.  EocetUridhf — mean  and  extreme  distanee$  from  the 
earth, — The  ecceDtrioity  of  the  orlnt  of  Mars  being  about  0*09, 
the  distance  is  subject  to  a  variation,  the  extreme  amount  of  which 
ii  less  than  one-tenth  of  its  mean  value.  The  extreme  distances 
ire 

144}  -{-IS  ss  157|  million  miles  in  aphelion. 
144} —  13  ^  131}  million  miles  in  perihelion. 

It  appears,  therefore,  that  the  mean  distances  of  the  planet  from  the 

earth  are 

In  Opposition 144} —  95  =  49}  million  miles. 

In  Conjunction 144}  -f-  ^5  =  239}  million  miles. 

In  Qoadrature a=  109  million  miles. 

These  distances  are  subject  to  yariation,  whose  extreme  limit  is 
iboat  15  millions  of  miles,  owing  to  the  combined  effects  of  the 
eeeentri<nties  of  the  two  orbits,  ^though  the  mean  distance  of  the 
pbnet  in  opposition  from  the  earth  is  about  half  the  distance  of  the 
nn,  it  may  in  certain  positions  of  the  orbit  come  within  a  distance 
of  85  hundredths  of  the  sun's  distance.  In  the  opposition  which 
took  place  in  September,  1830,  the  distance  of  the  planet  was  only 
38  hundredths  of  the  sun's  mean  distance. 

'2698.  Heliocentric  and  sj/nodic  motions,  —  The  mean  daily  He- 
liocentric motion  of  Mars  is  (2568) 

_  12%000  ^  jg„.gg  ^  3j,j 

Oo7 

The  mean  synodic  motion  is  therefore  (2569) 

ff  =  i  —  a  =  3548  —  1886  =  16"-62  =  2r-7. 

2699.  Scale  of  orbit  relativeli/  to  that  of  the  earth.  —  If  8,  fig, 
^53,  represent  the  position  of  the  sun,  and  s  m  the  distance  of  Mars, 
Qke  orbit  of  the  earth  will  be  represented  by  e  j!'  ^"  £'. 


S700.  IKi&te^At^ 
MKepeHod. — Tkt  Mttt  m 
ti  it"  when  Hm  n  in  mb- 
joDotion,  at  ^  wboi  in  ^i» 
dntnra  wart  of  &•  na,  at  i 
when  ID  (^ipodtioB,  aad  at  ^ 


Hie  anria  of  alowlin 
Bl^H  being  90°,  a^Aa 
mean  nhia  «f  aK  briM 
162,  thatoria'lidv^ 
ptBaNd  b;  1,  it  ftDom  iW 
the  angle  ^B  M  wilt  ka  abort 
48°,  and  therefim  ^b^9 
180"  — 48"  =  188°. 

SitiM  the  nuudie  pniia 

is  780  daja,  the  maaa  tiii 

_,    „.  between  qnadraton  aad  • 

il.780  =  104d.j,; 
and  tbe  mean  limo  between  qnidratnre  and  conjanotion  will  be 
g?x780  =  286d.j.. 

2701.  Apparent  motion.  —  The  vuiouB  changes  of  the  ai 
posiUons  of  tbe  planet  and  bud  during  the  ajnodio  pen 
therefore,  bo  easily  explained.     At  oonjunction  the  earth 
1^",  the  planet  and  sun  paaa  the  meridian  together.     In 
the  planet  being  above  tbe  horizon  oolj  daring  the  day,  la  ui 
After  conjunction,  the  planet  paases  the  meridian  in  the 
and  ia  therefore  visible  above  the  eastern  boriion  before  annnae.    iw- 
fore  conjunction  it  passes  the  meridian  in  the  afternoon,  aad  il 
therefore  visible  above  the  western  horiion  after  sonaet 

At  tbe  time  of  the  western  quadrature,  the  earth  bong  at  x",  tt> 
planet  passes  tbe  meridian  about  6  A.  H.,  and  at  the  tima  of  weatsi 
qnadTxture,  the  earth  being  at  e",  it  passes  the  meridian  abont  6  P.  K- 
The  planet  baa  these  positions  abont  286  daya,  more  or  loi^  aftv 
and  before  ite  conji 


THE  TBRRBSTRIAL  PLANETS. 


305 


wai  k  iherefore  above  the  horuon  chiefly  duriDg  the  earlier  part 
ef  the  night 

The  interval  daring  which  it  is  visible  more  or  less  in  the  absence 
«f  the  snn,  being  that  daring  which  it  passes  from  western  to  eastern 
eoadntare  throagh  opposition  is,  in  the  case  of  Mars^  104  x 
2  =  208  days. 

2702.  Statiom  and  reirogresnon.  —  The  elongations  at  which 
Km  is  stationary,  and  the  lengths  of  his  arc  of  retrogression,  vary 
to  some  extent  with  the  distances  of  the  planet  from  the  san  and 
«rth,  which  distances  depend  on  the  ellipticity  of  the  two  orbits, 
ni  the  direction  of  their  major  axes.     In  1854,  Mars  will  be  in 

rntioQ  on  Isi  March,  and  will  be  stationary  on  the  17th  January 
10th  April.     The  right  ascension  on  these  days  will  be. 


17  Jan R.  A. 


11»^  19--  32'- 


Xw  ^^pni  ••••••*  K.  A.    •..••.••.••.••••....•    J.V         4       oo 


14     36 


It  follows,  therefore,  that  the  extent  of  retrogression  in  right 
tieension  will  then  be  14^  30'*,  which  reduced  to  angular  magni- 
tude is 

(14--  36'-)  X  15  =  219'  =  3°  39'. 

2703.  Phofet.  —  At  opposition  and  conjunction  the  same  hemi- 
sphere being  turned  to  the  earth  and  sun,  the  planet  appears  with 
a  full  phase.  In  all  other  positions  the  lines  drawn  from  the 
planet  to  the  earth  and  sun,  making  with  each  other  an  acute  angle 
of  greater  or  less  magnitude,  the  phase  will  be  deficient  of  complete 
lolness,  and  the  planet  will  be  gibbous ;  the  more  so  the  nearer  it  is 
to  its  qaadratare,  in  which  position  the  lines  drawn  to  the  earth  and 
san  make  the  greatest  possible  angle,  which  being  the  complement 
3f  <"  8  M,  will  be  90**  —  48°  =  42°.     Of  the  entire  hemisphere 

presented  to  the  earth,  138°  will  therefore  be 
enlightened  and  42°  dark.  The  corresponding 
form  of  the  disk,  as  can  easily  be  deduced 
from  the  common  principles  of  projection,  will 
be  that  which  is  represented  in  fig.  754,  the 
dark  part  being  indicated  by  the  dotted  line. 

The  gibbosity  will  be  less  the  nearer  the 
planet  approocbes  to  opposition  or  conjunction. 
3704.  Apparent  and  real  diameter.  —  Tbo 
apparent  diameter  of  Mars  in  opposition  varies 
between  rather  wide  limits,  in  con.«er|uence  of  the  variation  of  its 
distance  from  the  earth  in  that  position,  arising  from  the  causes  ex- 
pbuDed  above.     When  at  its  mean  dibtance  at  opposition,  the  appa- 

26* 


Fig.  754. 


to8"-7. 

In  1880,  KKxt  after  oppontioti,  when  ill  dkitoBM  tfom  ^  anA 
KM  88A  million  of  duIn,  it  exhilatad  ft  4il>mrtlf  tt  SS"]  tin 
Gnaur  woe  of  1"  kt  lltat  distppoa  b^ng 

8&400000      ,._,    _ 

-g5^55-=18ftrȴH 

the  dkmeter  i/ of  the  planet  most  be 

D'  =  186-7  X  23  =  4Q8&  nOk*. 
2706.  FobuMi.  — If  T'bethe  Wume,th4to(the«u&hdwT, 
Whftre 

▼*_  (4085  V       ■ 

■  treo&l 

lite  TohiiiM  i«  thetefore  less  than  the  eerenth  put  of  that  of  At 
earth.    The  lelatiTe  TolnmeB  of  Han  and  tlie  euth  aia  repfaHBliJ      ' 
at  H  and  t,J!g.  765.  ■- 

2706.  Mau  cmd  detutty.  —  By  the  metfa 
heen  uoertaiiwd  that  the  maaa  of  Mars  is  ] 
Itaof  1000. 

We  shall  have  for  the  <Icnsitj,  therefore, 


B  enlaiDe^il  !■ 
>,  that  of  Aa  «lk 


145 
^183' 


:1'09. 


Tlie  deosiW  is  very  nearly  equal,  therefore,  to  that  of  the  earth 

2707.  Suptrficial  gravHy. — TLo  snper&ial  gi»Tit;  bong  d|IV> 
mined  bj  the  formula  (2639),  ire  shall  have 

*'  =  0M. 

9 
It  appears,  therefore,  that  the  force  of  gravity  on  the  anrfint  ^ 
Hars  is  a  little  more  than  half  ita  inteamty  on  the  snr&oe  of  At      ■ 
earth. 

2708.  Solar  ligU  and  Ixeat.  —  The  mean  distuice  of  the  OiA 
from  the  Ban  being  leai  tktt 

I  that  of  Mart  lo  the  nlio 
1  ,of  10  to  15,  the  appaml 
I  diameter  of  the  ann  a)  MH 
I  from  Mara  will  be  lev  thu 
I  ita  diameter  as  eeeo.  fM 
the  earth  in  the  same  ntiO' 
X,  Jig.  75A,  repewt 
■■  apparent  disk  of  tbt 
son  as  aeen  from  the  earth,  M  vill  represent  its  apparent  diak  ai  «V 
from  Hara. 


Fig.TS6. 


THB  TERRBSTRUL  PLAKEXa  807 

Sinoe  die  denaity  of  the  solar  radiation  deoreaaes  as  the  square 
'  the  distance  increases,  its  density  at  Mars  will  be  less  than  at  the 
nth  in  the  ratio  of  4  to  9. 

So  iar  as  the  illuminating  and  heating  powers  of  the  solar  rays 
»pend  on  their  denuty,  they  willj  therefore,  be  less  in  the  same 
roportion. 

2709.  Botatum. — There  is  no  body  of  the  solar  system,  the 
iQon  alone  excepted,  which  has  been  submitted  to  so  rigorous  and 
locessful  telescopic  examination  as  Mars.  Its  proximity  to  the 
uth  in  opposition,  when  it  is  seen  on  the  meridian  at  midnight 
ith  a  full  phase,  affords  great  facility  for  this  kiud  of  observation. 

By  observing  the  permanent  lineaments  of  light  and  shade  ex- 
(bited  by  the  disk,  its  rotation  on  its  axis  can  be  distinctly  seen, 
id  has  been  ascertained  to  take  place  in  24'''  37"^  lO**,  the  axis  on 
hich  it  revolTes  appearing  to  be  inclined  to  the  plane  of  the  planet's 
rbit  at  an  angle  of  28^  27'.  The  exact  direction  of  the  axis  is, 
owever,  still  subject  to  some  uncertainty. 

2710.  Dajfi  and  nights.  —  It  thus  appears  that  the*  days  and 
ights  in  Mars  are  nearly  the  same  as  on  the  earth,  that  the  year 
\  diversified  by  seasons,  and  the  surface  of  the  planet  by  zones  and 
dmates  not  very  different  from  those  which  prevail  on  our  globe. 
*he  tropics,  instead  of  bein^  23''  28',  are  28''  27'  from  the  equar 
Dr,  and  the  polar  circles  are  in  the  same  proportion  more  extended. 

2711.  Seaiotu  and  dimates.  —  The  year  consists  of  668  Martial 
lays  and  16  hours;  the  Martial  being  longer  than  the  terrestrial  day 
n  the  ratio  of  100  to  97. 

Owinff  to  the  eccentricity  of  the  planet's  orbit,  the  summer  on 
he  northern  hemisphere  is  shorter  than  on  the  southern  in  the  ratio 
»f  100  to  79,  but  owing  to  the  greater  proximity  of  the  sun,  the  in- 
lensity  of  its  light  and  heat  during  tLe  shorter  northern  summer  is 
greater  than  during  the  longer  southern  summer  in  the  ratio  of  145 
»  100.  From  the  same  causes,  the  longer  northern  winter  is  less 
aelement  than  the  shorter  southern  winter  in  the  same  proportion. 

There  is  thus  a  complete  compensation  in  both  seasons  in  the  two 
lemispheres. 

The  duration  of  the  seasons  in  Martial  days  in  the  northern  hemi- 
iphere  is  as  follows : — spring  192,  summer  180,  autumn  150,  winter 
147. 

2712.  Observations  and  researches  of  Messrs,  Beer  and  M&dler, 
—  It  ia  mainly  to  the  persevering  labours  of  these  eminent  obser- 
ren  that  we  are  indebted  for  all  the  physical  information  we  possess 
nipecting  the  condition  of  the  sur&co  of  this  planet.  Their  ob- 
lervations,  commenced  at  an  early  epoch,  were  regularly  organised 
It  the  time  of  the  opposition  of  1830,  with  a  view  to  ascertain  with 
certainty  and  precision  the  time  of  rotation  of  the  planet,  the  posi- 
tion of  its  axis,  and|  so  far  as  might  be  practicable,  a  survey  of  its 


nibe*.  Th«M  obnTtBtimw  Imts  beea  contiBud  totag  no;  n 
eoeding  oppondon,  id  vhich  llie  plutt  {laTing  nortliara  ■*-*'-*^ 
roM  to  ft  auffident  kltitnde,  and  via  made  TinUs  b  a  tdaaeon  t 

n I -t    I. J   -    I.-U  t—i,    '■     '    l-__*i. II i n 


Fnnnhoer,  of  fbnr  and  a  half  feet  (bad  bnglL  panUaetacaD 
■omted,  and  moved  \rj  elodwoA,  ao  aa  to  keep  us  planet  is  0 
fcld  of  view  notwilhatanding  the  dinnutl  motioB  a  the  e«<l 


WHh  tbb  iDstrament  they  wen  emUed  to  aae  a  magni^g  p 
Cf  800,  and  aa  the  diak  <tf  the  planet  anbtended  m  18B0  ■  -nm 
angle  of  22",  it  ma,  when  thoa  manifled,  newed  mider  an  an^ 
of  SSOC  or  110',  bnng  neariy  fear  tuaea  Uie  mppannt  diameter  g 
the  moon. 

8718.  Artograpkie  dtaraet^r.- — That-many  6t  the  linwBMl 
ohaarred  an  areographio,  and  not  atmoapfaerie,  u  estaUiabed  beyoD 
all  eonteatation  by  tbdr  permanew?.  They  an  not  alwaye  Tiiilili 
and  when  tiaible  not  alwaya  eqaally  dutinot;  bat  are  obaened  t 
'  t  how  diataot  may  be  the  iDtatnl 
tad  to  examination.  The  elabont 
I  of  HH.  Beer  and  Midler,  which  am 
»eneed  with  the  oppoaitiai  of  1880,  were  eontinaed  with  noweeiigi 
aaaidoity  in  erery  suooeeding  of^odtion  ot  the  planet  for  twtln 
yeara,  bo  &r  aa  the  Taiying  deolination  and  the  atate  of  the  veatbe 
at  the  epooha  of  the  oppositioD  permitted.  The  B&me  spot*,  cl» 
tacterised  by  the  same  forma,  and  the  same  varieties  of  light  m 
abade,  were  seen  agun  and  again  in  each  Bocceediog  oppositini 
Changes  of  appearance  were  manifeit,  but  through  tboee  change 
the  permanent  features  of  the  plaoet  were  always  discerned;  jnS 
as  the  seas  and  continents  of  the  earth  may  be  imagioed  to  be  dii 
tinguisbable  tbroogb  the  occamoDal  openings  in  the  clouds  of  om 
atmosphere  by  a  telcscopio  obserrer  of  Mara. 

2714-  TeUtcopic  viewt  of  Mart  —  areoffraphie  ehartt  o/ ihe  tv 
AetnupAerei .  —  A  large  collection  of  drawings  of  the  various  beni 
spheres  of  Mars  preaented  to  the  observer  has  beCD  made  by  HM 
Beer  and  Midler.  Thirty-five  were  made  during  the  oppositioii  ol 
1830,  upwards  of  thirty  during  that  of  1837,  and  forty  during  At 
of  1841,  from  a  comparison  of  which  charts  were  made,  sbovinj 
the  permanent  areographic  lineaoients  of  the  northern  and  sonthen 
hemisphere. 

Id  Plate  ym.  we  bavo  given  six  views,  selected  from  those  o 
Beer  and  Madler,  with  the  dates  subjoined.  In  Plate  IX.  u 
given  the  areographic  charts  of  the  tiro  hemispheres.  It  will  li 
b'oserved,  that  as  each  spot  approaches  the  edge  of  the  dink  its  appi 
nut  form  is  modified  by  the  effect  of  fore-shortening,  owing  to  tl 
obliquity  (if  the  surface  of  the  planet  to  the  visual  ray. 

2715.  Polar  tnoio  observed.  —  All  the  lineaments  exhibited  i 
these  dcKwings  were  found  to  be  periuanent,  except  the  remarkab 
white  spota  which  cover  the  polar  te^oDS.    These  circular  arei 


PUBLIC  U^ 


flCraOJECTlONBl 


^^^B^^ta^ 

THE  TSRBBSTBfAL  PLANBTa  809 

reseDted  the  appeaniice  of  a  daszling  whiteness,  and  one  of  ihem 
as  so  exactly  defined  and  so  sharply  terminated,  that  it  seemed 
ke  the  full  disk  of  a  small  and  very  brilliant  planet  projected  upon 
le  disk,  and  near  the  edge  of  a  larger  and  darker  one.  The  ap- 
earance,  position,  and  changes  of  these  white  polar  spots  have  sng- 
ested  to  all  the  observers  who  have  witnessed  them,  the  supposi- 
on  that  they  proceed  from  the  polar  snows  accumulated  during 
le  long  winter,  and  which,  during  the  equally  protracted  summer, 
Y  exposure  to  the  solar  rays,  more  full  by  7^  degrees  than  at  the 
oles  of  the  earth,  are  partially  dissolved,  so  that  the  diameter  of 
le  snow  circle  is  diminished. 
The  increase  and  diminution  of  this  white  circle  takes  pkoe  at 
pochs  and  in  positions  of  the  axis  of  the  planet,  such  as  are  in 
omplete  accordance  with  this  supposition. 

2716.  Position  of  areographic  meridians  determined. — ^The  leg 
ad  foot-shaped  spot  marked  pn  in  the  southern  hemisphere,  was 
isUnctly  seen  and  delineated  in  all  the  oppositions.  This  was  one 
f  the  spots  from  the  apparent  motion  of  which  the  time  of  rota- 
ion  was  deduced. 

The  spot  a  in  the  southern  hemisphere  connected  with  a  large 
djacent  spot  by  a  sinuous  line,  was  also  one  of  those  whose  position 
ns  most  satisfactorily  established.  This  spot  was  selected  as  the 
observatory  of  Greenwich  has  been  upon  the  earth,  to  mark  the 
neridian  from  which  longitudes  are  reckoned. 

The  spot  e/A,  chiefly  situate  in  the  southern,  but  projecting  into 
the  northern  hemisphere  between  the  90th  and  105th  degrees  of 
'Oogitude,  was  also  well  observed  on  repeated  occasions. 

According  to  Madler,  the  reddish  parts  of  the  disk  are  chiefly 
iiose  which  correspond  to  40^  long,  and  15^  lat.  S. 

The  two  concentric  dotted  circles  marked  round  the  south  pole 
adicate  the  limits  of  the  white  polar  spot  as  seen  on  different  occa- 
oona  in  1830  and  1837.  The  redness  of  this  planet  is  much  more 
"emarkable  to  the  naked  eye  than  when  viewed  with  the  telescope. 
In  some  cases,  during  the  observations  of  MM.  Beer  and  M&dler, 
U)  redness  was  discoverable,  and  when  it  was  perceived  it  was  so 
lint  that  different  observers  at  the  same  moment  were  not  agreed 
«  to  its  existence.  It  was  found  that  the  prevailing  colour  of  the 
•pots  was  generally  yellow  rather  than  red. 

Independently  of  any  effect  which  could  be  ascribed  to  projection 
IT  foreshortening,  it  was  found  that  the  lineaments  were  always  seen 
rith  much  greater  distinctness  near  the  centre  of  the  disk  than  to- 
rards  its  borders.  This  is  precisely  the  effect  which  might  be  ex- 
)ected  from  a  dense  atmosphere  surrounding  the  planet. 

2717.  Possible  satellite  of  Mars.  —  Analogy  naturally  suggests 
^  probability  that  the  planet  Mars  might  have  a  moon.  These 
^tteadaotB  appear  to  be  supplied  to  the  planets  in  augmented  nam« 


810  ASTRONOMY. 

ben  aa  they  recede  from  the  sua;  tnd  if  ihia  iiial<^  were  eon- 
plete.  it  would  joetify  the  inferenoe  that  Han  miiat  ai  kaat  ham 
one,  oeiog  more  remote  from  the  sun  than  the  earth,  wbUk  h 
pUed  with  a  aatellite.  No  moon  has  ever  been  diaoovend  in 
with  M arB.  It  haa,  howeyer,  been  contended  that  we  am  Ml 
fore  to  eonohide  that  the  pknet  ia  deatitate  of  aooh  an  npparfaga: 
Ibr  aa  all  aeoondary  planeta  are  mnch  leaa  than  their  primariei^  w 
aa  Man  ia  by  fiur  the  amalleet  of  the  anperior  phneta,  ita  anlallll^ 
if  Boeh  exiatody  mnat  be  extremely  amalL  The  seoood  aaleHilB  « 
Jafuter  ia  only  the  forty-third  part  of  the  diameter  ef  the  planet; 
and  a  satellite  which  would  only  be  the  fbrty-third  part  of  Ae  A 
ameter  of  Mara,  would  be  under  one  hundred  milea  in  diamelir. 
Buch  an  object  could  scarcely  be  discovered  even  1^  powofid  lel^ 
scopes,  especially  if  it  do  not  recede  fiur  from  the  diak  of  As 
planet 

The  frot  that  one  of  the  aatellitea  of  Saturn  haa  been  diaeofwai 
only  within  the  last  few  yean,  rendera  it  not  altogether  imprphaMi 
that  A  aatellite  of  Man  may  yet  be  disooyered. 


CHAP.  xrv. 

THE  FLANST0ID8. 

2718.  A  vacant  place  in  the  planetary  tertes.  —  At  a  Teiy  eiHy 
epoch  ID  the  progress  of  astronomy  it  was  observed  that  the  pio- 
gression  of  the  distaDces  of  the  planets  from  the  sun  was  charaeto^ 
ised  by  a  remarkable  numerical  harmony,  in  which  neverthelesi  a 
breach  of  continuity  existed  between  Mara  and  Jupiter.  This 
arithmetical  progression  was  firet  loosely  noticed  by  Kepler,  bnt  it 
was  not  uDtil  towards  the  close  of  the  last  century  that  the  mora 
exact  conditions  of  the  law  and  the  close  degree  of  approximatioB 
with  which  it  was  fulfilled,  with  the  exception  just  noticed,  waa  foUy 
explained. 

This  numerical  relation  prevails  between  the  distances  of  the  sno- 
cessive  orbits  of  the  other  planets  measured  from  that  of  the  Sist 
planet.  Mercury.  It  was  observed  that  such  distanced  formed  veiy 
nearly  a  series  in  duple  progression ;  so  that  each  dbtance  ia  twice 
the  preceding  one,  with  the  sole  exception  already  mentioned.  Al- 
though this  law  is  not  fulfilled  like  those  of  Kepler,  with  numerical 
precision,  there  is  nevertheless  so  striking  an  approximation  to  it  aa 
to  produce  a  strong  impression  that  it  must  be  founded  upon  aoniflt 
physical  cause  and  not  merely  accidental.  To  show  the  near  ap^ 
proximation  to  its  exact  fulfilment,  we  have  placed  in  the  fbUowing 


THE  PLANETOIDS. 


311 


tMe  ihe  Biiooesnon  of  calculated  distances  iVom  Mercury's  orbit, 
which  will  exact] J  fulfil  it  in  juxtaposition  with  the  actual  distances 
of  the  pUnetSy  the  earth's  distance  from  the  sun  being  the  unit. 


g^^^^^^^M  I^^A^^ri^  ^kmmm  M«fl^M*w 

Actul  INrtuMt  frrai  Itewrr. 

vOT^H  ••••■•■»••••■•■■•■■••«•■••••■•■•■«••••••• 

■wth « 

lion 

0-3302 
0-6724 
1-3448 
2-6896 
6-3792 
10-7684 
21*6168 

0-3862 
0-6129 
1-1366 

4-8157 

9-1617 

18^063 

AWmmt  plaavi  - 

JopiUr - 

wDaOOb  •■••••  •■•■»■••«■•■■•■•••••••••  M  ■••■••• 

By  comparing  these  numbers^  it  will  be  apparent  that  although 
the  succession  of  dbtances  does  not  correspond  precisely  with  a  nu- 
Berieal  series  in  duple  progression,  there  is  nevertheless  a  certain 
approach  to  such  a  series,  and  at  all  events  a  glaring  breach  of  con- 
tmoity  between  Mars  and  Jupiter.  / 

Towards  the  close  of  the  last  century,  professor  Bode  of  Berlin 
revived  this  question  of  a  deficient  planet,  and  gave  the  numerical 
progression  which  indicated  its  absence  in  the  form  in  which  it  has 
just  been  stated;  and  an  association  of  astronomers  was  formed 
Under  the  auspices  of  the  celebrated  Baron  de  Zach  of  Gbtha,  for 
the  express  purpose  of  organising  and  prosecuting  a  course  of  obser- 
ration,  with  the  special  purpose  of  searching  for  the  supposed  undis- 
covered member  of  the  solar  system.  The  very  remarkable  results 
which  have  followed  this  measure,  the  consequences  of  which  have 
not  even  jet  been  fully  developed,  will  presently  be  apparent. 

2719.  Ducovery  of  Ceres.  —  On  the  first  day  of  the  present 
oentniT,  Professor  Piazzi  observing  in  the  fine  serene  sky  of  Palermo, 
Doticed  a  small  star  of  about  the  7th  or  8  th  magnitude  which  was 
not  registered  in  the  catalogues.  On  the  night  of  the  2nd  again  ob- 
serving it,  he  found  that  its  position  relative  to  the  surrounding  stars 
was  sensiblj  changed.  The  object  appearing  to  be  invested  with  a 
Debaloos  base,  he  took  it  at  firet  for  a  comet,  and  announced  it  as 
such  to  the  scientific  world.  Its  orbit  being  however  computed  by 
Professor  Gauss,  of  Gdttingen,  it  was  found  to  have  a  period  of 
1652  days,  and  a  mean  dbtance  from  the  sun  expressed  by  2*735, 
that  of  the  earth  being  1.  ^ 

By  comparing  this  distance  with  that  given  in  the  preceding  table 
at  which  a  planet  was  presumed  to  be  absent,  it  will  be  seen  that 
the  object  thus  discovered  filled  the  place  with  striking  arithmetical 
precision. 

Piaxzi  nve  to  this  new  member  of  the  system  the  name  Ceres. 

2720.  Discovery  of  Pallas.  —  Soon  after  the  discovery  of  Ceres 
the  planet  pasnng  into  conjunction  ceased  to  be  visible.    In  search- 


Ids  fbr  it  iftor  emeri^iK  from  Uw  Mm*!  imji  in  MnA  1 

Oiben  noticed  OB  Uie  28Ui  ■  unall  itir  b  Oa « »--•-- 

at  A  place  vrhioii  tie  had  examined  in  the  ti     ,  _ 

wbera  he  knew  that  no  nwb  otgeet  waa  Am  uemntT  tt  t^fmmi 
u  a  atar  ef  the  aeventh  magnitad^  the  ff^itt*  whitfa  k  vyUi 
without  a  teleaet^.  In  the  eoDiae  <x  a  far  hema  he  Ibaal  Ik  jt- 
■ition  viiibl; eban|[ed  in rehtioa  to  tfce  tamoaiiaadtaa.  b fa, 
the  otjeot  prond  to  be  another  planet  bearing  »  itSki^  nadqir  ^ 
Cana,  and  vbat  was  then  totally  nnpraeemted  in  thn  ^jMH, 
moving  in  aa  orlnt  at  very  nearly  the  game  mean  liiafanwi  ftoH  tta . 
■on,  and  liaviiig  tbenfiwe  nearly  tlie  aame  period. 

Dr.  Olbera  called  this  planet  PaiLas. 

2721.   OBier^  h^padtaiM  o/aJradmndiilcmtL-'nkAtm- 
KtKBoa,  eombined  with  the  exe^itional  minntenaH  of  timm  In 
planete,  anggeated  to  Olben  the  atartling,  and  then,  aa  it  mnat  km 
upeared,  eztravagaDtly  improbable  byjiothaaia,  that  a  n^  jhHt  - 
«K  the  ordinRiT  magnitade  extated  fbraierly  at  the  rliitaiiiailiiAiki 
hyBode's  anuocy, — that  it  waa  broken  into  amall  fiumaak  dikt 
by  ioteraal  ezptaaion  from  aome  eanae  analcwooa  to  twomm  Mlia^    ' 
or  by  oollision  with  a  comet, — that  Cerea  and  Pallaa  wen  two  af  ill    - 
&agmeDls,  Rod  in  fine,  that  it  wu  very  likely  that  many  other  fiw- 
menta,  emaller  still,  were  revolviog  in  similar  orbits,  many  of  ahin 
migbt  reward  the  labour  of  fnture  observers  whg  might  diieet  ill ' 
attention  to  these  regions  of  the  firmament. 

In  support  of  this  ourioua  conjecture  it  was  urged  that  in  the  bhi  i 
of  sach  a  ostaatrophe  as  was  involved  in  the  suppositioD,  ''  * 
meets,  according  to  the  established  laws  of  physios,  would  u 
continue  to  revolve  in  orbits,  not  differing  muoh  in  thdr  ai 
distances  from  that  of  the  original  planet  j  that  the  obliqnitieaof  tk  f 
orbits  to  each  other  and  to  that  of  the  origioal  planet  m^  i»  f 
subject  to  a  wider  limitj  tbat  the  eccentricities  mii^t  also  hara  it-  f 
oeptional  magDitades  ;  and,  finally,  that  such  booiee  might  be  U-  h 
pected  to  have  magnitudes  so  iodefioitely  minute  as  to  be  oat  of  iD  L 
analogy  or  comparison,  not  only  with  the  other  primary  planets,  bat  L 
even  with  the  smallest  of  the  secondary  ones.  [i 

Ceres  and  Pallas  both  were  so  small  as  to  elude  all  attempta  (o  l| 
estimate  tbeir  diameters,  real  or  apparent.  They  appeued  lib  I 
■tellar  points  witb  no  appreciable  disk,  hot  surronnded  with  a  ndia-  y 
lous  haziness,  which  would  have  rendered  very  uocertain  any  nti-  |f 
auremcut  of  an  object  so  minute.  Sir  W.  Herachel  thought  tbif  : 
Pallas  did  not  exceed  75  miles  in  diameter.  Otbeta  have  adnttttd  ^ 
that  it  might  measure  a  few  hundred  miles.     Cerea  is  still  Bmallv.'  jk> 

The  obliquity  of  the  orbit  of  Ceres  to  the  plane  of  the  eeliplis  a  f- 
abovo  101°,  Eiod  tbat  of  Pallas  more  than  34}°.  Both  pUiMl^  ; 
therefore,  when  most  remote  from  the  ecliptic,  pass  &r  bennd  Ik  i 
Siaita  !)f  the  zodiac^  and  diAer  in  obliquity  horn  each  olMr  ij* 


1 


THX  PLAHXTOIDS.  818 

&r  exeeeding  the  entire  inclinition  of  uiy  of  the  older 

li  WM  fbrther  observed  by  Dr.  Olbers,  that  at  a  point  near  the 
node  ci  Pallas  the  orbita  of  the  two  planets  very  nearly 


■iitilj 


Thus  it  appeared  that  all  the  conditions  which  rendered  these 
lofiea  exceptional,  and  in  which  they  differed  from  the  other  mem- 
ten  of  the  solar  system,  were  precisely  those  which  were  consistent 
irilh  the  hypothesis  of  their  origin  advanced  by  Dr.  Olbers. 

2722.  Ditcovery  of  Juno.  —  A  year  and  a  half  elapsed  before 
tty  farther  discoyeiy  was  produced  to  favour  this  hypothesis.  Mean- 
vkQe,  observers  did  not  relax  their  zeal  and  their  labours,  and  on 
fapL  I9  1804,  at  ten  o'clock,  p.m..  Professor  Harding,  of  Lilien- 
id,  discovered  another  minute  planet,  which  observation  soon 
Itoved  to  aeree  in  all  its  essential  conditions  with  the  hypothesis  of 
iNbaVy  having  a  mean  distance  very  nearly  equal  to  those  of  Ceres 
Pdlas,  an  exceptional  obliquity  of  13^,  and  a  considerable 
tiieity. 

This  planet  was  named  Juno. 

Jnno  has  ^e  appearance  of  a  star  of  the  8th  magnitude,  and  a 
nddish  colour,  it  was  discovered  with  a  very  ordinary  telescope 
of  80  inches  focal  length  and  2  inches  aperture. 

2728.  Di9cov€rif  of  Vesta.  — On  the  29th  of  March,  1807,  Dr. 
Olbers  discovered  another  planet  under  circunistauccs  precisely 
sfanilar  to  those  already  rclatc<l  in  the  cases  of  the  former  discoveries. 
The  name  Vesta  was  given  to  this  planet,  which,  in  its  minute 
mmiitnde  and  the  character  of  its  orbit,  was  analogous  to  Ceres, 
BiUas,  and  Juno. 

Yesta  is  the  brightest  and  apparently  the  largest  of  all  this  group 
of  planets,  and  when  in  opposition  may  be  sometimes  distinguished 

S'  good  and  practised  eyes  without  a  telescope.  Observers  differ  in 
eir  impressions  of  the  colour  of  this  planet.  Harding  and  other 
German  observers  consider  her  to  bo  reddish  ;  others  contend  that 
she  is  perfectly  white.  Mr.  Hind  says  that  he  has  repeatedly  ex- 
amined her  under  various  powers,  and  always  received  the  impres* 
aion  of  a  pale  yellowish  cast  in  her  light. 

2724.  Discovery  of  the  other  Planetoith.  —  The  labours  of  the 
observers  of  the  beginning  of  the  century  having  been  now  proee- 
coted  for  some  years  without  further  results,  were  discontinued,  and 
it  is  probable  that  but  for  the  admirable  charts  of  the  stars  which 
bare  been  since  published,  no  other  members  of  this  remarkable 
group  of  planets  would   have   been  discovered.     These,  however, 

111.  27 


SU  iJXEOHoiir. 


MDtemiiig  all  the  stan  up  to  die  9di  or  lOtk 
within  a  lone  of  the  firmament  80^  in  width,  ^»ftwK^>g  to  If^oi 
each  aide  of  the  celestial  eqaatoTiiappUed  floimpQrtaaiaiid.obTMMi 
an  instrament  of  reeearohi  that  the  tnljeot  wis  agaia  nunmed  wMh 
a  better  proepect  of  tnoceflsfiil  reanlta.  It  was  onl j  Deoalmj  §m 
the  observer,  map  in  hand,  to  exanunOi  itgne  hj  degree,  the  warn 
within  which  snoh  bodies  axe  known  to  mov6|  ud  to  oompavi  akr 
by  star  the  heavens  with  the  map.  When  a  star  is  obaarved  wUflh 
is  not  marked  on  the  map,  it  is  watched  from  hour  to  hoar,  nl 
from  night  to  night.  If  it  do  not  change  ita  poritioii  it  nnsk  be 
inferred  that  it  £0  been  omitted  in  the  ocmstmction  of  Ae  h^ 
and  it  is  marked  npon  it  in  its  proper  plaoe.  If  it  change  its  por- 
tion it  must  be  inferred  to  be  a  pknet,  and  its  orbit  is *^ 

lated  from  its  observed  changes  of  pontion. 

By  these  means  H.  Henke,  an  amateor  observer  of 
Pnissia,  discovered  on  the  8th  December,  1845,  another  of  As 
small  pknets,  which  has  been  named  Astnoa. 

Since  that  time  the  progress  of  planetary  disoovenr  in  As  sias  , 
region  has  advanced  with  extraordinaiy  rapidity.  Thxea  plnslB  i 
were  discovered  in  1847,  one  in  1848,  one  in  1849,  thvae  k  UM^  ' 

two  in  1851,  and,  in  fine,  not  less  than  eight  in  1852. 

In  their  exceptioDal  minuteness  of  volame,  their  mean  distaneei 
from  the  sud,  and  the  very  variable  obliquities  and  eocentridties  of   i 
their  orbits,  they  all  resemble  the  first  four  discovered  in  the  begin-  | 
ning  of  the  century,  and  are  therefore  in  complete  accordanoe  inth  ^ 
the  conditions  mentioned  in  the  curious  hypothesis  of  Olbers  abois  | 
stated.  IE 

In  the  following  table  is  given  a  complete  list  of  the  planefeoili   ' 
discovered  up  to  the  close  of  the  last  year  (1852),  with  the  dski 
of  their  discovery,  and  the  names  of  their  dbcoverers. 

The  planet  discovered  by  M.  Gasparis,  on  the  17th  of  Hanlfi 
1852,  was  observed  by  that  astronomer  at  the  Naples  Observatorj, 
on  the  17th,  19th,  and  20th  March.  It  appeared  as  a  star  of  tti 
10th  or  11th  magnitude.  The  observations  were  published  in  thi 
''  Comptes  Bendus"  of  the  Academy  of  Sciences,  Parisi  tome  xniv* 
p.  532. 

The  planet  discovered  by  M.  Luther  was  observed  by  that  astM* 

nomer  at  Bilk  near  Dusseldorf,  on  the  17th  April,  and  again  by  X*  P 

Argelander,  on  the  22d  April,  at  Bonn.     The  observations  was  1: 

published  in  the  "  Comptes  Bendus''  of  the  Paris  Academy,  toM  jr 

Mxiv.  p.  647.  1^ 


1^ 


* 


\ 


1 


THS  PLANETOIDS. 


su 


\Me  Aawing  the  number  of  Planetoids  diicovered  before 
y,  1853,  the  names  conferred  upon  them,  their  discover- 
\e  dales' of  their  discovert/. 


KmM. 

OiMOTitrar. 

Wbea  diMOTortd. 

PUecof  ObMrraliM. 

1. 

PSanL 

Jan.  1, 1801. 

Palermo. 

Olbera. 

Maroh28.1802. 
Sept  1, 1804. 

Bremen. 

X. 

Harding. 

Lilienthal. 

k 

(Hban. 

March  29, 1807. 

Bremen. 

Henke. 

Dec.  8, 1846. 
Jal7  1, 1847. 

Drelaeen  (Proaiia). 

k 

Hanka. 

Dreiaeen. 

Hind. 

Ang.  13, 1847. 

London. 

K. 

Hind. 

Oct  18. 1847. 
April  2^  1848. 

London. 

■. 

Markree  (Irdaad). 

eia. 

DeOaspanf. 

April  12, 1840. 

Naples. 

benopa 

DeGaaparii. 

Haj  11,  I860. 

Naples. 

irift     (ealled 

Hind. 

Saptl3,1860. 

London. 

t  by  American 

roaoman). 

la. 

DaGaaparia. 

Not.  2, 1850. 

Naples. 

••• 

Hind. 

May  10, 186L 

London. 

omia^ 

DeOaaparia. 

Jnl7  20. 1861. 
March  17, 1862. 

Naples. 

IM. 

DeGaaparia. 

Naples. 

Bilk  (Dnasaldofi). 

ia. 

Lather. 

AprU  17, 1862. 

wmeiia. 

Hind. 

June  24, 1852. 

London. 

ana. 

Hind. 

Aug.  22, 1862. 

London. 

lalla. 

Chaoomae. 

Sept  20,1862. 

Marseilles. 

!tia. 

Ooldschmit 

Not.  16, 1862. 

Paris. 

iopa. 

Hind. 

Not.  le,  1862. 

liOndon. 

lla. 

Hind. 

Dee.  16, 1862. 

London. 

tet  was  diseorercd  by  M.  de  Gaaparis  fonr  days  later,  at  Naples,  belbra  that 
id  reeetred  the  infiHrmation  of  the  dlaooTery  of  Mr.  Hind. 

The  discovery  of  these  mainly  due  to  amateur  cutronO' 
)r.  Olbers  was  a  practitioner  in  medicine,  Messrs.  Henke, 
nd  Ooldschmit,  amateur  observers,  Mr.  Hind  has  been 
n  the  private  observatory  of  Mr.  Bishop,  in  the  Regent's 
Mr.  Graham  in  that  of  Mr.  Cooper,  at  Markree,  in  the 
Sligo,  in  Ireland.  It  appears,  therefore,  that  of  these 
•ec  members  of  the  solar  system,  the  scientific  world  owes 
lian  fourteen  to  amateur  astronomers,  and  observatories 
id  maintained  by  private  individuals,  totally  unconnected 
iiational  or  public  establishments,  and  receiving  no  aid  or 
'om  the  state.  Mr.  Hind  has  obtained  for  himself  the 
e  distinction  which  must  attach  to  the  discoverer  of  eight 
XKlies.  Five  are  due  to  M.  de  Gasparis,  assistant  astro- 
fche  Royal  Observatory  at  Naples. 

mann  Goldschmit  is  an  historical  painter,  a  native  of 
on  the  Maine,  but  resident  for  the  last  eighteen  years  in 
!e  discovered  the  planet  with  a  small  ordinary  telescope, 
the  balcony  of  his  apartment,  No.  12  rue  de  Seine,  in  the 
St  Germain. 
Their  remarkable  accordance  with  Dr,  Olberi  hypolKem. 


— Tto  orbits  of  several  of  those  oboerMl  a  18SS  hum  M?  jel 
been  oalculated,  but  all  those  which  hafo  beea  ooMgiileii  an  eoa* 
pised  between  the  mean  distances  2-2  and  8*8^  ttttl  to  the  ssrth 
odng  1*0.    The  magnitadcs  of  all  of  these  bodies^  iridi  one  or 
two  exoeptionsy  are  too  minute  to  be  asoertunsd  by  any  means  of 
measoTement  hitherto  discovered,  and  may  be  inftmd  with  gmft 
probability  not  to  exceed  100  miles  in  diameter.    The  Isiflwl  rf 
the  group  is  probably  less  than  600  mileB  in  ffiametar.    HsbbmI 
fidl,  therofore,  to  be  observed  in  how  lemaikable  a  mannw  thqr 
conform  to  the  conditions  involved  in  the  hypotheos  of  Dr.  Oibm 
2728.  Ibree  of  gravity  on  the  phnetoidi,  —  From  the  mhnto- 
ness  of  their  masses,  the  forae  of  gnmtj  on  the  sorfiieeB  ef  then 
bodies  must  be  very  inconsiderable,  and  this  woald  aoooonl  ftr  a 
much  greater  altitude  of  their  atmos|Aeree  than  is  ofasarfed  oi  Ifcs 
larger  planets,  since  the  same  volume  of  sir  feebly  attraoted  vosii 
dilate  into  a  volume  comparatively  enormous,     Hnssolar  pow 
would  be  more  efficadons  on  them  in  the  same  proportion.    Ims 
man  might  spring  upwards  sixty  or  eighty  perpendieahr  Ibal^  sid 
return  to  the  mund,  sustaining  no  greater  shock  thanwooU  boUl 
upon  the  earth  in  descending  mm  the  height  of  two  or  tbne  fat 
''On  such  planets/'  observes  Herschel,  ''giants  might  exists  asd 
those  enormous  animals  which  on  earth  require  the  buoyant  power 
of  water  to  counteract  their  weight" 


CHAP.   XV. 

TBE  MAJOR  I'LANETS. 

I.  Jupiter. 

2729.  Jouian  system,  —  Passing  across  the  wide  space  which  See 
beyond  the  range  of  the  three  planets  which,  with  the  earth,  revolve 
as  it  were  under  the  wings  of  the  sun, — a  space  which  was  raguded 
as  an  anomalous  desert  in  the  planetary  regions  until  oontempoaiy 
explorers  found  there  what  seem  to  be  the  ruins  of  a  shattered  worUL 
— we  arrive  at  the  theatre  of  other  and  more  stupendons  cosniosl 
phenomena.  The  succession  of  planets,  broken  by  the  absence  U 
one  in  the  place  occupied  by  the  planetoids,  is  resumedi  and  fimr 
orbs  are  found  constructed  upon  a  comparatively  Titanic  scale,  eaeh 
attended  by  a  splendid  system  of  moons,  presenting  a  miniature  of 
the  solar  system  itself,  and  revolving  round  the  common  centre  of 
light,  heat,  and  attraction,  at  distances  which  almost  confonnd  tiiS 
imagination. 


THB  MAJOR  PLANBT8.  817 

2730.  Period. — The  syDodic  period  of  Jupiter  is  ascertained  bj 
Qbeerration  to  be  398  days.  Hence  to  obtain  its  periodic  time  P, 
ve  have  (2589) 

1_      1  1  _      1 

p      865-25      398      4332-6 

The  period  is  therefore  4332-6  days,  or  11*86  years. 

2731.  SduKentrie  and  Synodic  motions.  —  The  daily  angular 
heliocentric  motion  of  Jupiter  is  therefore 

Tlie  mean  angle  gained  daily  by  the  earth  or  sun  upon  Jupiter,  is 
tlierefore 

00-9856  —  0*'083  =  0*'-9026 = 54'156. 

2732.  Dutance,  —  The  distance  of  Jupiter  from  the  sun  may  be 
computed  by  means  of  the  Harmonic  Law  (2621),  the  period  being 
known.     This  method  gives 

(ll-83)«  =  (5-2028)*. 

Tbe  mean  distance  of  Jupiter  from  the  sun  is  therefore  b\  times 
that  of  the  earth ;  and  since  the  earth's  mean  distance  is  95  millions 
of  miles,  that  of  Jupiter  must  be  494  millions  of  miles. 

The  eccentricity  of  Jupiter's  orbit  being  0048,  this  distance  is 
liable  to  Tariation,  being  augmented  in  aphelion  and  diminished  in 
perihelion  by  24  millions  of  miles.  The  greatest  distance  of  the 
planet  from  the  sun  is  therefore  518,  and  the  least  470,  millions  of 
miles. 

The  small  eccentricity  of  the  orbit  of  this  planet,  combined  with 
Its  small  inclination  to  the  plane  of  the  ecliptic,  is  of  great  import- 
ance in  its  effect  in  limiting  the  disturbances  consequent  upon  its 
mass,  which,  as  will  hereafter  appear,  is  greater  than  the  aggregate 
of  the  masses  of  all  the  other  planets  primary  and  secondary  taken 
together.  If  the  orbit  of  Jupiter  had  an  eccentricity  and  incli nation 
■s  considerable  as  those  of  the  planet  Juno,  the  perturbations  pro- 
duced by  this  mass  upon  the  motions  of  the  other  bodies  of  the  sys- 
tem, would  be  twenty-seven  times  greater  than  they  are  with  its 
present  small  eccentricity  and  inclination. 

2733.  Relative  scale  of  (he  orbits  of  Jupiter  and  the  Earth,  — 
The  relative  magnitudes  of  the  distances  of  Jupiter  and  the  earth 
from  the  sun,  and  the  apparent  magnitude  of  the  orbit  of  the  earth 
as  seen  from  Jupiter,  are  represented  in  fig.  756,  where  the  planet 
is  at  J,  the  sun  at  s,  and  the  orbit  of  the  earth  £  e/  "e!"  e". 

The  direction  of  the  orbital  motions  being  represented  by  the 
arrows,  it  will  be  evident  that  when  the  earth  is  at  E  the  planet  is  in 

27* 


THB  MAJOR  PLANETS.  319 

oppositioQi  at  1^  in  conjanctioQ,  at  xf  in  quadrature  west,  and  at  jf 
in  qnadntnre  east  of  the  son. 

2734.  A*mual  parallax  of  Jupiter,  — To  determiDe  the  angle 
s  J  E',  whidi  the  aemi-diaineter  of  Uie  earth's  orbit  subtends  at  Jupi- 
ter, or  the  aonnal  parmllaz  of  the  planet,  it  may  be  assumed  without 
coaterial  inezietiieui  tliat  8  x'  ia  nearly  equal  to  an  aro  described  with 
r  aa  centre,  and  b  j  m  ndiiUy  and  consequently  (^294) 

Bjif=  670-3  _ 

The  annual  peiallax  of  Jnpiter  is  therefore  11^,  and  consequently 
the  orbit  ai  the  earth  snbtends  at  the  plane!  an  angle  of  22°. 

2735.  YariaiUm  of  dulancefrom  the  earfA.— Since  the  greatest 
and  least  diatanoee  J  x^  and  j  x  of  Jupiter  from  the  earth  are  the 
Bum  and  dUfereoce  of  the  diatances  of  the  planet  and  earth  from  the 
BQD,  we  shall  have 

«  B'^^  ■■  494  +  96  »  &89  mUlioDS  of  miles. 

JBm494^96s899  millions  of  miles. 

J  B^  ■»  ^(494* -.95*)  =  486  mimoDS  of  miles. 

The  extreme  diBtanoes  of  the  planet  are  therefore  in  the  ratio  of  6 
to  5  nearly. 

By  the  elliptieity  of  the  earth's  orbit,  the  distances  at  opposition 
and  conjnneiMm  may  be  increased  or  diminished  by  1}  million  of 
milesy  and  by  that  of  the  planet's  orbit  by  24  millions  of  miles. 
From  both  caiueB  combined  they  may  vary  from  their  mean  values 
laore  or  Icbb  by  26}  millions  of  miles. 

2736.  1(9  prodiffioui  orhital  vdocitj/. — ^The  velocities  with  which 
the  planetB  move  throuffh  space  in  their  circumsolar  courses  are  on 
the  sanM  firadigioaB  ■caTe  aa  their  distances  and  magnitudes.  It  is 
impofisible^  by  the  mere  niAnerical  expression  of  these  enormous 
magnitodea  and  motions,  to  acquire  any  tolerably  clear  or  distinct 
notion  of  them.  A  cannon-ball  moving  at  the  rate  of  500  miles  an 
hour,  wonld  take  nearly  a  century  to  come  from  Jupiter  to  the  earth, 
even  wheo  the  planet  is  nearest  to  us,  and  a  stcam-engine  moving  on 
a  railway  at  50  miles  an  hour  would  take  nine  centuries  to  perform 
the  same  trip. 

Taking  the  diameter  of  Jupiter's  orbit  at  1000  millions  of  miles, 
its  circumference  is  above  3000  millions  of  miles,  which  it  moves 
over  in  4333  days.  The  distance  it  travels  is,  therefore,  700,000 
niiles  per  day,  30,000  per  hour,  500  per  minute,  and  %\  per  sccuud, 
— t  speed  sixty  times  greater  than  that  of  a  caonoD-ball. 

2537.  Interval*  between  oftpotsifioTiy  conjunction ^  and  quadrature, 
—  If  the  distaoce  of  the  pluoet  from  the  sun  bore  an  indefiuitcly 
great  ratio  to  that  of  the  earth,  the  quadratures  would  divide  the 
Btiiai-synodic  period  into  parts  precisely  equal ;  for  in  that  case  J  T^ 
Bad  J  K^'  would  be  practically  pnrallcl,  and  the  bent  line  if  &l!' 


mvU  beoMM  itnigH  u>A  wodU  ba  »  dlMite  flf  &•  Mtf ■  aAiL 
Althougb  thu  is  not  tha  eaBs,tiM  u|^  tanmA  bgrs^aila^ 
iMing  l«8s  thkD  180°  by  the  tm^tuit  ct  tiM  taA  wTm^  valyfOt 
iDterrils  into  whicli  the  Mmi-^ynodie  period  b  onided  na  aot  my 

'^aeluUhaTe  the  ugle  l^  ■  ^  =  180"  —  SS«  =s  1S8*,  nd  it 
ii  evident  that  the  time  of  guning  thii  u^e  will  b«r  die  ■■■ 
proportioii  to  the  lynodie  period  which  the  earie  ileelf  bean  to 
860°.  Hence,  it  foUowa.  that  if  t  axpnaa  the  mteml  fron  Iha 
qnadntnre  west  to  the  qnadiatare  eaat,  and  ^  the  Inteml  fitn  tk 
qiadratitte  eaat  to  the  qnadratare  wee^  m.  ahell  hare 


"860 


;  898  =  228i  d^r*. 


It  fbllowB,  therefinre,  that  the  intemd  between  Ofyiailka  and  q» 
diBture  ia  %7l  daja,  and  the  intgml  between  eo^jonetioo  and  q*- 
dratnra  ia  111}  daja. 

Theae  are  mean  nivM  of  the  intemla  whieh  an  aal;}eet  to  mt 
Btion  owing  to  the  eccentricities  of  the  orbiU  of  the  earth  and  fUmt 

2738.  Jupiter  ha*  no  tetuible  phaiet.  — Tbe  mere  inapeetion  d 
the  diagram,  _fig.  752,  will  show  that  this  planet  cannot  n  aeniililT 
ffibbouB  in  any  position.  The  position  in  which  the  anligfateaM 
hemiiipbere  is  in  view  most  obliquely  ia  when  the  earth  is  at  ^  cr 
tT,  and  the  planet  consequeDtly  in  qnadratDre,  and  even  then  tbt 
oentre  of  tbe  visible  faeniisphere  is  only  11''  distant  from  tbe  eentn 
of  the  enlighcenod  hemisphere  (2734). 

2739.  Appearance  in  the  Jirviament  at  night  —  SinoB  betwaw 
qnadniture  aod  oppoeition  tba  planet  iavboTefhe  horiaoQ  dnringtha 
greater  part  of  the  night,  and  appears  with  a  ftill  phaae,  it  ia  Ihm 
UYOurably  placed  for  observation  during  6  months  in  18  months 

2740.  Station*  and  reirogreuion.  —  From  a  oompariaon  of  tht 
orbiul  modons  and  distance  of  Jupiter  and  the  earth,  it  appeaie  thrt 
the  planet  is  stationary  at  about  two  months  before  an<^two  monlki 
after  opposition ;  aod  since  tbe  earth  gains  upon  tbe  planet  at  the 
daily  rate  of  0*'-907,  the  angle  it  gains  in  two  months  nnat  be 

0°-907  X  61=64''-43. 
The  angular  distance  of  the  points  of  station  from  oppoaitioO|  M 
seen  from  tbe  sun,  ia  therefore  about  54°,  which  onmapondilota 
elongation  of  114". 

The  planet  is  therefore  stationary  at  about  66"  ou  eeoh  ride  U 
ita  oppositioQ. 

Its  arc  of  retrogression  ia  a  little  less  than  10°,  and  the  tiaa  (t 
dearrihing  it  varies  from  117  to  123  days. 


THE  ICAJOB  PLANETS.  821 

•741.  Apparent  and  real  diameters.  —  Tlin  apparent  diameter 
of  Jupiter  when  in  opposition  varies  from  42"  to  48",  according  to 
the  relative  positions  of  the  planet  and  the  earth  in  their  elliptic 
orbits.  At  its  mean  opposition  distance  from  the  earth  its  apparent 
magnitade  is  45".  In  conjunction  the  mean  apparent  diameter  is 
Wj  its  valae  at  the  mean  distance  from  the  earth  being  37^". 

At  the  distance  of  399  millions  of  miles  the  linear  value  of  1"  is 

399000000       ^^o.     ., 

-206266"  =  ^®^  "^^"'^  5 

tod  consequently,  the  planet's  diameter  d'  will  be  S 

1/  =  1934  X  45  =  87030  miles. 

According  to  more  aoeonte  methods,  the  mean  diameter  is  ascer- 
uioed  to  be  88640  miles.  The  diameter  of  Jupiter  is  therefore 
11*18  times  that  of  the  earth. 

2732.  Jupiter  a  conspicuaw  object  in  the  firmament — relative 
tptendaur  of  Jupiter  and  Mart.  —  Although  the  apparent  magni- 
tade of  Jupiter  is  less  than  that  of  Tonus,  the  former  is  a  more  con- 
spicuous and  more  easily  observable  object,  inasmuch  as  when  in 
opposition  it  is  in  the  meridian  at  midnight,  and  when  its  opposition 
tikes  place  in  winter,  it  passes  the  meridian  at  an  altitude  nearly 
equal  to  that  which  the  sun  has  at  the  summer  solstice.  By  reason, 
therefore,  of  this  circnmstMOce,  and  the  complete  absence  of  all  solar 
light,  the  splendour  of  the  planet  is  very  great,  whereas  Venus,  even 
It  the  greatest  elongation,  descends  near  the  horizon  before  the 
eatire  cessation  of  twilight. 

The  apparent  splendour  of  a  planet  depends  conjointly  on  tho 
apparent  area  of  its  disk,  and  the  intensity  of  the  illumination  of  its 
waahct.  The  area  of  the  disk  is  proportional  to  the  square  of  its 
apparent  diameter,  and  the  illumination  of  the  surface  depends  cou- 
jointly  on  the  intensity  of  the  sun's  light  at  the  planet,  and  the 
reflecting  power  of  the  snr&ce.  On  comparing  Mars  with  Jupiter, 
ve  find  the  apparent  splendour  of  tho  latter  planet  much  greater 
than  it  onshl  to  be,  ai  eompared  with  the  former,  if  the  reflecting 
power  of  ttiese  snr&ces  were  the  same,  and  are  consequently  com- 
pelled to  ooDoliide  that  the  surface  of  Mars  is  endowed  with  some 
physical  quality,  in  virtue  of  which  it  absorbs  much  more  of  the  solar 
light  incident  jspon  it  than  that  of  Jupiter  does.  When  the  apparent 
diameter  of  the  latter  is  twice  that  of  the  former,  its  apparent  area  is 
fourfold  that  of  the  former.  But  the  intensity  of  the  solar  light  at 
Jupiter  Is  at  the  same  time  about  thirteen  times  less  than  at  5lars ; 
and  if  the  reileetive  power  of  the  sur&ces  were  equal,  the  apparent 
rplendour  of  Mars  would  be  more  than  three  times  that  of  Jupiter. 
The  reflective  power  mnst^  tlierefore,  be  less  in  a  sufficient  proportion 
to  explain  the  inferior  splendour  of  Mars^  unless^  indccd|  tUe  ^erj 


ImolMl^  nniporitian  ba  admittad  dut  Om  «^ta  ft  nOMrfU 
in  Jnidter  iDdependent  of  nlar  iUsmiiutioii. 

S748.  Str/an  and  vohme.  —  V  ■  tad  T  bft  &■  w^m  at 
TolmiM  of  the  eartli,  a*  uid  t'  being  tkoM  of  Jnpitar,  ««  rinl  Ipl 

^  =  126  X  ■       V  =  18974  x  v. 
The  nirlioe  of  Jupiter  is  tfaerefare  abtm  126  tiiiiai,  md  ito  valaa 
■boat  1400  times,  that  of  the  aartli. 

To  prodnoe  a  globe  niah  aa  that  of  Jnpiter,  it  wonld  be  naomf 
to  moold  ioto  a  nagle  globe  1400  globea  like  that  of  As  earth. 

The  reladre  magnitodea  of  the  ghibea  of  Jtq|it*r  nd  tba  aril. 
tn  repreaented  in^.  767 17  3  and  i. 


ns-TH. 


2744.  ^b&ir  liglit  and  Ktat  —  The  mean  distaoee  of  Ji]alB  1 
from  the  sua  being  5-2  times  that  of  ihe  earth,  the  apparent  iliiiaiilM 
of  the  Bun  to  the  iahabitanls  of  that  planet  will  be  less  than  ila  » 
parent  diameter  at  the  earth  in  the  praportioQ  of  6-2  to  1.  ni 
relative  apparoot  magnitudes  of  the  disk  of  the  sod  at  Japilei  andat 
the  earth  are  represented  in^.  758  at  1  and  j. 


THE  MAJOR  PLANETS.  323 

The  density  of  solar  radiation  being  in  the  exact  proportion  of 
the  apparent  superficial  magnitudes  of  the'disks,  the  illuminating 
•od  heating  powers  of  the  sun  will,  ceteris  paribus,  be  less  in  the 
me  proportion  at  Jupiter  than  at  the  earth. 

Ab  haa  been  already  observed,  however,  this  diminished  power 
M  well  of  illnmination  as  of  warmth,  may  be  compensated  by  other 
phjsical  provisions. 

2745.  Roiaticm  and  direction  of  the  axis,  —  Although  the  linea- 
ments of  light  and  shade  on  Jupiter's  disk  are  generally  subject  to 
Tiriations,  which  prove  them  to  be,  for  the  most  part,  atmospheric, 
Nevertheless  permanent  marks  have  been  occasionally  seen,  by  means 
of  which  the  diurnal  rotation  and  the  direction  of  the  axis  have 
been  ascertained  within  very  minute  limits  of  error.     The  earlier 
observers,  whose  instruments  were  imperfect,  and  observations  con- 
sequently inaccurate  comparatively  with  those  of  a  more  recent  date, 
aaoertained  nevertheless  the  period  of  rotation  with  a  degree  of  ap- 
|iroximation  to  the  results  of  the  most  elaborate  observations  of  the 

E resent  day,  which  is  truly  surprising,  as  may  appear  by  the  fol- 
>wing  statement  of  the  estimates  of  various  astronomers : — 

H.      M.      8 

Cassiid  (1665) 9  56 

BUTabelle 9  56 

Schroter  (1786) 9  55    83 

Airy 9  55    24-6 

Madler(1885) 9  55    26-56 

The  estimate  of  Professor  Airy  is  based  upon  a  set  of  observations 
made  at  the  Cambridge  Observatory.  That  of  Madler  is  founded 
npon  a  series  of  observations,  commencing  on  the  3rd  of  November, 
1834,  and  continued  upon  every  clear  night  until  April,  1835,  during 
which  interval  the  planet  made  400  revolutions.  These  observations 
were  favoured  by  the  presence  of  two  remarkable  spots  near  the 
equator  of  the  planet,  which  retained  their  position  unaltered  for 
several  months.  The  period  was  determined  by  observing  the  mo- 
ments at  which  the  centres  of  the  spots  arrived  at  the  middle  of 
the  disk. 

The  direction  of  the  apparent  motion  of  the  spots  gave  the  posi- 
tion of  the  equator,  and  consequently  of  the  axis,  which  is  inclined 
to  the  plane  of  the  planet's  orbit  at  an  angle  of  3^  6'. 

The  length  of  the  Jovian  day  is  therefore  less  than  that  of  the 
terrestrial  £iy  in  the  ratio  of  596  to  1440,  or  1  to  2-42. 

2746.  Jovian  years, — Since  the  period  of  Jupiter  is  4332  6  ter- 
restrial days,  it  will  consist  of 

4332-6  =  10484-9 
Jovian  days.* 

*  The  daj  htm  computed  is  the  sidereal  d&j,  which,  in  the  case  ot  \\v^ 
rnnperior  plmaetB,  dilTers  from  the  mean  solar  day  by  a  quantity  bo  \u«v^- 
nidemai  thmtitmaj  be  neglected  id  such  illustraUons  as  theee. 


S747.  Smmu— At  A*  Jvfin  nilimii  Oi  la^tf  «•« 
iatwTartcUliiiMmiutl)a4^fi7*-4l*<^.  OwisgtoteTCVMi 
oWqnity  of  the  plane  of  tbs  alMMt'*  omnto  ta  4Klflf  4lia| 
iwt  mneb  exoeediDg  tbe  eidid  fvt  oT  4*  gUndlgr  tf  Ai  «li 
•qoaur,  the  d^feresee  of  the  ezlnBS  knrtk  «  ttt  d^v  ii''«| 
■nnnMr  ud  nudwiiitar,  ano  it  U^  l■^itB^^i^  mm^  ■MMriM 


The  dinrn*]  pbenomenB  at  midwmter-uid  midsninaNt  «■  A 
euth  in  latitndet  higher  thia  661°  en  only  exluUled  an  Jrip 
within  a  amsll  drole  oioanuarilnDg  the  pole  tt  m  dietaoee  <f  S*  V 

The  extremes  of  temperatora,  eo  &r  u  the;  d^Mnd  oa  the  laj 
log  (liBtance  of  the  pUnet  from  the  ran,  being  in  the  pioportioad 
the  squares  of  the  aphelion  and  perihelion  diatancee,  xre  aa 
518';470'::5:6neftrij. 

It  appears,  therefore,  that  except  in  the  near  Deighbonrhood  a 
the  poles  the  Ticiwitudes  of  temperature  and  aeaaon  to  vhich  A 
Btu-bce  of  this  planet  is  exposed,  whether  arimng  from  the  ohIi([al 
of  its  axis  or  the  eccentridty  o£  its  orbit,  are  ooofiued  within  « 
tremel;  narrow  limits. 

2748.  Tele»c<^{c  appearance  of  Jupiter.  —  Of  all  the  bodiia  I 
the  eystem,  the  moon  perbapg  alone  excepted,  Jnpiter  preaeuli  < 
the  telesoopio  observer  the  most  magnificent  ^tectaole.  NotwU 
standing  its  vast  distance,  snoh  is  Ila  stupendons  magnitude  that 
is  seen  andcr  a  visoal  angle  nearly  twice  that  of  Mars.  A  teleeasj 
of  a  given  power,  therefore,  shows  it  with  an  apparent  disk  fo 
times  greater.  It  has,  consequently,  been  snbmitted  to  examinatii 
by  the  most  eminent  observers,  and  its  appeoruicea  described  wi 
great  minuteness  of  detail.  The  apparent  diameter  in  oppoatk 
(when  it  is  on  the  meridian  at  midnight)  is  abont  the  fortieth  pi 
of  that  of  the  moon,  and,  therefore,  a  telescope  with  the  very  nwd 
Tate  magnifying  power  of  forty,  presents  it  to  the  ofanrretwith 
disk  equal  to  that'  with  which  the  full  moon  is  seen  with  the  uki 
eye. 

2749.  Magnifying  poteen  necaiary  to  Aov>  Aefiaturaoft 
diik.  —  A  power  of  four  or  five  is  sufficient  to  entbh  Uie  ofaaerr 
to  see  the  planet  witb  a  sensible  disk ;  a  power  of  thirty  thowt  (I 


THE  MAJOB  PLANETS.  826 

promioenfc  belts  and  the  oval  fonn  of  the  disk  produced  by 
tte  obkieness  of  the  spheroid ;  a  power  of  forty  shows  it  with  a 
jfiak  aa  laige  as  that  which  the  fiiU  moon  presents  to  the  naked  eye; 
&■!  to  be  enabled  to  observe  the  finer  streaks  which  prevail  at  greater 
Jfataaeea  from  the  planet's  equator,  it  is  not  only  necessary  to  see 
'fkm  planel  under  &vonrable  oircumstanoes  of  position  and  atmo- 

iphm,  but  to  be  aided  by  a  well-defining  telescope  with  magnifying 

powers  varying  from  200  to  300. 

2750.  JMtM  —  their  arrangement  and  appearance, — ^The  planet, 
when  thus  viewed,  appears  to  exhibit  a  dbk,  the  ground  of  which 
11  a  light  yellowish  colour,  brightest  near  its  equator,  and  melting 
padnidly  into  a  leaden-coloured  grav  towards  the  poles,  still  retain- 
1^,  nevertheless,  somewhat  of  its  yellowish  hue.   Upon  this  ground 
tn  seen  a  series  of  brownish-gray  streaks,  resembling  in  their  form 
aid  arrangement  the  streaks  of  clouds  which  are  often  observed  in 
As  sky  on  a  fine  calm  evening  after  sunset.     The  general  direction 
tf  ths«e  streaks  is  parallel  to  the  equator  of  the  planet,  though 
MBetimea  a  departure  from  strict  parallelism  is  observable.     They 
M  not  all  equallv  conspicuous  or  distinctly  defined.    Two  are  gene- 
ally  ateikingly  observable,  being  extended  north  and  south  of  the 
flanet'a  equator,  separated  by  a  oright  yellow  zone,  being  a  part  of 
the  general  ground  of  the  disk.     These  principal  streaks  commonly 
extend  around  the  dobe  of  the  planet,  being  visible  without  muim 
change  of  form  dunng  an  entire  revolution  of  Jupiter.     This,  how- 
eiver,  is  not  always  the  case ;  for  it  has  happened,  though  rarely,  that 
one  of  these  streaks,  at  a  certun  point,  was  broken  sharply  off,  so  as 
to  present  to  the  observer  an  extremity  so  well  defined  and  unva- 
lyiog  for  a  considerable  time  as  to  supply  the  means  of  ascerteioing, 
with  a  very  close  approximation,  the  time  of  the  planet's  rotation. 
The  borders  of  these  principal  streaks  are  sometimes  sharp  and 
even,  bnt,  sometimes  (those  especially  which  are  further  from  the 
equator),  rugged  and  uneven,  throwing  out  arms  and  o&hoote. 

2751.  Thoee  near  the  polei  more  faint.  —  On  the  parts  of  the 
disk  more  remote  from  the  equator,  the  streaks  are  much  more  faint, 
narrower,  and  less  regular  in  their  parallelism,  and  can  seldom  be 
distinctly  seen,  except  by  practised  observers,  with  good  telescopes. 
With  these,  however,  what  appears  near  the  polos,  in  instrumente 
of  infisrior  power,  as  a  dim  shading  of  a  jellowish-gray  hue,  is  re- 
■olved  into  a  system  of  fine  parallel  stredks  in  close  juxteposition, 
which  becoming  closer  in  approaching  the  pole,  finally  coalesce. 

2752.  Diaappear  near  Ae  limb,  — In  general,  all  the  streaks  be- 
come less  and  less  distinct  towards  either  the  eastern  or  western  limb, 
disappearing  altogether  at  the  limb  itself. 

27o3.  Jfe/te  not  zenographical  features,  but  atmospJieric.  —  Al- 
though these  streaks  have  ioBnitely  greater  permanency  lli^n.  ihA 
arrmagementB  of  the  chads  of  oar  atmosphere,  and  are,  aa  ^^  \:AkX^ 
nr.  28 


m  ASTRONOUT. 

■an,  ffrto  more  portn.niienl  ibnn  is  Decea^arj  for  the  eiaol  AetBrn)- 
luliaD  of  tfae  plnmn'^  roiHti'in,  they  are  neverthcle'!)  eDlircIf  desb- 
tate  of  that  pei-maucuce  wLiuh  would  chojactetise  Z«at^djt^  in- 
torn,  mob  u  are  obsemd,  tot  ezampk,  os  Hwi.  The  itaifa,* 
tbe  eontm;,  tre  sabjeot  (o  slow  but  evident  TmrietkiiM,  n  tlol  dto 
tbs  lepee  m  some  monthi  the  eppenuee  d  the  dnk  ia  Wri^ 
•hanged. 

2754.  ZUoeopu;  dramttg*  of  Jupiter  ly  JBiOn-  tnul  ArdU 
—  TheM  genetal  oheamtioiu  on  the  imMxtiOM  of  Jnpiter'i  dU 
will  be  Tendered  more  dearlj  intellig^Mo  bj  referenee  to  tbe  ld» 
seopio  drftirio^  of  tbe  planet  KiTen  in  [Jate  X.  In  j^,  1,  u  pMi 
n  telescopio  new  of  tbe  disk  bj  Sir  John  Henohel,  as  it  appnnl 
In  the  2(Meet  refleetor  at  Sloncdi  on  the  SSrd  Sept,  188S.  Ik 
other  newa  were  made  bj  M.  Hidter  from  obeerraliaie  takn  ii 
1886,  and  183S,  at  the  datea  indieatod  on  die  plate. 

2756.  (^mrvatinu  and  trntthttiotu  of  Jft^Jn-.— The  two  Unk 
■poti  repreeeoted  mjigt.  2,  8,  and  4,  were  thoie  by  which  the  liM 
cf  roution  waa  determined  (2745).  l^j  were  fint  obaerred  \l 
Mtdler,  do  tbe  8rd  of  Nov.,  1884.  The  e^ct  of  the  ivtalin* 
theae  epote  wm  bo  appuent  that  their  change  of  podtion  with  nk- 
tion  tp  tlie  centre  of  the  disk,  id  the  tbort  interval  of  five  minot^ 
was  quite  perceivable.  A  third  spot,  much  more  fiiot  than  tbn^ 
was  visible  at  the  iame  time,  tbe  distnnoea  separating  the  Rpoli  U- 
log  about  24°  of  tbe  planet's  surface.  It  was  e8timat«d  Ui»t  iW 
diameter  of  each  of  the  two  spots  represented  in  the  diagranu  *W 
8Q80  miles,  and  the  distance  between  them  was  sometimes  obsemd 
to  increase  at  the  rate  of  half  a  degree,  or  330  miles,  in  a  moDlk. 
Tbe  two  spots  continued  to  be  distioctlr  viuble  from  tbe  3rd  of 
November,  1834,  when  the;  were  first  obserred,  until  the  18th  d 
April,  1835 ;  bat  during  this  interval  tbe  streak  on  which  tbtf 
were  placed  bad  entirely  disappeared.  It  became  graduatlj  ftisH 
in  January  (see  Jig.  4),  and  entirely  vanished  in  February;  tta 
spots,  however,  retaining  all  tbeir  distinctness.  The  planet,  sAst 
April,  passing  towards  conjunction,  was  lost  in  the  light  of  the  tni; 
and  when  it  reappeared  in  August,  after  oonjuootion,  the  spoia  hid 
altogether  van  is  bed 

The  observations  being  cootinned,  the  drawiun,  fiijt.  5,  and  S, 
were  made  from  observations,  on  the  16tb  and  17th  of  JaoDiiJi 
18S6,  when  the  entire  aspect  of  the  disk  waa  obanged.  Tbe  tet 
figures  5  and  6,  represent  opposite  hemispheres  of  the  planet  1^ 
furmer  presents  a  striking  resemblance  to  tbe  principal  belta  ia  tbt 
drawing  of  Sir  J.  Herscbet,^.  1. 

It  was  remarked  tbat  tbe  two  spots,  when  carried  round  by  iba 
rotation,  became  invisible  at  55"  to  57°  from  the  centre  of  the 
disk.  This  is  an  efiect  whioh  would  be  produoed  if  tbe  apota  wen 
openinga  in  the  mass  of  douda  floatiDg  in  the  atmoaphere  of  tha 


-^-■•J 


THE  MAJOK  PLACETS.  827 

« 

pIiDct,  and  would  be  explicable  in  the  same  manner  as  is  the  dis- 
appearance of  spots  on  the  sun  in  approaching  the  edges  of  the  disk. 
A  proper  motion  with  a  elow  yelocitji  and  in  a  direction  contrary  to 
the  rotation  of  the  planet,  was  obserred  to  affect  the  spots,  and  this 
modon  continued  with  greater  uniformity  in  March  and  April,  after 
the  disappearance  of  the  belt. 

It  was  calculated  that  the  Telocity  of  their  proper  motion  over  the  sur- 
het  of  the  planet,  was  at  the  rate  of  from  three  to  four  miles  an  hour. 
Although  the  two  black  spots  were  not  observed  by  M&dler  until 
the  first  days  of  NoYember,  they  had  been  previously  seen  and  ez- 
amined  by  Schwabe,  who  observed  them  to  undergo  several  curious 
dianges,  in  one  of  which  one  of  them  disappeared  for  a  certain  in- 
terval, its  place  being  occupied  by  a  mass  of  fine  dots.  It  soon, 
however,  reappeared  as  before. 

From  all  these  circumstances,  and  many  others  developed  in  the 
coarse  of  his  extensive  and  long-continued  observations,  Madler 
coonden  it  highly  probable,  if  not  absolutely  certain,  that  the  at- 
Mspbere  of  Jupiter  is  continually  charged  with  vast  masses  of 
doads  which  completely  conceal  his  surface;  that  these  clouds  have 
a  permanence  of  form,  position,  and  arrangemcDt  to  which  there  is 
aothing  analogous  in  the  atmosphere  of  the  earth,  and  that  such 
ymnanence  may  in  some  degree  be  explained  by  the  great  lensth 
ad  very  email  variation  of  the  seasons.  He  thinks  it  probable 
thit  the  inhabitants  of  places  in  latitudes  above  40^  never  behold 
the  firmament,  and  those  in  lower  latitudes  only  on  rare  occasions. 

To  these  inferences  it  may  be  added  that  the  probable  cause  as- 
■gned  for  the  distribution  of  the  masses  of  clouds  in  streaks  parallel 
tft  the  equator,  is  the  prevalence  of  atmospheric  currents  analogous 
tft  the  trades,  and  arising  from  a  like  cause,  but  marked  by  a  con- 
itiDcy,  intensity,  and  regularity  exceeding  those  which  prevail  on 
the  earth,  inasmuch  as  the  diurnal  motion  of  the  surface  of  Jupiter 
ii  more  rapid  than  that  of  the  earth  in  the  combined  proportion  of 
the  velocity  of  the  diurnal  rotation  and  the  magnitude  of  the  cir- 
camference,  that  is,  as  27  to  1  nearly. 

It  is  also  probable  that  the  bright  yellowish  general  ground  of 
Jointer's  disk  consists  of  clouds,  which  reflect  light  much  more 
MroDgly  than  the  most  dense  masses  which  are  seen  illuminated  by 
the  sun  in  our  atmosphere ;  and  that  the  darker  streaks  and  spots 
obierved  upon  the  disk  are  portions  of  the  atmosphere,  either  free 
from  clouds  and  through  which  the  surface  of  the  planet  is  visible 
more  or  less  distinctly,  or  clouds  of  less  density  and  less  reflecting 
power  than  those  which  float  over  the  general  atmosphere  and  form 
the  ground  on  which  the  belts  and  spots  are  seen. 

That  the  atmosphere  has  not  any  very  extraordinary  Leigh t  above 
the  surface  of  the  planet,  is  proved  by  the  sharply  defined  edge  of 
the  diak.    If  its  height  boM  any  considerable  proportion  to  tk« 


ASTRONOMY. 

of  the  plinet,  tlie  lielit  toirards  tli«  edges  of  Ote  iiA  wmM 
gndiullj  fiUntar,  un  the  edgn  woold  n  biIiiIbm  nl  flt 

The  revene  ia  tbe  o 


2766.  Spheroidal  form  of  Aa  ftmti. — Hia  didk  «f  Joilv, 

" f  o^ft. 

r  tbe  ellipse  oojocidiDe  witb  tbo  axii  of  ra' 
iDg  perpefidicnlar  to  the  geaenl  mnolHii  of  tbo  bdta. 
■npimai  o  BtrikiDg  oosfirauttioD  of  tho  mnlta  ittiinwl  in  tti  : 


ieon  with  mignifyinr  powers  m  low  ib  80,  ii  arid— Uy  o 
loner  axis  of  the  ellipse  ooioddiDe  with  tho  axii  of  nti " 
heing  perpefidicnlar  to  the  geaenl  £roalHii  of  tbo  bdta. 


moanmrnent  of  tho  oufiaturo  of  tho  earth ;  and,  aa  ia  tt»  wm  of 
Ao  earth,  the  depoe  of  oblateiMM  of  Jnpiter  ia  fond  to  bo  Oal 
whieh  would  be  prodtnod  upon  a  riobe  of  the  ntne  Hi^dki^ 
baviDg  a  rotation  anoh  aa  the  planet  la  ofaoemd  to  ham 

At  die  mean  Stance  from  the  earth,  tho  apparent  &Balai  tf 
the  disk  are  asoertained  bj  exact  mierametrio  mcamm  to  b*— 


HMD  dluetv—... 


The  polar  diameter  is  therefore  less  than  the  equatorial,  in  Aa  nlii 
of  356  to  384,  or  100  to  108  nearly.  Other  estimates  girt  the  lalio 
as  100  to  106. 

2757.  JupUer't  tabiOilt*.  — When  Qilileo  direoled  the  fint  kli- 
aoope  to  tbe  ezamin&tdon  of  Jupiter,  he  obeerred  foor  minnta  rin 
which  appeared  in  tbe  line  of  Uie  equator  of  tbe  planet.  He  kiak 
these  at  first  to  be  fixed  stars,  but  was  soon  nndeoeiTed.  Be  rV 
them  altematelj  approaoh  to,  and  recede  from  the  planet;  ohawfld 
them  pass  behind  it  and  before  it,  and  osciiUte,  as  it  wete,  to  tti  ' 
right  and  tbe  left  of  it,  to  certain  limited  and  equal  distanoes.  Ha  i 
aoon  arrived  at  tbe  obvious  oonclusion  that  these  objeota  wen  Ml 
fixed  stars,  but  that  they  were  bodies  which  revolved  rovnd  JnpiW 
in  orbits,  at  limited  distances,  and  that  each  ancoeBave  bodj  ■■ 
eluded  the  orbit  of  the  others  within  it;  in  short,  that  thejr  Mti 

a  miniature  of  the  solar  system,  in  which,  however,  Jnpiter  hsa- 
self  played  the  part  of  the  sun.  As  the  teteect^  impro*ad,  k 
became  apparent  that  these  bodies  were  small  globes,  lelated  ti 
Jnpiter  in  tbe  same  manner  exaotly  as  the  moon  is  related  to  It* 
earth ;  that,  in  fine,  they  were  a  system  of  four  moons,  aeeompailj- 
ing  Jnpiter  round  tho  sun.  •■ 

2758.  Rapid  change  and  grtat  variety  ofphamt.- — fiat  e^  « 
nected  with  these  appendages  there  is  perhaps  nothing  men  remsi^  >• 
able  than  the  period  of  their  revolntions.  That  moon  whisfa  ^  ^ 
nearest  to  Jnpiter,  completes  its  revolution  in  forty-two  bonis.  U  ^ 
that  brief  space  of  time  it  gpee  tbrougb  all  its  variona  phaaso:  itii  i" 
•  thin  oreeoent,  halved,  gibbons,  and  ^11.     It  must  bo  lemomnn^  . 


THE  MAJOR  PLANETS.  829 

bowerer,  that  the  day  of  Japiter,  instead  of  being  twenty-four  bonra, 
k  leas  than  ten  houxa.  This  moon,  therefore,  haa  a  month  equal  to 
a  little  more  than  four  Jovian  days.  In  each  day  it  passes  through 
ooa  complete  quarter;  thus,  on  the  first  day  of  the  month  it  passes 
tnm  the  thinnest  crescent  to  the  half  moon ;  on  the  second,  from 
dw  balf  moon  to  the  full  moon ;  on  the  third,  from  the  full  moon 
to  tlie  last  quarter;  and  on  the  fourth  returns  to  conjunction  with 
dw  Sim.  oo  rapid  are  these  changes  that  thoy  must  be  actually 
mible  aa  they  proceed. 

The  apparent  motion  of  this  satellite  in  the  firmament  of  Jupiter 
ii  at  the  rate  of  more  than  8^  per  hour,  and  is  the  same  as  if  our 
■con  were  to  move  over  a  space  equal  to  her  own  apparent  diameter, 
ii  nther  leas  than  four  minutes.  Such  an  object  would  serre  the 
purpoee  of  the  hand  of  a  stupendous  celestial  clock. 

The  second  satellite  completes  its  revolution  in  about  eighty-five 
ttiTSiUial  hooray  or  about  eight  and  a  half  Jovian  daya.  It  passes, 
thenfuw,  from  quarter  to  quarter  in  twenty-one  hours,  or  about 
two  Jofkn  daT%  ita  apparent  motion  in  the  firmament  being  at  the 
m»ef  ahe«t4*-fi6per  hour;  which  is  as  if  our  mooe  were  to  move 
•fcr  a  apace  equal  to  nine  times  ita  own  diameter  per  hour,  or  over 
ill  own  diameter  in  less  than  seven  minutes. 

TIm  movements  and  changes  of  phase  of  the  other  two  moons  are 
Ml  io  imind.  The  third  passes  through  its  phases  in  about  170 
hon,  or  seventeen  Jovian  days,  and  its  apparent  motion  is  at  the 
mla  €t  about  1^  per  hour.  The  fourth  and  last  completes  its  changea 
k  400  hoars,  or  forty  Jovian  days,  and  ita  apparent  motion  is  at 
the  rate  of  little  less  than  1^  per  hour,  being  double  the  apparent 
mCioD  of  our  moon. 

Thua  the  inhabitants  of  Jupiter  have  four  different  months  of 
fear,  eight,  seventeen,  and  forty  Jovian  days,  respectively. 

2750.  Elongation  of  the  iateUites, — The  appearance  which  the 
aslellitea  of  Jupiter  present  when  viewed  with  a  telescope  of  mode- 
mla  power,  ia  that  of  minute  stars  ranged  in  the  direction  of  a  line 
dnwn  through  the  centre  of  the  planet's  disk  nearly  parallel  to 
the  direction  of  the  belts,  and  therefore  coinciding  with  that  of  the 
iknefa  equator.  The  distances  to  which  they  depart  on  the  one 
■de  or  other  of  the  planet,  are  so  limited  that  the  whole  system  is 
iesloded  within  the  field  of  any  telescope  whose  magnifying  power 
is  not  considerable ;  and  their  elongations  from  the  centre  of  the 
planet  can  therefore  be  measured  with  great  precision  by  means  of 
the  wire  micrometers. 

When  the  apparent  diameter  of  the  planet  in  opposition  is  45^j 
the  greatest  elongations  of  the  satellites  from  the  centre  of  the 
fknetfs  disc  are  aa  follow:  — 

28* 


it  fiiUowi,  tlenfore,  tli&t  the  mtin  Bjntm  fa  0amiMl  irilkli  * 
nnlmKOf  miMut  1200"  in  extent,  bong  twa4liiidi  «f  ttt^it- 
not  diuaelar  of  the  moon.  If,  tbsrefbra,,  wm  conwiin  ll«  Mlin 
^Mk  to  be  oentrically  GUperpoaed  on  tliataf  Jnitsr,  not  colj  woiU 
■Jl  the  Mtallitea  bo  covered  bj  it,  bat  that  vhieli  elongUM  itidf 
mort  from  the  planet  would  not  approeob  ncuei  to  tbe  mooo'i  edgt 
then  rmi  WTth  of  its  apparent  diameter. 

If  lU  tbe  ntellicea  were  at  the  aame  time  at  their  gieftteit  eloe- 
gtioMi,  thaj  WDoId,  relative!;  to  the  sppareot  diameter  of  tk* 
pUne^  pment  the  eppamnoa  i^annted  m^.  760. 


Itf-TM. 

2760.  Dittanea  from  JupUer.  —  The  aotoal  distuon  of  ikl 
ntellites  from  the  centre  of  the  planet  maj  be  imuediatel;  inbani, 
from  a  comparison  of  their  greateat  elonealioQa  with  the  ^ipanet 
■emi-diameter  of  the  planet  8inoe,  in  ue  case  abora  rappoMd, 
the  apparent  semi-diameter  of  the  planet  is  22"'6,  tbe  distances  will 
be  found  expressed  with  reference  to  the  wmi-diameter  as  the  oil) 


by  dividing  the  greatest  elongations  expressed  i 
This  gives  for  the  diatancea:  — 


I  bj2S-t. 


IV... 


5S6 


t 

Relatively  to  the  magnitude  of  tbe  planet,  therefore,  tbe  sat^Ui 
revolve  much  closer  to  it  than  the  moon  does  to  the  earth.  Tbe 
distance  of  the  moon  is  nearly  60  semi-d  lame  ten  of  tbe  euth,  while 
tbe  distance  of  the  most  remote  of  Jupiter's  moons  ia  not  more 
thin  26  semi-diameters,  and  that  of  the  nearest  only  nz,  from  bis 
oentre. 

Owing,  however,  to  the  greater  dimensions  of  Jupiter,  the  Mtnil 


THE  MAJOR  PLANETS. 


881 


liiiftuioefl  of  the  attellites,  expressed  in  miles,  are  (except  tliafc  of  the 
fint)  greater  than  the  distance  of  the  moon  from  the  earth. 

2761.  Barmonic  law  observed  in  (he  Jovian  system.  — That  the 
nme  law  of  gravitation  which  reigns  thronghout  the  material  nni- 
veraey  preTsdls  in  this  system,  is  rendered  manifest  hy  the  accordance 
of  the  motions  and  distances  of  the  satellites  with  the  harmonic  law. 
In  the  following  table  numerical  relations  establishing  this  are  ex- 
hibited :— 


P* 

D 

p 

D» 

I* 

D» 

T. 

eo 

43 

218 

1840 

8-9 

n. 

••0 

86 

886 

7226 

8-2 

TIL 

1&-4 

172 

3052 

20,684 

81 

lY. 

27-0 

400 

10,688 

100,000 

81 

Hm  want  of  exact  equality  in  the  numbers  in  the  last  column,  by 
which  the  ratio  of  the  squares  of  the  periods  to  the  cubes  of  the  dis- 
tuieaa  are  expressed,  is  to  be  ascribed  partly  to  usins  round  numbers 
odIj,  and  partly  to  the  effects  of  the  mutual  disturbances  produced 
by  the  satellites  upon  each  other  and  by  the  spheroidal  form  of  the 
planet  itself. 

2762.  Singular  relation  between  the  motions  of  the  first  three 
satellites.  —  On  comparing  the  periods  of  the  first  three  satellites,  it 
ii  evident  that  they  are  in  the  ratio  of  the  numbers  1,  2,  and  4. 
For  we  have — 

43  :  86  :  171  : :  1  :  2  :  4. 

Since  the  mean  angular  velocities,  or,  what  is  the  same,  the  mean 
apparent  motions  as  seen  from  Jupiter,  are  fouud  by  dividing  360^ 
by  the  periodic  times,  it  follows  that  these  motions  for  the  three 
ntcllites  are  in  the  inverse  ratio  of  1, 2,  and  4,  that  is,  as  1,  },  and  i ; 
uid,  therefore,  that  the  mean  apparent  motion  of  the  second  satellite 
ii  half,  and  that  of  the  third  one-fourth  of  the  mean  apparent  motion 
of  the  first. 

It  follows,  also,  that  if  twice  the  mean  motion  of  the  third  be 
added  to  the  mean  motion  of  the  first,  the  sum  will  be  three  times 
the  mean  motion  of  the  second.  This  will  be  rendered  evident  by 
expresfing  these  motions  by  general  symbols.  Let  m'y  m",  and  m"\ 
express  the  mean  hourly  apparent  motions.     Wc  shall  have — 

m=  im!  m'"  =  i  wi' ; 

and  consequently 

m'  +  2m'"  =  m'  +  }m'  =  3  m'  =  3  m". 

2763.  Correspond int/  relation  between  their  mean  lomjitudes.  — 
The  longitudes  of  satellites  are  referred  to  by  their  primaries  as  visual 
centres.     Thus  the  mean  longitudes  of  Jupiter*s  tatcllites  are  the\t 


■iip  laguhr  distiBOM  ftom  Um  fell  atnl  of  Alia  M  mt»  tmm 
Jnplar.  Now,  U  fbUm  thrt  A«  nhlte  wUA  iH  taw  Am« 
to  pnnil  betwMD  th»  mnii  motioiu  of  Dm  flattluMaliffill^dM 
prvraila  between  thnr  meu  loi^tada*.  I«t  Atm  hm^ttim  M 
■117  pTopoaed  tiiB«  hef,f,  P*;  ud  ■&«•  pnd  b|l«nI,ADV 
wbkli  ell  the  eebJlitee  will  hxn  lOffamMiUr  hrtp^vfln,  M 
tftem  be  l',  l",  l*".  Tfae  ui^ee  or  erai  mand  dnoan^U  the  ii- 
leml  wfll  be  l' — r,  l" — r,  L^ — r* ;  and  RDM  Otw  vul  npMt 
•nd  be  pToportiotul  to  the  meen  eppannt  medon^  wa  Aell  fctt  ■ 

from  wbieii  n  iiueiiud 

8 1"  _  (l' +  2  l") = 8  r  -  cr  +  2  r). 

It  ippean,  thereftm,  the  ^Aivimm  between  tbree  times  tbe  lugj- 
tade  of  ^e  Moond  end  the  ram  of  the  lonntude  of  the  firet  and 
twioe  that  of  the  thiid  to  hmiiiUe;  but  mat  this  inTamblE  dif- 
ftnnee  Ii^  does  not  appear  from  tba  men  niatlan  of  the  pcnods.  A 
rin^  obaemtion  of  ttie  poritiona  of  the  thne  eat«Ilit«3  et  an;  pm- 
poaed  moment,  ia  anffident  to  aaoertun  tfaia  ^ference ;  since  wbit- 
arer  it  ma;  be  at  any  one  momenl,  it  mnat  alwaja  continne  to  be. 
Now,  it  may  be  thns  eaaJIj  aseertained  by  obaamtionii  made  at  as; 
wopoaed  time,  that  tbia  diSerenee  ia  ezaotly  180°.  W«  dwH  thm 
have,  aa  a  pennaoeot  ralalion  bMwen  the  poaitiaD  of  Aaaa  ttni 


81."— (l'  +  2l'^  =  180''; 
ao  that,  whenever  the  poaitioaa  of  any  two  of  them  an  ^ren,  tbt 
position  of  the  other  csn  be  foand. 

It  followa  from  thia  relation,  that  the  three  mtellitea  can  nam 
have  at  the  name  time  the  same  phase ;  foi  if  they  had,  they  Botf 
neoesaarily  have  the  same  visual  direotion,  and  oonaeqnently  tbt 
Mme  longitude,  which  would  be  incompatible  with  the  pteeediog  ■•■ 
latioD.  If  two  of  tbero  have  nearly  the  Rme  phase,  the  third  malt 
have  a  phase  difTering  from  it  by  180°,  90°,  or  60°,  aiooor^i  ta 
the  satellites  which  agree  in  their  phase. 

If  the  second  and  third  have  nearly  the  same  phaa^  we  ahaU  hsia 
t"  ^  l*" ;  and  therefore — 

8  h" —  l'— 2 1."  =  l" — l'  =  180". 
The  firet  will  have  a  position,  and  therefore  a  phaae,  in  direct  oppo- 
sition to  the  common  phase  of  the  second  and  Uiird.    If  one  be  d«v, 
the  other  will  be  full,  and  vtce  venA. 

It  the  first  and  seoood  have  a  common  phaae,  wa  ahall  ban 
l'  =  l"  ;  and  therefore — 

3l'  — L'  — 2l'"  =  2Cl'— i."0  =  180». 
l'  — l"'  =  90°. 


THB  MAJOR  PLANETS.  888 

Tbo  third  nteHite  will  therefore  be  90^  from  the  common  direction 
of  the  other  two,  and  will  Uierefore  have  a  phase  different  from 
theirs  by  90^.  If  one  be  full  or  new,  the  other  will  be  in  the 
qoartersy  and  vice  versd. 

In  fine,  if  the  first  and  third  have  a  common  phase,  we  shall  have 
l'=l'"j  and,  consequently — 

8  l''  — 8  L'  =  180^        il'-^il  =  60^ 

The  aeeond  will  therefore  have  a  position  60^  different  from  the 
common  direction  of  the  other  two,  and  its  phase  will  differ  in  the 
sune  degree  from  their  common  phase.  If  one  be  full,  the  other 
will  be  gibbons;  and  if  one  be  new,  the  other  will  be  a  crescent ; 
the  breadth  of  the  gibbous  phase  being  120^^  and  that  of  the 
descent  60^ 

The  student  will  find  no  difficulty  in  tracing  the  effects  of  this  re- 
ladoD  in  all  other  phases. 

An  attempt  has  been  made  to  trace  the  remarkable  relation  be* 
twcen  the  periods  here  noticed  to  the  effects  of  the  mutual  gravitation 
of  the  satellites;  and  Laplace  has  shown  that,  if  such  a  relation 
prevailed  nearly  at  any  one  epoch,  the  mutual  gravitation  of  the 
■tellitea  would  render  it  in  process  of  time  exact.  There  would 
nem,  therefore,  to  be  a  tendency  to  such  a  relation,  as  a  consequence 
of  the  ceneral  law  of  gravitation. 

2764.  Orbits  of  satellites.  —  The  orbits  of  the  satellites  are  el- 
fipMt  of  very  small  ellipticity,  inclined  to  the  plane  of  Jupiter's 
orbit  at  very  small  angles,  as  is  made  apparent  by  their  motions 
being  always  very  nearly  coincident  with  the  plane  of  the  planet's 
^equator,  which  is  inclined  to  that  of  its  orbit  at  the  small  angle  of 
8*>  y  30". 

2765.  Apparent  and  real  magnitudes.  — The  satellites,  although 
redoeed  by  distance  to  mere  lucid  points  in  ordinary  telescopes,  not 
only  exhilnt  perceptible  disks  when  observed  by  instruments  of  suf- 
Ident  power,  but  admit  of  pretty  accurate  measurement  At  oppo- 
dtion,  when  the  apparent  diameter  of  the  planet  is  45'',  all  the 
latellites  snbtend  angles  exceeding  1",  and  the  third  and  fourth 
appear  under  angles  of  1}"  and  1^".  By  observing  these  apparent 
diameters  with  all  practicable  precision,  and  multiplying  them  by 
the  linear  value  of  1",  as  already  determined  (2741),  their  real  di- 
imeters  may  be  ascertained  as  follows : — 

MUm. 

I r>'194  X  1984  =  2809. 

II V^OIO  X  1934  =  2069. 

Ill l''-747  X  1934  =  8378. 

IV 1^M95  X  1984  =  2891. 

It  appears,  therefore,  that  with  the  exception  of  the  second, 
which  is  ezaetly  equal  in  magnitude  to  the  earth's  moon,  a\V  tV^*^ 


odMiB  «e  M  k  mvoli  bmr  wlBf  ftd  on  of  thi^  At  AM,  k 

giMter  than  the  pUiMt  Hemuj,  vhOa  tte  taHh  li  MJ  mM; 
equal  to  iL  - 

2766.  Appartnt  tnaffKituda  at  WM  yVoM  JifpOar. — ^)r«a»- 
yaring  thw  real  flianinfrni  nith  ihrir'HirtintiM,  thn  ■mirant  iHi»ii 
ten  ot  the  Mvenl  Mietlites,  aa  aeen  fioB  JapiMr,  nsy  be  aaalj 
Hcertained.  Bj  dmding  tbe  actoal  dkttiwi  of  the  nlaUitea  tma 
Jnpta  b;  206^65,  we  obtain  die  linear  nloe  of  I"  at  eoefa  dii- 
tuoe;  and  br  dinding  the  wtotl  diameten  ot  the  wlillilw  n- 
WfteArtijbjuinTiijMfim  obt^,  in  neondi,  thrir  ^^mnt ^faa^ 
tan  as  aeen  from  Jnpiter. 

In  maUng  thta  eaUnlation,  bowever,  it  is  neeeaHVj  to  lifea  Me 
Mooont  tbe  magnitude  of  the  eemi-diatneter  «f  tbe  pleaal;  tkm  il 
ii  from  tbe  sumce,  and  not  from  tbe  eentre,  that  the  wldDli  b 
.    viewed. 

It  fdlowi,  from  a  ealenlalioB  made  on  tbeae  printiple^  thial  Aa 


ampannt  mi^itndM  of  (ha  fbsr  mteBitaa,  aaea  ftnn  aqr  pnl  <( 
the  anrftea  not  *  ....  ...... 

tbeBntSG'Sr 
tat  the  fonrth 


tu  fwnored  from  tbe  eqaatot  of  tha  tlnot,  ant  fer 
die  Bnt  SG'  MT,  Ibr  tbe  aeooDd  Id*  80^,  br  the  tUtd  IV  IV,  ■! 


The  first  ntellite,  therefore,  has  an  apparent  diameter  equal  to  diat 
of  the  mooD ;  tbe  eeoood  and  third  are  nearly  eqnal  and  aboat  half 
that  diameter;  and  tbe  apparent  diameter  of  the  other  latellile  ii 
abont  the  fourth  part  of  that  of  the  tnooo. 

It  maj  l>e  easily  imagined  whatvarioaB  and  interesting  soctoreil 
phenomena  are  witnessed  by  the  inhabitants  of  Jupiter,  when  the 
TariouB -msgnitades  of  these  fonr  moons  are  combined  with  tba 
qaick  sucocsuon  of  their  phases,  and  tbe  rapid  apparent  motiona  of 
toe  first  and  sccood. 

By  the  relation  (2768)  between  the  mean  motiona  of  tbe  fint 
three  ntellites,  they  nover  can  be  at  the  same  time  on  the  aame  nds 
of  Jnpiter ;  so  that  whenerer  any  ono  of  them  ia  abaent  from  tba 
firmament  of  tbe  planet  at  night,  one  at  least  of  tiie  otinn  nnl 
be  present  The  Jovian  nights  are,  therefore,  alwaya  moenfi^ 
except  during  eclipses  (whiob  take  place  at  every  rerotuliaD),  and 
often  enlightened  at  once  by  three  mooDs  of  diffennt  apparcoit  m^ 
nitudes  and  seen  noder  different  phases. 

2767.  Parallax  of  the  tatellite».  —  Owing  to  tbe  anall  prapot^ 
tioD  which  the  distances  of  tho  aatellites  bear  to  the  anmi  rtianirUT 
of  tbe  planet,  tbe  effects  of  their  parallax,  as  oheerrod  from  the  iit- 
&oe  of  Jupiter,  are  out  of  all  analogy  with  any  phenomena  of  a 
like  kind  upon  the  earth.  The  nearest  body  in  tbe  ouTene  to  tba 
oarth,  tbe  moon,  is  at  the  distance  of  sixty  semidiamelen,  and  its 
horiioutal  parallax  is  consequeatlv  less  than  1°;  while  Ae  mort 
remote  of  Jupiter's  satellites  is  only  twentyHMveD,  and  tha  aaanal 
only  aif  semidtameters  from  his  oentra. 


TBI  JUJOB  PLANETS.  886 

Bj  the  metbod  explained  in  2327}  the  horizontal  parallaxes,  k, 
^}  iTy  i/^y  <^  the  four  satellites,  may  be  determined,  and  are  — 

«--^_»&.  ^--.^^g—O.  H^j^-SQ. 

2768.  Apparent  magnxiudes  of  Jupiter  seen  from  the  satdlitei, 
—  Since  the  apparent  diameter  of  the  planet,  seen  from  a  satellite, 
ii  twice  its  horisontai  paralbix  (2327),  it  follows  that  the  apparent 
diameter  of  Jnpiter  seen  from  the  first  satellite  is  19^,  from  the 
second  12^  and  from  the  third  7"",  and  from  the  fourth  4-25.''  The 
disk  of  Jnpiter,  therefore,  appears  to  the  first  with  a  diameter 
eighteen  times  greater,  and  a  surface  320  times  greater  than  that  of 
the  full  moon. 

2760.  Sateliitet  invisible  from  a  circumpolar  region  of  the 
planet,  —  It  is  easy  to  demonstrate  in  general  that  an  object  cannot 
be  seen  from  any  part  of  the  surface  of  a  planet,  which  is  at  a  dis- 
tance fi^m  its  pole  less  than  the  horizontal  parallax  of  the  object. 
Let  N  P  s,  fg.  760,  be  a  meridian  of  the  planet,  n  s  its  axis,  o  an 

object  at  a  distance,  o  c,  from  its 
centre.  Suppose  a  line  op  drawn 
from  o,  touching  the  meridian  at  p, 
the  angle  p  o  c  will  be  the  horizontal 
parallax  of  o;  and  since  the  angle 
opc  =  90°,  the  angles  pco  and 
P  o  c  taken  together  are  90^.  But 
Pig.  760.  since  the  angle  n  c  o  is  also  90^,  it 

follows  that  the  angle  N  c  p,  and, 
therelbrei  the  arc  n  p  which  it  measures,  is  equal  to  the  horizontal 
parallax  P  o  c. 

Now  it  is  evident,  that  o  is  not  visible  from  any  part  of  the  meri- 
dian between  p  and  n.  If,  therefore,  a  parallel  of  latitude  be  sup- 
poeed  lo  be  described  round  the  pole  at  a  distance  from  it  equal  to 
the  horisootal  parallax  of  any  object,  such  object  cannot  be  seen 
from  any  part  of  the  circumpolar  region  included  within  such  parallel. 
It  follows  finom  this,  from  the  values  of  the  horizontal  parallaxes 
of  the  aatellites  foond  above  (2732),  and  in  fine  from  the  fact  that  the 
■itellites  move  nearly  in  the  plane  of  the  planet's  equator,  that  the 
first  satellite  is  invisible  at  all  parts  within  a  parallel  described  round 
the  pole  ftt  a  distance  of  9*5'',  the  second  at  6"^,  the  third  at  3*6'', 
and  the  foarth  at  2*1^. 

2770.  JRotation  on  their  €uce$,  —  One  of  the  peculiarities  in  the 
motion  of  our  moon  which  distinguishes  it  in  a  remarkable  manner 
from  the  planetii  is  its  revolution  upon  its  axis.  It  will  be  remem- 
beredi  that  tiM  j^Unett  generally  rotate  on  their  axes  in  times  some- 


sw  A0noiMitf'* 

wlul  analogomi  to  ihtt  of  die  mA.  NoW|  on  te  tailiu]f^  ll« 
mooD  revolves  on  *Hb  ism  in  tfie  Mune  time  ihni  il  t^M  In  f^ 
vidve  ronnd  the  earth;  in  oonieqnenee  of  whioh  aidlfMftaMBft  of 
its  motionsi  it  tame  the  Bame  heousphere  ooatmnaDj  to— idi  llie 
earth. 

Some  obeervatione  of  Sir  William  Henehel  haw  naadewi  il  pva- 
hable,  that  the  Jovian  moons  also  refdw  on  their  asei  onoe^  in  ti» 
time  of  their  reepeotlve  revolntiotts  ronnd  the  pkaet  These  obnr- 
vations  eannot  be  repeated  withoat  the  aid  of  teleaeopes  a»  wwwilhl 
as  those  of  the  elder  Herscheli  and  it  maj  be  ezpeoled  taiA  tibess 
of  Lord  Rosse  and  others  may  supply  fnrther  evidsooe  €■  tikis 
qnestion. 

2771.  Mau  of  Jupiter.— ThB  ratio  of  tiie  mass  ef  Jvpitor  to 
(hat  of  the  snn,  can  be  dednoed  from  the  motion  of  may  of  the 
satellitesi  by  the  method  explained  in  (2685). 

If  r  axid  p  eicpress  the  distance  and  period  of  the  pfauMl^  t'and 
^  those  of  the  satellitei  and  M  and  ^  the  msssss  of  tba  am  and 
planet,  we  shall  have—- 

i = (f  )■ "  (7)' 

By  substituting  in  this  formula  the  distances  and  periods  for  eseh 
of  the  four  satellites^  we  shall  find  the  following  values  of  --p : 

I.  ~  =  1130.    II.  51  =  1123.    m.  ~  =  1121.    IV.  ^  =  1095. 
m'  m'  M'  iff 

The  small  discrepancy  between  these  values  is  due  chiefly  to  the 
causes,  already  explained,  for  the  departure  of  the  harmonic  law 
from  absolute  precision. 

The  following  are  the  estimates  of  the  mass  of  the  planet  ob> 
tained  by  processes  susceptible  of  greater  precision : — 

Laplaoe 1070. 

Nicolai 1064. 

Airy 1048-69. 

Santini 1060. 

Bessel 1046. 

The  last  three  computations  were  conducted  on  principles  such  u 
to  secure  the  matcst  attainable  precision,  and  these  estimates  are 
confirmed  by  observations  on  the  perturbations  produced  by  Jupiter 
on  the  smaller  planets. 

Since  the  mass  of  the  sun  is  about  855,000  times  that  of  the 
earth,  while  it  is  only  1050  times  that  of  Jupiter,  it  follows,  that 
the  mass  of  Jupiter  exceeds  that  of  the  earth  in  the  ratio  of  8550 
to  10-50,  or  338  to  1. 

The  comparatively  great  mass  of  Jupiter  explains  the  very  short 
penoda  of  his  satellites  compared  with  that  of  the  moon. 


THI  MAJOB  FLANETS. 


887 


Al  gnater  disUnoes  from  Jnpiter  than  that  of  the  moon  from  the 
Mith,  Uiej  nevertheleBS  revolve  in  periods  much  shorter  than  that 
of  the  mooDy  and  are  affected  by  centrifagal  forces,  which  exceed 
tkal  of  the  moon  in  a  talio  which  may  be  determined  by  the  pe- 
riods and  dbtanoesy  and  which  most  be  resisted  by  the  attraction  of 
a  eential  mass  proportionally  greater  than  that  of  the  earth.  It 
voold  bo  easy  to  show  that,  if  the  earth  were  attended  by  a  similar 
system  of  moons,  at  like  distances  from  its  centre,  their  periods 
woald  bo  aboat  eighteen  times  greater  than  those  of  Jupiter's 
■tfllitgfl 

2772.  Their  mutual  perturbations, — The  mutual  attraction  of 
the  mwimt%  ci  the  satellites,  and  the  inequality  of  the  attraction  of 
the  nm  vpon  them,  produce  an  extremely  complicated  system  of 
disturbing  actions  on  their  motions,  which  has  nevertheless  been 
brooght  with  great  saooess  under  the  dominion  of  analysis  by 
Lqilaoa  and  Lagrange.  This  is  especially  the  case  with  the  three 
imier  satellites,  whose  motions,  but  for  this  cause,  would  be  sensibly 
unifonn.  The  effect  of  these  disturbing  forces  is  nevertheless  miti- 
pted  and  limited  by  the  very  souill  eccentricities  and  inclinations 
of  the  orbits  of  the  satellites. 

2773.  Density,  —  The  volume  of  Jupiter  being  greater  than  that 
of  the  earth  in  the  ratio  of  1400  to  1,  while  its  mass  is  greater  in 
the  inferior  ratio  of  338  to  1  nearly,  it  follows,  that  the  density  of 
the  matter  oomposing  the  planet  is  less  than  the  mean  density  of 
the  earth  in  the  ratio  of  the  above  numbers.     Wc  have,  therefor 


d 


338 
1400 


=  0  2415. 


Its  mean  density  is,  therefore,  less  than  onc-fuurth  of  that  of  the 
earth;  and  since  the  mean  density  of  the  earth  is  5  07  times  that 
of  water,  the  density  of  Jupiter  is  1-37  times  that  of  water. 

2774.  Mattes  and  densities  of  the  satellites.  —  The  masses  of 
the  satellites  are  determined  by  their  mutual  disturbances,  by  means 
of  the  seneral  principle  explained  in  (2037),  and  the  densities  are 
deduced  as  usual  from  a  comparison  of  these  masses  with  their 
volomes.  In  the  following  table  are  given  the  masses  as  compared 
with  the  primary  and  with  the  earth,  and  their  densities  as  compared 
with  the  earth  and  with  water. 


m  1. 

Mwi.  UMt  af  Butt 

DrMity.  that  of  Eulh 
-  1. 

1 

Dniallr.  that  of  Water 
-  1. 

I. 
II. 

UL 
IV. 

00)00173 

aonon23i 

(hJ00Ot»6 

0«»OI27 

0K)0576 

0i)0773 
0-0SM7 
0D1422 

0-02016 
0-u:tul5 
ommj:»m4 
0-03925 

01143 

0-1710 

o:w7o 

0-222O 

1 

Ul. 


29 


'■  Thus  it  appears  that  the  dendtj  of  the  uttir  mmnphdng  fBmm 
iatellites  is  much  smaller  than  those  of  may  otlMr  bedhi  of  tbe 
ijstem,  whose  densities  are  known. 

It  follows^  therefore,  that  the  first  satsllite  nrast  bo  ooinpoiwd  of 
natter  which  is  twice  as  light  as  eork,  the  density  of  wUeh  m  0-240; 
and  that  of  the  third,  wh^  oonsisU  of  the  hetTiest  wnttoTi  is  nol 
more  dense  than  the  lightest  sort  of  wood,siMh|  tor  enaple^  ai  dw 
common  poplar,  whose  density  is  0*888  (787). 

It  is  remarkable  that  this  eztremelT  smaU  dogrso  of  dooai^  is 
not  found  in  the  earth's  satellite,  the  densitj  of  whieh,  thoodi  mb 
than  that  of  the  earth,  is  still  more  than  twice  the  denaitj  ofwater. 

The  planets  Mercury  and  Mars,  which  are  so  neariy  of  the  saae 
magnitudes  ss  the  third  and  fowth  satellites,  show,  in  m  flCrikiag 
manner,  the  difference  of  the  matter  oomposing  thena  by  tbo  gnat 
difference  of  their  densities.  The  mean  speeific  wdght  of  tho  BMrto* 
rials  composing  these  planets  is  nearly  tae  aamo  as  that  of  those 
which  compose  the  earth,  while  the  materials  of  tiie  thiid  Mldils 
are  thirteen  times,  and  that  of  the  fourth  twentj^TO  times  l%htMr. 

2775.  Superficial  gravi^  on  Jupiier.  —  The  gravity  by  wUah 
bodies  placed  on  the  surface  of  this  planet  are  afRsoted,  oaltting  tlw 
consideration  of  the  modifying  effects  of  its  spheroidal  form  and  its 
rotation,  may  be  computed  by  means  of  its  mass,  and  its  mean  semi- 
diameter  by  the  method  already  explained. 

Let  m'  =  Jupiter's  mass,  that  of  the  earth  being  =  1 ; 

r^  =  Jupiter's  mean  semi-diameter,  that  of  the  euih  heiog 

(/  =  superficial  gravity,  that  of  the  earth  being  =  1, 
we  shall  then  have  (2647),  (2771)  — 

m'        338 

2776.  Caxirifagal  force  at  Jupiter* $  equator,  —  In  the  case  of 
Jupiter,  owing  to  the  great  degree  of  its  oblateness  and  its  ra|wl 
rotation,  this  force  of  superficial  gravitation  is  subject  to  wm^ 
greater  variation  than  on  the  earth.  To  determine  this  variatio&T  i^ 
will  be  necessary  to  compute  the  centrifugal  force  by  which  hodia 
placed  on  the  equator  of  the  planet  are  affected. 

Let  c  =  centrifugal  force  related  to  the  terreatrial  gravity  ts 
the  unit, 
g  =  1608  feet, 

V  =  the  velocity  of  Jupiter's  equator  in  feet  per  second  dut 
to  his  rotation, 
Ire  shall  then  have  (313)— 


THE  MAJOR  PLANETS.  S89 

The  Ta]iie  of  v  dodnced  from  the  equatorial  diameter  of  the 
pboet  (2756)  and  the  time  of  rotation  (2747)  is  42760 ;  and  it 
follows,  therefore,  that  c  =  0*234.  Deducting  this  from  the  super- 
ficial gravity  nndiniiuibhcd  hy  rotation,  already  computed  (2775), 
te  shall  find  the  effective  equatorial  superficial  gravity 

2616  — 0-234  =  2-382. 

2777.  Variation  of  superficial  graviti/  from  equator  to  poU,  — 
The  well-known  theorem  of  Clairault,  already  quoted  (2384),  hy 
which  the  oblateness,  the  yariation  of  superficial  gravity,  and  the 
oentrifogal  foroe,  are  connected,  supplies  the  means  of  determining 
this. 

Let  e  and  to,  as  in  2384,  express  respectively  the  fraction  of  its 
vhole  length  by  which  the  equatorial  exceeds  the  polar  diameter, 
tnd  the  fimction  of  its  whole  weight  by  which  the  weight  of  a  body 
and  the  pole  exceeds  the  weight  of  the  same  body  at  the  equator, 
and  in  fine,  let  c  express  the  equatorial  centrifugal  force  as  a  fraction 
of  the  effective  equatorial  superficial  gravity.  By  the  theorem  of 
Clainolt,  these  three  quantities  are  related  in  the  manner  expressed 
in  the  following  formula : — 

e  4-  w  =  2-5  c. 

Bat,  from  what  has  been  already  explained,  e  =  0  08^ 

0        0-234       ^  ^Q^ 

tnd  eonaequently  w  =  0-16. 

From  whence  it  follows  that  the  weights  of  bodies  are  increased 
by  16  per  cent  when  transferred  from  the  pole  to  the  equator. 

A  mass  of  matter,  therefore,  which  upon  the  earth's  surface  would 
weigh  1000  pounds,  would  wei^h,  if  placed  upon  Jupiter's  equator, 
2382  pounds,  and  if  placed  at  nis  pole,  would  weigh  2763  pounds. 

The  height  through  which  a  body  would  fall  in  a  second  would 
be  16-08  X  2-382  =  38-3  feet  at  its  equator,  and  44*4  at  the  pole. 

The  length  of  a  seconds  pendulum  varies  in  the  exact  ratio  of 
the  forces  of  gravity  which  produce  its  vibration  (542) ;  and  if  the 
length  of  the  seconds  pendulum  on  the  surface  of  the  earth  be 
taken  in  round  numbers  as  39  inches,  that  of  a  seconds  pendulum 
at  Jupiter's  equator  would  be  39  x  2-382  =  92  01  inches,  and  at 
the  poles  107*77  inches. 

2778.  Densiti/  must  inrreane  front  the  surface  to  the  centre.  —  It 
is  ca^y  to  show  that  the  oblatencss  of  Jupiter  is  incompatible  with 
the  supposition  of  his  uniform  density.  It  was  demonstrated  by 
Newton  that,  if  the  earth's  density  were  uniform,  its  oblateness 
would  be  ^Iq  ;  and  the  same  would  be  true  of  any  spheroid  of  uni- 
form density,  revolving  on  its  axis  in  the  same  time.  But  the  ob- 
lateness  will  be  increased  in  the  same  ratio  as  the  eqoaTe  oi  \Xi^ 


ASTRONOMT. 

of  rotation  mi  as  tlie  dendtj  are  dimiDubed.     If,  t 

f>Tcsa  tbo  time  of  rotation  of  Jupiter,  tliat  of  (he  earth  being  1, 
(/  the  tJicoa  donHit;  of  Jupiter,  tbat  of  tiie  earth  being  1,  ibe 
iteneES  which  the  pbnet  would  have  if  ita  deDEiCf  wero  uniform 


.M  I 


1 


1 


"  5m  ^  «•  **  ,/• 


1 
""  2-40C 


and  (i  =  0-22" 

_      2-406' 
*  ~  230  X  0-; 


=  01104. 


the  obiatcness  deduced  from  on   irration  beitig  only  0-08,  it 
ra  that  the  deDsity  oanDot  be        '  .id. 

is  easy  to  perceive  that,  if  tensity  augmeutcd  from  the 

■  e  to  the  surfsci^,  the  effect  ir,  ^„o  centrifngol  force  upon  the 
i~.^pODeDt  paria  of  the  mans  wouM  have  a  teodency  to  retider  tbe 
oblatcDCES  Btill  greater  than  it  nould  be  with  tbo  Mine  mass  having 
an  uniforiD  (lensily.  Since,  therefore,  the  actual  oblateneM  ii  iu- 
compalible  cither  with  an  uniform  density,  or  with  a  density  d^ 
crrasing  from  the  fliirface  to  the  centre,  it  follova  that  the  dend^ 
mnet  incrcaao  frota  the  surface  to  the  centre. 

The  mean  density  of  the  planet  being  0228,  it  follows,  therefen, 
that  tlio  mean  density  of  Uic  superficial  stretum  tnnst  be  less  than 
tbix,  though  in  what  proportion  cannot  be  determined  by  these  data. 

If  the  mean  superficial  density  of  Jupiter  bear  the  aame  prtqnrtinn 
to  the  mean  density  of  its  entire  mass,  as  the  mesn  Bupei£eial 
density  of  the  earth  bears  to  the  mean  density  of  its  entire  maaa,  it 
will  follow,  that  the  mean  superficial  density  of  Jupiter  will  ba 
half  its  mean  density,  and  will,  consequently,  be  0-114;  and  siace 
the  mean  density  of  the  earth  related  to  that  of  water  aa  the  unit, 
is  5-67,  it  would  follow  upon  this  aupposition,  that  the  sotaal  meal 
density  of  the  superficial  atratum  of  Jupiter  would  be  0-114  =  li-67 
=  0-645. 

Water,  which  discharges  so  many  important  fnnotiona  in  the  ji^j- 
sioal  economy  of  the  earth,  bas  a  specific  gravity  2-8  times  less  thaa 
tbe  mean  spcdfic  gravity  of  the  superficial  stralam  of  the  e'obe.  If  a 
like  fluid  on  Jupiter,  serving  like  purposes,  be  similarly  related  to  tlia 
mean  density  of  its  surface,  its  specific  gravity  would  therefoie  be — 

which  would  be  more  than  three  times  lighter  than  sulphurie  ether, 
the  lightest  known  liquid,  mid  nearly  equal  in  levity  to  oork. 

2779.  Uii/ily  of  the  Jovian  tyiUm  at  an  iUtatratiiM  of  the  tcAtr 
^item.  — It  is  not  merely  as  a  model  on  a  small  aoale  of  the  ttit' 


,  « 


TUB  MAJOR  PLANETS.  841 

ijBtemi  flo  fiir  as  relates  to  the  analogy  presented  by  the  motions  of 
the  satellites  round  Jupiter  to  the  motion  of  the  planets  round  the 
sao,  and  the  striking  confirmation  of  the  theory  of  gravitation  af» 
forded  by  the  exhibition  of  the  play  of  Kepler's  Laws,  that  the 
Jovian  system  b  to  be  regarded  with  interest  by  the  physical  astron- 
omer. AH  the  effects  of  the  reciprocal  gravitation  of  the  planets 
one  upon  another,  which  mathematicians  have  succeeded  in  ex- 
plaining upon  the  principles  of  the  theory  of  gravitation,  all  the 
perturlmtions  and  inequalities,  many  of  which,  in  the  case  of  the 
planets,  will  take  thousands  of  centuries  to  complete  their  periods 
and  re-commence  their  course,  all  these  are  exhibited  on  a  greatly 
reduced  scale  in  the  Jovian  system.  As  the  central  mass  is  reduced 
in  a  thou^nd-fold  proportion,  and  the  distances  of  the  bodies  re- 
volving round  it  in  a  still  greater  ratio,  the  cycles  of  the  perturbations 
and  inequalities  are  similarly  reduced.  Millions  of  years  are  reduced 
to  thousands,  centuries  to  months,  months  to  days,  days  to  hours. 
Phenomena,  the  periods  of  which  would  far  surpass,  not  the  life  of 
man  only,  but  the  whole  extent  of  time  embraced  within  human 
records  and  traditions,  are  reproduced  and  completed  in  this  minia- 
tore  system,  within  such  moderate  limits  of  time  as  to  bring  them 
within  the  scope  of  actual  observation.  The  analyst  is  thus  enabled 
to  see  practically  verified,  those  conditioos  of  equilibrium  and  sta- 
Inlity,  which  it  would  take  countless  ages  to  develope  in  the  solar 
lystem. 

II.  Satuen. 

2780.  Saiumian  syUftm,  —  Beyond  the  orbit  of  Jupiter  a  space 
hat  little  less  in  width  than  that  which  separates  that  planet  from 
the  sun  is  unoccupied.  At  its  limit  we  encounter  the  most  extra- 
ordinary object  in  the  system,  —  a  stupendous  globe,  nearly  nine 
hundred  times  greater  in  volume  than  the  earth,  surrounded  by  two, 
it  leasts  and  probably  by  several  thin  flat  rings  of  solid  matter,  out- 
lide  which  revolve  a  group  of  eight  moons ;  this  entire  system  moving 
with  a  common  motion  so  exactly  maintained,  that  no  one  part  falls 

apon,  overtakes,  or  is  overtaken  by  another,  in  their  course  around 

the  son. 
Such  is  the  Saturnian  system,  the  central  body  of  which  was 

known  as  a  planet  to  the  ancients,  the  annular  appendages  and  satel- 

litei  being  the  discovery  of  modem  times. 

2781.  Period.  —  By  the  usual  methods  the  period  of  Saturn  has 
been  ascertained  to  be  10759  22  days,  or  29-48  years. 

2782.  Heliocentric  motion.  —  The  mean  heliocentric  motion  is 
tberefore 

H^  =  12.230  annually. 

=  1018°  monthly. 
=  0033°  '^-. 2'  daily. 


S788.  .G^<M^KMa(M».— TkaappmnftMnAArHterfii     I 
■QB  being  O-0g56°,tb«  mean dulj ijnodio  »o«ion, cr lit ■—  Im(j 
iaoratne&t  of  elongalioa,  ia 

0-0866°— (H]8S»  = 
■nd  tho  BTOodie  period  b  tiwnfim 

•^    =877* 


Hie  interral  between  the  ■ 
tbarefora  t  year  and  thutean  daja. 
2784.  i>i<((mce.— The  mean  i'-^ 


BTC  opporitkM  if  ftt  |ta«h 


(24-48f=(9-54)P. 

Ihareftm9-H;  «mn 
OBHtlr  9-6S87S61,  that  «r  At  mfc 

IVking  the  earth'i  roeao  AtaMH 
95  millioDH  of  milen,  that  rf  8An 
will  then  be  906  milliona  of  buIm.        | 

The  eccen  tridt;  of  Satani'a  orint  beng 
0-056,  this  diatanoe  ia  liable  to  in-  , 
tion,  being  aogmented  in  spheKoD,  wA 
dimiQifhea  in  perihelion,  bj  a  twenlwtt 
of  its  wbole  amoant  The  grealett 
diatanoe  of  the  planet  from  the  loa  n 
therefore  950,  and  the  least  ia  850,  ail- 
lions  of  miles. 

2785.  Relative  KaU  of  oiiit  ami 
dutance  from  the  earA. — The  lelatrn 
proportion  of  the  orbita  of  Satan  nJ 
the  earth  are  represented  in  Jh.  Itl, 
wbere  x  sf  k"  is  the  earth'a  orbi^  asl 
8  8*  Saturn's  distance  firom  the  m. 
The  four  positions  of  the  earth  iafi- 
oatedare, 

I    when  the  planet  is  in  oppoB&m. 
x'"  when  the  planet  is  in  oonjanctioa. 
tf    in  quadrature  west  of  the  eon. 
^'  in  quadrature  east  of  the  Ban. 

2786.  Annual ]wallax  of  Satwn. 
—  Since  s  s'  is  0  54  times  8  ^,  n 
sbsll  bavu  for  the  angle  8*81^, 


THB  MAJOR  PLANBTS.  848 

Tiie  8emi-&m6ter  of  the  earth's  orbit  therefore  sabtends  at 
Satom  an  angle  of  only  6°.  The  apparent  diameter  of  a  globe, 
vhich  woold  fill  the  entire  orbit  of  the  earth  seen  from  Satom, 
voakl,  therefore,  be  do  more  than  12^,  or  twenty-four  times  the 
apparent  diameter  of  the  san  as  seen  from  the  earth. 

2787.  Chreat  Mcale  of  the  orhit4il  motion,  —  The  distanoe  of 
Satom  from  the  son  is  therefore  so  enormons,  that  if  the  whole 
earth's  orbit,  measoring  nearly  200  millions  of  miles  in  diameter, 
were  filled  with  a  son,  that  sun  seen  from  Satnra  woold  be  only 
aboot  twenty-foor  times  greater  in  its  apparent  diameter  than  is  the 
actual  son  seen  from  the  earth.  A  cannon-ball  moving  at  500 
miles  an  hour  woold  take  91,000  years,  and  a  railway  train  moving 
50  miles  an  boor  woold  take  910,000  years  to  move  from  Satom 
to  the  son.  Light,  which  moves  at  the  rate  of  nearly  200,000 
miles  per  second,  takes  5  days,  18  hours,  and  2  minutes  to  move 
over  the  same  distanoe.  Yet  to  this  distanoe  solar  gravitation 
tnnsmits  its  mandates,  and  is  obeyed  with  the  otmost  promptitode 
and  the  most  onerring  precision. 

Taking  the  diameter  of  Satora's  orbit  at  1800  millions  of  miles, 
its  drcamforence  is  5650  millions  of  miles,  over  which  it  moves  in 
10,759  days.  Its  daily  motion  is  therefore  525,140  miles,  and  its 
hourly  21,880  miles. 

2788.  Divuum  of  $yno(f£c  period.  —  Since  the  angle  tf  efB  = 
6^  the  angle  £  8  b'  =  84''  and  s'  s  i/"  =  96''.  Since  the  synodic 
period  is  878  days,  the  intervals  between 

84 
opposition  and  qoadrature    =  ^^  X  378  =  88-2. 

96 
conjunction  and  quadrature  =  ^^  X  378  =  100*8. 

It  appears,  therefore,  that  in  88  days  after  its  opposition  the 
plaoet  is  in  its  eastern  quadrature,  and  passes  the  meridian  about  6 
to  the  afternoon.  After  a  further  interval  of  101  days  it  arrives  at 
conjunction ;  after  which  it  acquires  western  elongation,  passing  the 
meridian  in  the  forenoon;  and  at  101  days  from  conjunction  it 
attains  its  western  quadrature,  passing  the  meridian  at  about  6  a.m. 
After  another  interval  of  88  days  it  returns  to  opposition. 

2789.  No  pha$eji,  —  It  is  evident  from  what  has  been  explained 
in  relation  to  Jupiter  (2738),  that  neither  Satura  nor  any  more 
distant  planet  can  have  sensible  phases. 

2790.  Variation  of  the  plane fs  distance  from  the  earth.  —  The 
distances  of  Satura  from  the  earth  are  therefore 

g'  E    =  906  —  95  =  811     millions  of  miles  in  opposition, 
g'  K^'  =  906  +  95  =  1001   millions  of  miles  in  conjunctioa 
ts' k'    =  =  900  0  millions  of  miles  in  quadrature. 


M4  '  igraoHMiT. 

■ 

ThMt  dtttanoes  are  lulijeQt  tof  aome  ?uuilioii|  owing  to  At 
tiieities  of  the  orbils  of  Saturn  and  the  earth.  Tko  anMNiBt  a(  iMk 
wiatbn,  arisinff  from  the  eooentridg^  of  fiatiim'a  orliit^  kp  aa  ki 
been  showoi  100  mUliona  of  milea.  The  vaiiatiaii  dao  to  tiie  <«tft. 
orbit  is  ooroparativelj  amalli  being  undor  two  milliooa  of  aik^    • 

2791.  Staiiont  and  retr€gremum,'^Viom  a  compaiipon  of  tb 
orbital  motion  and  farming  diatanee  between  the  earth  and  Saln^ 
it  appears  that  the  stations  d  the  planet  take  pkoe  at  abont  §&  diyi 
before  and  after  opposition,  Sinoe  the  earth  gaina  upon  the  pfaoit 
at  the  mean  rate  of  0*9526®  per  daj,  the  ang^e  at  tiie  son  e» 
re^Kading  to  65  daya  wiU  be 

0-9526*  X  66  =  61-92®; 

whioh  eoResponds  to  aa  elongation  of  118*..  The  jdanet  is  dMnftn 
stotionary  at  elongstion  67®  east  and  west  d  oppoeition. 
Its  are  of  retrogression  Taries  from  6®  4r  to  6®  55^. 

2792.  Appofmt  <md  real  duunelfr.—Thia  planet  appean«i 
star  of  the  nrst  magnitude,  with  a  fiint  reddish  light.  Its  appenst 
brightness,  compareid  with  that  of  Mars,  is  greater  than  that  wfaidi 
is  dae  to  their  apparent  magnitudes  and  distancesy  a  circomstuee 
which  is  explained,  as  in  the  case  of  Jupiter,  by  the  more  feeUy 
reflective  power  of  the  surface  of  Mars. 

The  disk  is  visibly  oval,  and  traversed  like  that  of  Jupiter  by 
streaks  of  light  aud  shade  parallel  to  its  greater  axis ;  but  these  belts 
are  much  more  faint  aud  less  pronouuoed  than  those  of  Jupiter. 
One  principal  gray  belt,  which  lies  along  the  greater  axis  of  ths 
disk,  is  almost  unchangeable. 

Sir  William  Herscbel  imagined  that  the  disk  had  the  form  of  aa 
oblong  rectangle,  rounded  at  the  corners,  the  length  being  in  tha 
direction  of  tbo  belts.  More  recent  observations  and  micrometrieal 
measurements  made  at  Konigsberg,  by  Professor  Bessel,  and  at 
Greenwich,  by  Mr.  Main,  have  shown,  however,  the  true  form  to  be 
an  ellipse.  According  to  these  measures  the  apparent  magnitwi^ 
of  the  greater  axis  of  the  disk  is  17-053",  and  that  of  the  leaser 
axis  15*394".  The  observations  of  Professor  Struve,  made  with  the 
Dorpat  instruments,  ^ive  17*991  for  the  greater  axis;  the  difference 
of  the  two  estimates  0*938  being  less  than  a  seoond. 

At  the  mean  distance  of  Saturn  the  linear  value  of  a  seoond  is 

906000000  ^  ^3^,^.5 

2*06265 

The  actual  magnitude  of  the  greater  axis  would  therefore  be 

4392*5  X  17053  =  74000  Bcssel. 
4392*5  X  17-91)l  =  79160  Struve. 

The  oblateness  expressed  as  a  fraction  of  the  greater  axis  is  0*097, 
or  a  little  less  than  a  tenth. 


THE  HAJOB  PLAVBTS.  846 

Tfce  kMer  uii  el  the  pUoet  tlierefBre,  aooording  to  StniTe,  meft- 
nm  71,100  milw,  and  ue  mean  diameter  75,000  milos. 

2793.  Surface  and  volume.  — Taking  the  mean  diameter  of  the 
jikiwt  ae  0-46,  that  of  the  earth  being  1,  the  surface  will  be  9-46'= 
89.5,  and  the  Tolnme  9-46*  =  847  times  greater  than  those  of  tho 


(uth. 
Tbei 


lUiin  Tolniaef  of  Safcm  u>d  the  earth  are  represcDted  u 


2794.  Dimmal  relatiim. —  VratA  ohs^mtioo  on  the  apparent 
■otion  of  the  Moli  00  the  diik  of  the  planet,  it  haa  been  ucerlaioed 
la  have  a  ■wtMO  of  totKtkm  npon  the  shorter  alia  of  the  ellipse 
twmed  by  ha  £tk  iM  10^  29"^  IT:  A  terT«strial  d»7  ii  therefore 
•qna]  to  2-S  Brtiriien  dava. 

2795.  JheiAMffM  ^  Uie  axi$  to  the  orbit.  —  The  nseral  direo- 
lioB  of  tbs  BMtioB  at  rotation  has  been  ascertained  t«M  such,  that 
Ihc  inelinaliDD  of  the  eqoator  of  the  planet  to  the  phuM  of  the  orbit 
k  S6°  48'  40",  mi  iti  unlinatioD  to  the  plane  of  the  Mliptio  is  iS" 
Vf  47-7". 

The  axis,  like  that  of  the  earth,  and  those  of  the  ottier  planets, 
■bose  lotatk*  hm  ban  aMerMnad,  is  carried  parallel  to  itself  in 
the  orUtal  molioB  of  the  plaiMt. 

The  eooMOMaoa  of  Ihia  anaflgoMnt  ie  that  the  jear  of  Satuni 
it  varied  by  the  same  soocession  of  teasons  Bnbjeot  lo  the  same  range 
of  lemperatnre  as  those  which  prerail  on  oar  globe. 

2796.  Satimian  day*  and  nii/hu.  Year. — The  alternation 
of  Ught  and  darkness  is  therefore  nearly  the  same  aa  upon  Jupiter. 
This  tmpid  retnm  of  day,  after  an  interval  of  five  hoan  night,  seems 
to  antinie  the  character  of  a  laa  among  the  major  planets,  as  the 
iaterral  of  twelve  hours  certunly  does  among  the  minor  planets. 

The  year  (tf  Satoro  is  eqnal  in  duradon  to  10,759  tematxui 


W  ASTRONOMY,  ' 

itya,  or  to  258,192  boiits.  Bat  since  •  leirestm]  ilajr  u  hjuI  la 
S'3  Salurnian  dajs,  Ihc  nuinkcr  of  Sntunibn  iJajs  in  ^e  Sitarsni 
year  must  lie  247,457- 

2797.  Btt/f  and  almosphem.  —  Streaks  of  lighl  and  ^ade, 
jwmllel  io  their  general  direotion  to  the  ptnnet'B  equator,  hsre  bna 
observed  on  Saturn,  similar,  in  ail  respects,  to  the  belts  of  JufHta, 
nd  Dffordins  like  evidence  of  an  atmosphere  Burrounding  the  plsoet, 
attended  witn  the  like  Bystcm  of  currents  analogous  to  the  tnia. 
Such  an  inference  involveB,  ns  ia  the  former  case,  the  admisaoo  id 
liquid  producing  vapour  to  form  clouds  and  other  meteoralogid 
phenomena. 

2798.  Solar  liijht  and  heal.  —  The  spporent  diameter  of  ibe  suit 
u  seen  from  Saturn  ie  954  times  less  than  as  Ecen  from  the  eanb; 
and  BiDce  its  mean  apparent  diBincter,  aa  seen  from  the  cuth,  ia 
1923",  its  apparent  diameter,  aa  seen  from  Saturn,  mu5t  he 

The  compnrative  apparent  maeniludcs  arc  represented  in^^.TM, 
where  G  represente  the  disk  of  axe  Bun  as  seen  from  the  earth,  ua 
8  as  seen  from  Saturn. 


The  intensit  J  of  solar  light  is  less  io  the  ratio  of  1  to  9-M* = IH  ; 
and  its  optical  and  caloriGo  inflaenees  with  this  reduced  intiMlf 
are  subject  to  the  obaervatiouB  Blraadj  made  in  the  eaae  of  Japitet 
(2744). 
2799.  Stvg*. — Tb%  iB^eft^ion  tS  \.\i%  ^c\«sftQ^  b«.viD(  iiivwtsd 
Mairoaotaen  with  the  power  t*  K^^to»tVwi^,  ^ot  it^Cn^  -^ 


TUE  MAJOR  PLANETS.  847 

hundredB  of  times  closer  to  the  objects  of  their  observation,  one  of 

the  earliest  results  of  the  exercise  of  this  improved  sense  was  the 

discovery  that  the  disk  of  Saturn  differed  in  a  remarkable  manner 

from  those  of  the  other  planets  in  not  being  circular.     It  seemed  at 

first  to  be  a  flattened  oblong  oval,  approaching  to  the  form  of  an 

elongated  rectangle,  rounded  off  at  the  corners.     As  the  optical 

powers  of  the  telescope  were  improved,  it  assumed  the  appearance 

of  a  great  central  disk,  with  two  smaller  disks,  one  at  each  side  of 

it     These  lateral  disks,  in  fine,  took  the  appearance  of  handles  or 

ears,  like  the  handles  of  a  vase  or  jar,  and  they  were  accordingly 

called  the  ansas  of  the  disk,  a  name  which  thoy  still  retain.     At 

length,  in  1650,  Huygens  explained  the  true  cause  of  this  phcuo- 

nenoD,  and  showed  that  the  planet  is  surrounded  by  a  ring  of  opaque 

lolid  matter,  in  the  centre  of  which  it  is  suspended,  and  that  what 

tppear  as  ansa)  arc  those  parts  of  the  ring  which  lie  beyond  the  disk 

of  the  planet  at  either  side,  which  by  projection  arc  reduced  to  the 

form  of  the  parts  of  an  ellipse  near  the  extremities  of  its  greater 

uis,  and  that  the  open  parts  of  the  ansse  are  produced  by  the  dark 

<ky  vbible  through  the  space  between  the  ring  and  the  planet. 

The  improved  telescopes  and  greatly  multiplied  number,  and  in- 
creased zeal  and  activity  of  observers,  have  supplied  much  more 
definite  information  as  to  the  form,  dimensions,  structure,  and  posi- 
tion of  this  most  extraordinary  and  unexampled  appendage. 

It  has  been  ascertained,  that  it  consists  of  an  annular  plate  of 
x&atter,  the  thickness  of  which  is  very  inconsiderable  compared  with 
the  superficies.  It  is  nearly,  but  not  precisely  concentric  with  the 
planet  and  in  the  plane  of  its  ef|uator.  This  is  proved  by  the  coin- 
cideQoe  of  the  plane  of  the  ring  with  the  general  direction  of  the 
belts,  and  with  that  of  the  apparent  motion  of  the  spots  by  which 
the  dionial  rotation  of  the  planet  has  been  ascertained. 

When  telescopes  of  adequate  power  are  directed  to  the  ring  pre- 
sented under  a  favourable  aspect,  dark  streaks  are  seen  upon  its  sur- 
Cice  aimilar  to  the  belts  of  the  planet.     One  of  these  having  been 
observed  to  have  a  permanence  which  seemed  incompatible  with  the 
admission  of  the  same  atmospheric  cause  as  that  which  has  been  as* 
signed  to  the  belts,  it  was  conjectured  that  it  arose  from  a  real  sepa- 
ration or  division  of  the  ring  into  two  concentric  rings  placed  one 
within  the  other.     This  conjecture  was  converted  into  certainty  by 
the  discovery,  that  the  same  dark  streak  is  seen  in  the  same  position 
On  both  sides  of  the  rin^.     It  has  even  been  aiBrmed  by  some  ob- 
servers that  stars  have  been  seen  in  the  space  between  the  rings; 
hut  this  requires  confirmation.    It  is,  however,  considered  as  proved, 
that  the  system  consists  of  two  concentric  rings  of  unequal  breadth, 
One  placed  outside  the  other  without  any  mutual  contict. 

The  plane  of  the  rings,  being  always  at  right  angles  to  the  axis 


MB  MaauamMBL 

«r  ftke  phnet^  ia,  lilM  die  ftzii,  mriid  ¥y  Ik  crtild  MliM^  At 
planet  parallel  to  itself,  ao  that  duiiig  the  jear  of  Safean,  U  wdm- 
goea  changea  of  poaitkm  in  lelalion  to  die  ndiM  leatea  ef  tta 
pbnet^  or  to  a  line  drawn  from  the  asn  analiya  to  thaae  vhioh 
the'earth'a  eqnator  nndemea.  Biaee  ik%  fhm  ef  the  linp  eoia- 
eidea  with  that  of  the  &Unrnian  emnte,  theraiMPe,  it  nffl  be  A- 
reeted  to  the  ann  at  the  epoeha  ef  ue  Satnniaii  aqnlnucea;  tmi^ 
in  fltnerali  the  angle  whidi  the  ndina  feetor  frooi  the  ann  Baku 
with  the  plane  of  the  ring,  will  be  the  ann'a  deelinalioo  aa  aeea 
from  Satorn.  This  ang^,  therafine,  at  the  Satnnuan  aolatieea  wiH 
be  equal  to  the  obliqnity  of  Salnrn'a  eqnator  to  hia  orbit|  that  ii^  to 
26''48'4(r  (2795),  and  at  the  Satnrnian  eqnuMzea  wiU  be  O*". 

2800.  BaiUum  of  modm  of  rmg  amd  nielmai&m  io  ed^fHe.'^ 
The  inveatigation  of  the  poaitioQ  of  the  plane  of  the  ring  in  apaet  j 
waa  nndertdLen  and  eondneted  with  great  abilitjr  and  aneeam  \rj 
Firof.  Beoael,  by  meana  of  an  elaborate  eompariaon  of  nil  the  ie- 
eorded  obeervationa  on  the  phaaea  of  the  ring  from  1701  te  MIfc 
The  retalt  proved  that  the  line  of  intnaeotWD  of  the  pkoe  ef  Ibt 
ring,  and,  therefore,  that  of  the  eqnator  of  the  phnit,  with  the 
plane  of  the  ediptie,  ia  parallel  to  that  diamelnr  of  the  edmitl 
aphere,  which  conneota  the  two  opposite  points  whoae  longitodea  aie 
166''  53'  8-9''  and  846''  58'  8-9",  the  former  being  the  longitude  of 
the  point  at  which  the  rings  pass  from  the  sonth  to  the  north  of  the 
ecliptic,  and  which  is,  therefore,  the  ascending  node  of  the  lian. 
It  also  resulted  from  this  investigation  that  the  angle  formed  by  the 
plane  of  the  rings,  and,  therefore,  of  the  Satnrnian  equator  with 
the  plane  of  the  ecliptic,  is  28''  lO'  44*7''. 

These  lonsitudes  and  obliquity  were  thoee  whioh  oonTOpcaideJI  te 
the  let  of  January,  1800.  It  was  shown  that  die  nodea  of  the 
ring  have  a  retrograde  motion  on  the  ecliptie  at  the  mean  rate  of 
46*462"  per  annum. 

It  resulted  from  the  observations  of  Professor  Stmve,  made  with 
the  great  Dorpat  refractor,  that  the  obliquity  of  the  j^ane  of  the 
ring  to  that  of  the  ecliptic  is  28^^  5'  54",  subjeot  to  a  poeaiUe  enor 
of  6'  24". 

The  observations  and  measurements  of  these  two  eminent  astro* 
nomers  are,  therefore,  in  as  perfect  accordance  as  the  degree  of  pe^ 
fection  to  which  the  instruments  of  observation  have  been  bro^t 
admits. 

2801.  Obliquity  of  ring  to  the  ji^%e^9  orbit  —  The  poatioo  of 
the  plane  of  the  nog  in  relation  to  the  ecliptic  being  thna  deter- 
mined, its  position  in  relation  to  that  of  Saturn's  orlnt  can  be  ascer- 
tained ;  and  this  is  the  more  necessary  to  be  done,  inaamnoh  as  oon- 
siderable  discrepancy  prevails  between  the  statomenta  of  diflerent 
authorities  respecting  this  clement. 


THB  MAJOR  PLANETS. 


849 


Lot  ^fig.  764,  be  tbe  SBoending  node  of  Saturn's  orbit,  and  a' 
tte  aseenduig  nod^  of  the  rioff,  a  a'  being  conscquenti j  an  arc  of 
the  ediptio.  Let  r/  be  the  direction  of  the  plane  of  the  ring,  n' 
its  intenection  irith  the  orbit  of  the  planet,  of  which,  therefore,  a  n 


I1g.7«4. 

k  an  iro,  and  n  the  point  where  the  plane  of  the  ring  intersects  that 
of  llie  orbit  It  has  been  found  that  the  longitude  of  a  is  111^ 
56'  37-4'';  and  since  Uiat  of  a'  is  lee""  53'  8#,  we  have  a  a'  == 
64^  56^  31-5^.  The  angle  n  a  a',  which  is  the  obliquity  of  Saturn's 
oibity  being  2^  29'  35*7",  and  the  angle  n  a'  x,  the  obliquity  of  tho 
nag  to  the  orbit  being  28°  \^  44-7",  it  follows,  by  formulae  of 
qiherical  trigonometry,  that  a  n  a'  or  the  obliquity  of  the  ring  to  the 
orbit  of  the  planet,  is  26''  48'  40" ;  that  a  n,  or  the  distance  of  the 
iBterBection  of  the  plane  of  the  ring  with  the  plane  of  the  planet's 
orbit  from  the  ascending  node  of  the  planet,  is  58°  57'  30";  and,  in 
fne,  the  distance  n  a  of  the  same  point  from  the  ascending  node  of 
tbe  ring  is  4°  32[  30". 

2802.  Condttums  which  determine  the  phases  of  the  ring,  — 
The  relation  between  the  phases  of  the  ring  and  the  position  of  the 
planet  is  easily  ascertained.  Let  a  be  the  semi-diameter  of  the 
rings  as  seen  undiminished  by  projection  ;  let  5  be  the  lesser  semi- 
axis  of  the  ellipse  produced  by  the  projection  of  the  ring ;  and  let  D 
be  tbe  angle  which  the  visual  ray  makes  with  the  plane  of  the  ring. 
We  ahall  then  have,  by  the  common  principles  of  projection, 

h  =  a  X  sin.  D. 

Bat  since  the  visual  ray  is  the  line  drawn  from  tbe  planet  to  the 
etrth,  it  is  evident  that  the  angle  d  will  be  tbe  dccliDation  of  the 
earth  as  seen  from  the  planet  Now,  if  l  express  tho  arc  of  tho 
ecliptic  between  the  earth  and  tbe  ascending  node  of  tbe  ring  as  seen 
from  tbe  planet,  and  o  the  obliquity  of  the  plane  of  the  ring  to  the 
ecliptic,  we  shall  have,  by  the  common  principles  of  trigonometry^ 

sin.  D  =  sin.  o  x  sin.  l  ; 
and  consequently 

b       .        ^     . 

— =  sm.  o  X  sm.  L. 
a 

But  since  the  distance  of  tbe  earth  from  tbe  ascending  nod^  ^ 

ui.  30 


iHB  from  Qi»  plimet  »  eqaal  to  130°,  dlmlni^cd  bj  the  SlMm  I 
of  Sltom  ftom  the  Game  [«int  a:^  geca  froiu  lie  cuUi,  L  oaj  te  | 
tdun  in  th*  preoedtug  formula  to  express  titc'  klter  dittiDMiAl 
'iba  bnng  the  wtoe. 

If  the  poailioD  of  the  plnact  with  relation  to  tlie  ascending  n 
tf  the  ring  be  known,  the  precediog  formula  will  tberefore  m 
dodBOa  the  obliqnitj  from  the  pilose  of  the  ring,  or  niee  c-rnui. 

Siiwa  O  =  aB"*  10'  UT,  wo  ahaU  have  sin.  o  =  017-21    Wi 
■hftll  theiefon  hive 

^  =  0-4722  x,m.i, 

bj  whieh  the  pha.s«!i  of  the  riog  for  aaj  gtvco  disl&occ  from  h 
lwdein»7  beeomjiuloil.  , 

In  the  fiiUowing  table  the  ratio  -  of  the  eemi -axis  of  the  eliips 

ftrmed  by  the  plojcctioa  of  the  ring,  and  tho  niio  —  of  (be  leE<r 

■emi-ezii  to  the  lenii-diiiTiieter  of  ibc  planet,  arc  gif  ca  for  cterj  IC 
from  the  node. 


t 

W" 

10° 

pp 

«o 

M> 

MO 

Wt 

W" 

••• 

i 

0-osa 

»» 

0-soa 

o-w« 

»su 

out 

(Mil 

(MM 

1« 

MB 
1« 

From  this  table  it  appeals  that  the  L 
the  planet  moves  from  the  ascending  node  of  the  ring  nntil  it  is  MT 
from  that  point,  at  which  its  ratio  to  the  major  eemi-ezu  b  Hatii 
472  to  1 000,  being  a  little  less  than  half  the  inqor  aemi^us.  Ftok 
the  numbers  given  in  the  third  line  of  the  table  it  appean  that  tk 
lesser  eemi-axis  becomes  e<iaal  to  the  equatorial  aemidiuaeter  of  lh> 
planet  at  about  71°  from  the  ascending  node  of  the  ring,  and  eice«di 
It  bj'a  twentieth  of  its  length  at  90°.  But  as  the  polar  diametR 
of  the  planet  is  less  by  a  tenth  than  the  eqnatc^al,  it  follows,  that 
at  90°  from  the  node  of  the  ring  the  lesser  Bemi«xis  exceeds  tbt 
polar  semi -diameter  of  tho  planet  by  an  eight«enth  of  its  length :  it 
follows,  therefore,  that  a  oorresponding  breadth  of  the  ring  will,  >■ 
this  case,  be  visible  above  tho  disk  of  the  planet. 

Since  the  entire  breadth  of  the  rings  in  throe-fourths  of  the  wmi- 
diamctcr  of  the  planet,  and  since  they  arc  reduced  one-half  before- 
shortening  their  apparent  breadth  measured  in  the  direction  of  du 
lesser  axis  of  the  ellipse  at  90°  from  the  node  is  three^ighlhs  of  the 
■emidiametcr  of  the  planet,  it  follows,  therefore,  that  a  seventh  pail 


THB  MAJOR  PLAKETB. 


851 


gf  tbe  en^n  Inwddi  «f  the  rings  is  visible  above  the  disk  of  tbe 
pluet  at  90°  from  die  node,  the  entire  npper  segment  of  (ho  disk 
beiog  projected  won  the  ring. 

From  90°  to  the  descending  node  of  tbe  ring,  tbe  like  phases  are 
preMnted  in  a  contraij  order;  &nd  while  the  planet  moves  from 
fte  dcaModing  to  the  aaeending  node,  a  similar  series  of  phases  aro 
presented ;  the  pontioD  of  Uie  plane  of  the  ring  with  relation  to  the 
poles  of  die  planet,  however,  being  reversed ;  that  which  is  in  one 
cue  interpqaed  between  the  observer  and  tbe  northern  hemisphere 
of  the  planet  will  bo  interposed  in  the  other  case  between  him  and 
the  southern  hemisphere. 

In  the  diamnia,  iS^.  766 — 769,  die  phaBoa  of  tbe  rinp  indicated 
is  the  prece£og  teble  are  exhibited. 


Fig.  769. 

If  the  tblckncsa  of  tbe  ring  were  uniform  and  sufficiently  gw' 
to  sabteod  ■  sensible  visual  angle  at  Saturn's  diatance,  tlie  pbtee 
preMOted  to  tho  planet  at  the  nodes  of  the  ring  would  be  nuh  u 
that  represented  in  f.j.  1Gb.  The  phases  at  1,  2,4,  and  6-7  jtKS, 
kfter  pasmng  the  nodes,  are  roughly  sketched  in^i.  765 — 109. 

2803.  Apparent  and  real  divumiionii  of  tJi^.ring>.~l!b6bniAtl 
of  the  rings  as  well  as  of  the  intervals  which  Beparale  them  fom 
Mch  other  and  from  the  planet,  have  been  Eubmitled  to  very  pre- 
cise micrometria  observBtiona ;  and  the  rusults  obtiuncd  by  diffennt 
observers  do  not  differ  from  each  other  by  a  fortieth  part  of  the 
whole  quantity  measured.  In  the  following  table  are  given  the 
results  of  the  micrometric  observations  of  Profeeaor  Stmve,  reduced 
to  the  mean  distance. 


— 

kM 

IL 

n_i. 

R-'Mt 

g.  iD^^ludiDg  tntor™l.... 

a-V 

Mia 

THK  KAJOn  PI.ASETS. 


853 


ehtivc  dimcnsinnK  of  the  tvn  rlngF,  an<l  of  the  planet  within 
"e  repmented  ™jig.  770,  projected  upon  the  common  plane 
iii0  uid  tlM  planet's  equator.  Each  diTision  of  the  sab- 
eua  repTMants  5,000  miles. 


rinul  angle  sobteDded  at  the  earth  by  Qie  extreme  diameter 
iZtemal  ring,  when  the  planet  is  in  opposition,  is  48",  which 
one  thirtj-serentb  part  of  the  moon's  apparent  diameter. 
.  Thieknttt  of  ihe  ring*.  —  The  thickncBB  of  the  rines  ia 
mely  minute,  that  the  nicest  tnicrometria  obserrationa  nave 
'  failed  to  supply  the  data  necessary  to  determine  it  with 
Tee  of  precision  or  certainty.  It  is  so  inconsiderable,  that 
he  plane  of  the  ring  is  directed  to  the  earth,  and,  oone^ 
,  the  edge  alono  is  presented  to  the  eye,  it  is  invisible  eren 
lescopca  of  great  power,  or,  if  seen,  it  is  so  imperfectly 
u  to  elude  all  micrometric  observation.  When  it  waa  in 
ritioD  in  1833,  Sir  J.  Herschel  obserrcd  it  with  a  telescope, 
ronid  certainly  have  rendered  distinctly  visible  a  line  of  U^VtV 


aiiB4wwtiotb  rf  «  aeeeed  in  bmdik    StaMlkB 


tlw  IhiakneM  u  Ism  tbu  230  milH. 

erer,  that  it  mkj  pcwnbl;  be  m  gi«*t  M  SM  mila«. 

The  thiokneeB  ia,  therafbra,  oertunty  kM  tfau  th«  lOOA  part  «f 
Ao  flxtraiM  bmdtli  of  the  two  rings,  and,  nocording  to  the  scale  on 
wbioh  ih»Jig.  7&6  i*  dnwn,  it  would  be  represeoted  b;  the  thick- 
MM  flf  a  HU  ti  tha  Tglune  now  before  tho  reader. 

'  \  of  Ac  riny.  —  Ifdioeentric  phaiitt.  —  Tba 


tlMj  mold  be  viewed  from  the  aun.  Tbcre  the  illaminatiiig  r 
tin  itanal  nys  an  identioal,  aod  their  direction  is  that  of  the  radius 
reoMr  of  Um  pUmt  n«  angle  which  this  line  makes  with  the 
plua  «f  the  SatoinUii  aqMlor,  is  the  dcclinktioD  of  the  sua  u  seen 
Iron  SatnTD.  Let  tUiangle  be  expressed  b;  d',  the  diitinoe  of 
tiie  moa  tnia  the  Srtanian  Temal  equinoilal  potot  l',  »nd  the  in- 
elinauoo  of  the  Sabmian  e<|uiLtor  to  the  orbit  o'.  We  eball  then, 
u  in  the  former  caae,  Lave 

EUb.  d*  =  dn.  (/  X  rin.  L'; 
and  if  If  ezpreai  lener  aBioi-axea  of  the  eOipaa  to  whieh  At  mt^ 
ia  redooed  by  projeotioo,  as  seen  from  the  Bim,  we  shall  haw* 
^         ■      ^       ■       - 

—  =  BID.  tf  X  BID.  V. 

By  thia  formula  the  ratios  of  n'  to  a  and  r  may  be  deteniUBed  fir 
all  TtltMS  of  l',  as  in  ibo  former  ctM.  In  the  following  table  tbtM 
are  ^ven  as  they  have  been  computed,  for  o'=i  26°  4^40". 


./ 

u> 

^ 

Kfi 

«. 

W 

tCfi 

10= 

•«• 

«p 

1 

0-m 

irut 

inn 

0-230 

MJO 

imo 

04M 
0-W 

04U 

MM 
I'M 

2806,  ShndoK  projecUd  on  the  planet  h/ the  ringt.  —  Stiwe  the 
lines  by  which  these  phases  are  determined  are  those  of  the  sokr 
ruys,  it  is  evident  that  the  parts  of  the  rings  interoeptod  by  the 
planet,  and  those  of  the  planet  intercepted  by  tbe  rings,  are  exactly 
those  which  rociprocally  bound  the  lihadows  prnjccted  od  them. 

Tbe  preceding  table  of  hcliocontric  phases  will  therefore  sem 
for  the  de terra inati on  of  the  limits  of  the  shadows. 

At  the  equiooxes,  the  edge  nf  the  rings  being  presented  to  the 
Bun,  the  shadow  projected  on  the  equator  of  the  planet  will  depend 
altogether  on  the  thickness  of  the  rings,  and  the  apparent  '^"Ft-t'' 


THB  MiUOR  PLANBTS. 


855 


of  the  mkUy  as  seen  from  the  planet  The  latter  being  only  3},  the 
solar  rays  which  touch  the  edge  of  the  thickness  may  be  considered 
as  nearly  narallel,  and  the  breadth  of  the  shadow  will  be  nearly 
equal  to  the  thidcness  of  the  ring.  The  shadow  will  therefore,  in 
this  case,  be  in  a  thin  dark  line^  extending  along  the  eauator  of  the 
planet,  fy.  771j  oovering  a  lone  of  the  firmament  whose  breadth 


Kg.  771. 


Kg.  772. 


BMBt  be  about  fifteen  times  greater  than  the  apparent  diameter  of 
the  ann.  A  total  solar  eclipse  at  the  equator  of  the  planet  would, 
therefore^  be  produced  by  the  shadow  of  the  ring,  and  would  con- 
tiiine  until  the  sun  would  gain  or  lose  44'  declination. 

When  the  planet  presents  the  phase  represented  in^^.  767,  its 
enlightened  hemisphere  would  be  traversed  by  the  shadow  repre- 
nnted  in^.  772,  and  in  like  manner  the  shadows  produoed  under 
dM  phaasBji^i.  768,  769,  are  represented  in  Jigs.  773,  774. 


Fig.  778. 


Fiff.  774. 


2807.  Shadow  projected  hy  the  planet  on  the  ring.  —  The 
shadow  projected  on  the  surface  of  the  ring  by  the  gl(»bc  of  the 
planet  will  vary  with  the  sun's  declinurion,  as  seen  from  the  piauct, 
because  the  angle  at  which  the  plane  of  the  ring  is  inclined  to  the 

18  of  the  shadow  of  the  planet  is  equal  to  the  declination. 

At  the  equinoxes,  the  declination  biiing  0^,  the  plane  of  the  ring 


ns  untomit. 

pHHs  tbran^  the  tifs  of  dia  ■badow,  md  As  hnuKkct  fta  in 
of  the  ring  on  wbicb  the  sbiclinr  ftlb  ii  neulj  eqml  to  lbs  iliiwii 
tnof  the  plBDat,the  ngle  of  theooooof  theBh«linriiat«eaoiii^ 
8*,  noce  it  is  very  neuly  eqnil  to  the  tpperant  diuMler  of  the  m 
u  seen  ftoin  Saturn. 

If  a  expnst  the  an  of  the  ezUnbl  edgb  of  thk  Ai^  bn  wUdb 
the  ahadow  fidb,  it  is  evident  that 

an.j«=— ,  ■ 

reijpnsring,  as  before,  the  eqoatorial  BeAi-diameter  of  thn  Hhniil, 
and  •  the  semi-diameter  of  the  onter  edge  Of  the  nop.  niWaaa 
tinadf  dLhuiaiuad  Whg  givoD  t4  theee,  M  have 

Henoe  it  appeaia  that  >  =  68°  18'  48";  and  in  lika  Banmr  It  u^ 


THE  MAJOR  PLANETS.  867 

be  shown  that  the  shadow  covers  8-4^  52'  of  the  inner  edge  of  the 
inner  ring. 

The  lateral  edges  of  the  shadow  in  this  case  are  rectilinear  and 
sensibly  parallel,  a  consequence  due  to  the  angle  of  the  cone  being 
insignificant,  yTy.  775. 

As  the  declination  of  the  sun  increases,  the  section  of  the  cone  of 
the  shadow  by  the  plane  of  the  ring  becomes  elliptical,  and  the  edges 
of  the  shadow  on  the  ring  are  curved,  fig,  776,  while  its  breadth  is 
more  contracted.  When  the  sun  comes  to  the  Satumian  solstice, 
and  its  declination  is  26^  48'  40",  the  vertex  of  the  elliptic  section 
of  the  cone  fidls  upon  the  enter  edge  of  the  ring,  and  the  shadow 
has  the  form  of  an  elliptic  segment  at  the  extremity  of  the  major 
axis  of  the  ellipse,  fig.  777. 

2808.  Tht  thadowB  partialljf  visible  from  the  earth,  —  It  is 
evident  that,  the  vboal  ray  of  an  observer  placed  on  the  sun  coin- 
ciding with  the  lominous  ray,  none  of  the  shadows  produced  by  the 
projection  of  the  ring  on  the  planet  or  of  the  planet  on  the  ring, 
eonld  be  visible  to  him,  since  the  object  producing  the  shadow  would 
be  interposed  with  geometrical  precision  between  his  eye  and  the 
shadow.  Bat  if  the  observer  be  transferred  to  the  earth,  the  visual 
rty  win  form  an  angle  with  the  luminous  ray,  which,  though  it  can- 
nol  in  any  case  exceed  6^,  is  sufficient,  under  certain  circumstances 
of  nlative  position,  to  remove  the  observer  from  the  direction  of  the 
huuDona  lay  to  such  an  extent  as  to  disclose  to  him  a  part,  though 
a  mall  part,  of  the  shadow  which  to  an  observer  at  the  sun  is  wholly 
intoreepted. 

In  thia  manner,  when  the  planet  is  in  quadrature,  a  small  part 
of  the  shadow  it  projects  npon  the  rins  is  visible  on  the  east  or  on 
the  mat  aide  of  the  disk,  according  as  the  sun  is  west  or  east  of  the 
plaaet;  and  in  like  manner,  the  difference  between  the  angles  which 
the  viaoal  and  Inminons  rays  form  with  the  plane  of  the  ring  dis- 
cloeeSy  in  certain  cases,  a  small  breadth  of  the  shadow  projected  on 
the  planet's  disk  by  the  ring,  which  is  accordingly  seen  ns  a  thin 
dark  streak  crossing  the  disk  of  the  planet  in  contact  with  the  ring. 

These  phenomena  prove  that  both  the  planet  and  the  ring  consist 
of  matter  having  no  light  of  their  own,  and  deriving  their  entire 
illumination  from  the  sun. 

2809.  Conditions  under  which  the  ring  becomes  invunble  from 
the  earth.  — The  rings  of  Saturn  viewed  from  the  earth  may  become 
invisible,  either  because  the  parts  presented  to  the  eye  are  not  illu- 
minated by  the  sun,  or,  being  illuminated,  have  dimensions  too 
small  to  subtend  a  sensible  visual  angle. 

It  has  been  explained  that,  in  every  position  assumed  by  the 
planet  in  its  orbital  motion,  one  side  or  the  other  of  the  rings  is 
illuminated  with  more  or  less  intensity,  except  at  the  Saturuian 
equinoxes,  when,  the  plane  of  the  ring  passing  through  the  8un«  its 
edge  alone  is  illuminated.    Owin<r  to  the  extreme  IbmiiesB  oi  \2i\ci 


piirf*  of  natter  Mmporing  tbe  rit^  Quj  ceua  In  IUb  wm  Cb  le 
vinble,  exoept  bj  feeble  and  nntntun  indiostiaaa  abMrnl  witt 
bigb  magnifying  powers,  vbidi  will  be  ootioad  kanafltr.  Ik  hm 
Men  inferred  1^  Bir  John  Hersobol,  from  obanntiou  mada  wiA 
telewopoB  of  great  power,  tbat  the  tn^jor  limit  at  thar  iiiiJiiTiBi 
thieknesB  is  260  milea.  The  ^riaul  angle  whkli  t^  iTiiiiVimm 
voold  subtend  at  the  distanoe  of  Saturn  In  oppontioO)  is  (2T90) 
250 


Tlw  nraal  angle  woold,  there&ra,  ba  len  ihan  tlia  JtAaaBlli  prt  rf 

mnewd. 

The  rings,  therefore,  disappear  from  this  oMne  at  Satn^  afifr 

■axes,  whiob  appear  at  intermls  of  14('  years. 

When  the  dark  side  of  the  riagi  is  expoaed  lo  the  eartk,  H  fa  arf- 
dent  that  tiie  rdd  and  earth  moal  te  oi 
opposita  sides  of  the  plane  of  Ae  liip,rirf 
therefore  that  plana  must  bhw  soA  ■  pitf> 
tion  that  ita  direction  would  peai  IwIMb 
the  sun  and  the  earth.  Iliii  mA  afc 
happen  within  a  certain  limited  disteaeatf 
the  planct'B  equinoxes. 

Let  a,  Jiff.  778,  represent  the  plaoa  of 
the  Bnn,  e  e'  the  orbit  of  the  earth,  and  f 
the  place  of  Sutum  at  the  time  of  nthn  M 
his  equinoxes.  From  what  baa  been  b1< 
ready  explained,  it  appears  that  in  tUs 
pontion  the  edge  of  the  ring  is  preaeatsd 
to  8.  Since  the  ring  is  oamed  paralM  la 
itself  in  the  orbital  motion  <tf  tke  plMiirt, 
the  edge  of  the  ring,  before  airiving  rt  tta 
point  p,  must  have  been  directed  enaM» 
■ively  to  the  points  of  the  earth's  orint 
between  z  and  the  diameter  ee',  and,  sftei 
passing  p,  must  be  directed  snoeessiTClT  to 
the  poiotB  between  the  diameter  e^  and  ^. 
If  liuca  EFsnd  e'p'  be  drawn  framind 
j!  parallel  to  Ep,  the  edge  of  the  ring  will 
be  directed  across  some  part  of  the  earth's 
orbit,  so  long  as  the  planet  is  nadng  be- 
tween p  and  t'.  At  p  it  will  be  diraotod 
to  E,  and  at  F*  to  z*.  Before  arriving  at  p, 
the  edge  of  the  ring  will  be  directed  to  the 
left  of  the  earth's  orbit,  aod  after  pasting 
x',  to  the  right  of  it. 

It  is  evident,  therefore,  that  befim  tbi 
planet  smvea  at  P,  whaterer  bs  tha  poaitiaa 


THE  MAJOR  PLANETS.  859 

of  the  earth  in  its  orbit,  the  earthy  as  well  as  the  bud,  mast  be  to 
the  right  of  the  direction  of  the  edge  of  the  rings,  and  consequently 
on  their  illuminated  ude ;  and  after  passing  p',  the  earth,  as  well  as 
the  sun,  must  be  to  the  lef^  of  the  edge  of  the  rings,  and  therefore 
still  on  the  illuminated  side.  The  rings,  therefore,  must  everywhere 
be  Tisible,  except  when  the  planet  is  at  or  between  the  points 
p  and  P^. 

When  the  planet  is  at  either  of  the  points  p  or  p',  it  may  happen 
that  at  the  same  moment  the  earth  is  at  the  corresponding  point  £ 
or  k'.  In  that  contingency  the  edge  of  the  ring,  being  the  only 
part  exposed  to  the  observer,  would  be  invisible  because  of  its  mi- 
nuteness, in  the  same  manner  as  when  the  planet  is  at  p.  In  that 
case  the  disappearance  of  the  planet  would  be  of  short  duration,  be- 
caose  the  orbital  motion  of  the  earth  would  soon  bring  it  on  the 
enlightened  side  of  the  ring.  Thus,  if  when  the  planet  is  at  p  the 
earth  is  at  e,  the  latter,  moving  much  faster  than  the  planet,  advances 
before  it,  and  being  then  on  tiic  same  side  of  the  ring  with  tbe  sun, 
the  illaminated  side  is  exposed  to  the  earth,  and  therefore  visible ; 
ind  if  when  the  planet  is  at  p'  the  earth  is  at  e',  the  latter  moving 
towards  ^  while  the  planet  advances  to  the  right  of  p',  the  earth  and 
planet  are  both  on  the  left  of  the  edge  of  the  rings,  and,  as  before, 
the  enlightened  side  of  the  rings  is  exposed  to  the  earth,  and  they 
are  therefore  visible. 

If,  while  the  planet  is  between  p  and  p,  the  earth,  moving  from 
^  towards  £,  pass  through  the  point  to  which  the  edge  of  the  rings 
ii  directed,  the  rings  will  after  such  passage  cease  to  be  visible,  be- 
caoae  the  earth  will  then  be  on  their  dark  side.  It  is  possible  that 
afier  this,  and  before  the  planet  arrives  at  p,  the  earth,  moving  from 
I  towards  ^,  overtaking  the  direction  of  the  edge,  may  again  pass 
through  the  point  to  which  it  is  directed.  If  this  happen,  the  rings 
wfll  acain  become  visible,  because  the  earth  will  thus  pass  from 
their  urk  to  their  illuminated  side. 

If,  in  this  case,  while  the  earth  moves  towards  yI  and  e',  the 
planet  pass  through  p,  the  rings  will  a<rain  become  invisible,  because, 
their  edge  passing  from  one  side  of  the  sun  to  the  other,  the  side 
present^  towards  f!  will  be  dark,  and  that  towards  E  illuminated. 
If  in  thb  case  the  earth,  moving  from  e'  towards  e',  again  pass 
through  the  point  to  which  the  edge  of  the  rings  is  directed,  it  will 
again  pass  from  the  dark  to  the  enlightened  side,  and  the  rings 
will  again  become  visible. 

The  angle  E/^s,  being  the  annual  parallax  of  »Satum  (2744),  is 
6\  and  consequently  e/^e'  or  psp'  is  1*2°.  But  since  the  annual 
keliocentric  motion  of  Saturn  is  12°'22,  the  time  of  moving  from  v 
fioi<  is 

J|^  X  365  =  35«i  days. 


or  aboat  6}  dajs  less  tbto  Ae  time  die  ssifli  takw  lo 

pkte  revoltttion ;  so  thai  while  tlie  phnsl  imrraa  from  B  lo  i^  fts 

fltrih  moves  through  aboat  864^  of  ita  otUl 

It  appears,  therefore,  thai  the  interval  dnring  wliiab  tte  _ 
within  snch  a  distanoe  of  its  eqoinootid  point  as  to  nnder  tha 
appearanoe  of  the  rings  from  one  or  olher  of  tiieaa  aovwal  oii 
possible,  the  earth  m2ces  very  nearly  a  oompbto  ravolnlloBy  aid  k 
therefore  at  one  time  or  other  in  a  position  to  meet  tfie  dheeliea  of 
the  edges  at  least  once,  and  the  lelalive  position  of  it  snd  the  plnal 
may  be  snch  as  to  cause  several  disappesranees  of  the  riogs  wfttn 
six  months  before  and  after  the  Satnnuan  eqninoz. 

All  these  various  phenomena  were  witnessed  at  tlie  last  fttsnisi 
equinox  in  1848.  The  northern  mxxhee  of  the  ring  had  then  hsai 
visible  for  nearly  fifteen  yeaiis.  The  motions  of  tlie  jdaiiet  and  As 
earth  brought  the  plane  of  the  ring  to  that  position  oa  the  tSttd  of 
April,  in  which,  its  edge  being  presented  to  the  earth,  il  beeaariih 
visible,  the  sun  being  still  north  of  the  plane.  On  the  8rd  of  Bap> 
tember,  the  sun,  passinff  through  the  plane  of  the  ring^  JUmaiiBBlBi 
its  southern  sur^use,  and,  the  euih  being  on  the  same  aide^  die  ifa^ 
was  visible.  On  the  12th,  the  earth  again  passing  fSknm^  thai 
plauc  of  the  ring,  its  northem  snrfiico  was  exposed  to  the  observer, 
which  was  inyisible,  the  sun  being  on  the  soathem  side.  The  ring 
continued  thus  to  be  invisible  until  the  18th  of  January,  1849, 
when,  tbo  earth  once  more  passing  through  the  plane  of  Uie  rina, 
the  southern  surface  illuminated  by  the  sun  came  into  view.  This 
side  of  the  ring  will  continue  to  be  exposed  to  both  the  earth  and 
the  sun  until  1861-2,  the  epoch  of  the  next  equinox,  when  a  like 
succession  of  appearances  and  disappearances  will  take  plaee,— 4b6 
sun  and  earth  eventually  passing  to  the  northern  side,  on  whioh 
they  will  continue  for  a  like  interval. 

2810.  Schmidt* &  observations  <ind  drawings  of  Saium  wA  At 
ring  seen  edgeways.  —  At  the  last  Satumian  equinox,  whidi  took 
place  in  1848,  a  series  of  observations  was  made  at  Bonn,  the  re- 
sults of  which  have  demonstrated  the  existence  of  great  inequalitieB 
of  surface  on  the  rings,  having  the  character  of  mountains  of  con- 
siderable elevation.  The  observations  were  made  and  published| 
accompanied  by  seventeen  drawings  of  the  appearanoe  of  the 
planet,  its  belts,  and  ring,  by  M.  Julius  Schmidt,  of  the  Bonn  Ob- 
servatory.* 

We  have  selected  from  these  drawings  four,  which  are  given  in 
Plate  XL 

On  the  26th  of  June,  the  planet  presented  an  appearance, /S^.  I, 
closely  resembling  that  of  Jupiter,  except  that  a  dark  streak  was 
seen  along  its  equator,  produced  by  the  shadow  of  the  ring,  the 

— -  I  ,    111      my.    ^_M__iu__«_^__^..^^___-_pj  I  ■    I    -^ 

*  \8troD.  Nachr.  Schamacher,  Vol.  xxfiii.  No.  650. 


THE  MAJOR  PLANKTS.  861 

cwth  being  then  a  little  tbove  the  common  plane  of  the  ring  and 
die  ran.  A  few  feeble  streaks,  of  a  greyish  ooloar,  were  visible  on 
each  hemisphere,  which  however  disappMred  towards  the  poles.  A 
very  feeble  star  was  seen  at  the  western  extremity  of  the  ring,  which 
was  sappoeed  to  be  one  of  the  nearer  satellites.  The  ring  exhibited 
the  appearance  of  a  broken  line  of  light  projecting  from  each  side 
of  the  planet's  disk. 

After  this  day  the  shadow  across  the  planet  disappeared,  but  was 
i^n  feintly  seen  on  the  25th  of  July. 

The  ring  continued  to  be  invisible  until  the  3rd  of  September, 
when  a  very  slight  indication  of  it  was  seen,  but  on  the  next  night 
it  became  distiinotly  visible  with  an  interruption  in  two  places,  as 
lepresented  in  fig,  2.  The  bright  equatorial  bolt  was  divided  into 
two  unequal  parts  by  the  ring,  the  northern  portion  being  the  nar- 
rower. Three  small  satellites  were  seen  in  the  prolongation  of  the 
direction  of  the  ring. 

On  the  5th,  the  ring  was  symmetrically  broken  on  both  sides. 

On  the  7th,  the  western  side  was  divided  into  three  parts. 

On  the  11th,  the  ring  and  planet  presented  the  appearance  repre- 
sented v^fig.  4. 

The  broken  and  changing  appearances  of  the  ring  on  this  occa- 
sion, can  only  be  explained  by  the  admission  of  great  inequalities 
of  sarface,  rendering  some  ^rts  of  the  ring  so  thick  as  to  be  visible, 
and  others  so  thin  as  to  be  invisible,  when  presented  edgeways  to 
the  observer. 

2811.  Observations  of  Ilenchd. — These  observations  of  Schmidt 
are  corroborative  of  those  made  at  a  much  earlier  epoch  by  Sir  W. 
Her&chcl,  who  discovered  the  existence  of  appearances  on  the  surface 
of  the  rings  indicating  niouotain  inequalities. 

2812.  SupptMttd  multiplicity  of  ritujs, — Some  observations  made 
at  Rome  and  elsewhere  gave  grounds  for  the  conjecture,  that  the 
outer  ring,  instead  of  being  double,  is  ([uintuplc,  and  that  instead 
of  having  a  single  division,  there  are  four.  It  was  even  affirmed 
with  some  confidence,  that  the  ring  wan  septuple,  and  consisted  of 
seven  concentric  rings  suspended  in  the  same  plane.  These  conjec- 
tures were  founded  upon  the  supposed  permanence  of  the  black 
circular  and  concentric  streaks  which  are  observed  upon  the  surface 
of  the  rings,  and  which  are  quite  analogous  to  the  belts  of  the  planet. 
This  assumed  permanence  has  not,  however,  been  re-observed, 
althoagh  the  planet  has  been  examined  by  numerous  observers,  with 
telescopes  of  very  superior  power  to  those  with  which  the  observa- 
tions were  made  which  formed  the  ground  of  the  conjecture. 

The  passage  of  Saturn  diametrically  across  any  fixed  star  of  suffi- 
cient magnitude,  at  the  epoch  of  the  Satumian  solstice,  when  the 
plane  of  ue  ring  is  inclined  at  the  greatest  angle  to  the  visual  linO) 

III.  31 


I  ■ 


Prof(\<sor  EiK'kc  noticed  an  appoaruiico  which  indicated  a  i 

und  even  niude  dr.iwings  in  which  such  a  division  is  indicate 

Berlin  Trans.  1838.)   On  the  7th  September,  1843,  Messrs 

and   Dawes,  unaware  apparently  of  Enck^'s  observations, 

nine-feet  Newtonian  reflector,  constructed  bj  Mr.  Laasell,  n 

^1       •  they  considered  to  be  a  division  of  the  outer  ring.     The  obs 

I  was  made  under  a  magnifying  power  of  450,  which  gave  a 

j  defined  dit^k  to  the  planet,  and  exhibited  the  principal  div 

■•''■    !-  the  rings  as  a  continuous,  distinctly  seen,  black  streaky  63 

all  round  the  surface  uf  the  ring.     A  dark  line  on  the  on 


:J        'i- 


I. 


^ ..   I    :  near  the  extremities  of  the  ellipse,  was  not  only  di8tinct]y  i 

I    '  an  estimate  of  its  breadth  compared  with  that  of  the  principa] 


•  I  _  _         _ 

,  : ;     I  was  made  by  both  these  observers,  from  which  it  appeared 

'  *     ■  breadth  was  about  one-third  of  the  space  which  aepaimlea 


* 


\ 
I 


.*  principal  ringf*.     Its  place  upon  the  outer  ring  was  a  little  ] 

half  the  entire  width  of  the  ring  from  the  outer  edge,  an 
equally  vii^ible  at  both  ends  of  the  ellipse.    No  appearances 
discovered  of  any  other  divisions,  although  the  shading  of 
j  j  on  the  inner  ring  was  distinguished. 

j  2814.  Researdies  of  Beud  corroborate  theae  conjecturei,' 

i|  -  compared  all  the  observations  made  on  the  rings  from  1700 

>  !  with  the  view  of  determining  with  more  precision  the  nodi 

ring,  and  found  that  the  ring  has  frequently  been  seen  when 

to  have  been  invisible,  if  the  several  concentric  rings  of 

i  i  consists  were  all  in  the  same  plane  and  had  a  uniform  surfii 

I  found  that  the  appearances  and  disappearances  had  no  o 

I  regular  epochs,  and  did  not  correspond  with  each  other,  evi 


THE  MAJOR  PLANETS.  868 

2815.  Diteovery  of  an  inner  ring  imperfectly  refUctioe  and 
parfidUy  transparent,  —  But  the  most  sarprisiDg  result  of  recent 
telencopic  observatioDS  of  this  planet  has  been  the  discovery  of  a  ring, 
emnpneed,  as  it  would  appear,  of  matter  reflecting  light  much  more 
imperfectly  than  the  planet  or  the  rings  already  described;  and  what 
b  atill  more  extraondinary,  transparent  to  such  a  degree,  that  the 
body  of  the  planet  ean  be  seen  through  it. 

Ib  1838,  Dr.  Oalle,  of  the  Berlin  observatory,  noticed  a  pheno- 
venoo,  which  he  described  as  a  gradual  shading  off  of  the  inner 
ling  townds  the  surface  of  the  planet,  as  if  the  solid  matter  of  the 
ring  were  ooq tinned  beyond  the  limit  of  its  illuminated  surface,  this 
eooliiiiialion  of  the  8ur%u»  being  rendered  visible  by  a  very  feeble 
flbnuBatioo  auoh  as  would  attend  a  penumbra  upon  it ;  and  roea* 
nrai  of  this  obscure  surface  were  published  by  him  in  the  '^  Berlin 
^UMtions"  of  that  year. 

The  tiibjeet,  however,  attracted  very  little  attention  until  towards 
the  close  of  1850,  when  Professor  Bond,  of  Bosto%  and  Mr.  Dawes 
ii  EnsIaDd,  not  only  recognised  the  phenomenon  noticed  by  Dr. 
Oalle,  Dui  ascertained  its  character  and  features  with  great  precision. 
The  observations  of  Professor  Bond  were  not  known  in  England 
Mill  the  4th  of  December;  but  the  phenomenon  was  very  fully  and 
aUisfkelorily  seen  and  described  by  Mr.  Dawes,  on  the  2i)th  of  No- 
venber.  That  astronomer,  on  the  3rd  of  December,  called  the 
sttentioB  of  Mr.  Lassell  to  it,  who  also  witnessed  it  on  that  evening 
St  the  observatory  of  Mr.  Dawes ;  and  both  immediately  publishea 
tlieir  observationB  and  descriptions  of  it,  which  appeared  in  Europe 
simultmneously  with  those  of  Professor  Bond. 

It  was  not,  however,  until  1852  that  the  transparency  was  fully 
asoertftined.  From  some  observations  made  in  September,  Mr. 
Staves  strongly  suspected  its  existence,  and  about  the  same  time  it 
was  clearly  seen  at  Madras  by  Captain  Jacob,  and  in  October  by 
Mr.  Lassell  at  Malta,  whither  be  had  removed  his  observatory  to 
obtain  the  advantages  of  a  lower  latitude  and  more  serene  sky.  The 
lenlt  of  these  oWrvations  has  been  the  conclusive  proof  of  the 
wniqoe  phenomenon  of  a  semi-transparent  annular  appendage  to  this 
planet. 

2816.  Drawing  of  the  planet  and  rings  as  seen  hg  Mr,  Dawes. 
—The  planet  surrounded  by  this  compound  system  of  rings  is 
represented  in  Plate  XII.  The  drawing  is  reduced  from  the  original 
sketehy  made  by  Mr.  Dawes,  of  the  planet  as  seen  from  his  refractor 
of  6i  inch  aperture,  at  Wateringbury,  in  November  1852.  Another 
representation  of  the  planet  as  seen  by  Mr.  Lassell  at  Malta,  in 
December,  1852,  has  been  lithographed,  and  is  almost  identical  with 
that  of  Mr.  Dawes.  In  both,  the  form  and  appeurance  of  the  ob- 
senrs  ring  and  its  partial  transparency  are  rendered  quite  manifest 
Thi  priaeipsl  division  of  the  bright  rings  is  visible  thtongJ^ouX  \\A 


MM  A8TB0S0MT. 

entire  droomfcraioe.  Tlia  bhok  Hm,  saopoMd  to  b»  a  fifUoi  rf 
the  oater  ring,  is  yuible  in  the  dnwing  of  Hr.  Ikwei;  hit  wwb0I 
at  all  seen  by  Mr.  LanelL 

A  remarkably  bright  thin  line,  at  the  inner  edge  of  the  ioMr 
right  ring,  whioh  appears  in  Plate  XXL,  was  diadnwLy  seen  bj  Mr* 
Dawes  in  1851  and  1852. 

The  inner  bright  ring  is  always  a  little  brighter  than  the  plinet 
It  is  not^  howeveri  nmformly  bright  Its  illnmination  is  wxd 
intense  at  the  enter  edge,  and  grows  gradoally  fiunter  towards  the 
inner  edge,  where  it  is  so  feeble  as  to  render  it  somewhat  diflieiH 
to  ascertain  its  exact  limit  It  would  seem  as  if  the  impoftetlj 
reflective  qo^li^  there  approaches  to  that  of  the  obscure  ring  reoe&tij 
discovered.  The  open  space  between  the  ring  and  the  i^anek  hi 
the  same  colour  as  the  surrounding  sky.  • 

2817.  BesseTs  calculation  of  ike  mas$  of  the  ringM.  —  Bessel  hai 
attempted  to  determine  the  mass  of  the  system  of  rings  by  the  ptf- 
tnrbation  they  produce  upon  the  orbit  of  the  sixth  satellite.  He 
estimates  it  at  l-118th  part  of  the  mass  of  the  planet  The  thiek- 
ness  of  the  rings  being  too  minute  for  measurement,  no  estimtta  ci 
the  density  of  the  matter  composing  them  can  be  hence  obtaioed: 
but  if  the  deoBity  be  assumed  to  be  equal  to  that  of  the  pkpe) 
(which  will  be  explaioed  hereafter),  it  would  follow  that  the  thick 
ness  of  the  rings  would  be  about  138  miles,  which  is  not  far  froo 
the  estimate  of  their  thickness  made  by  observers.  If  this  thick 
ness  be  admitted,  the  edge  of  the  rings  would  subtend  an  angle  ol 
the  l-32Dd  part  of  a  second  at  Saturn's  mean  distance.  Hence  i 
will  be  understood  that  the  ring  must  disappear,  even  in  powerfii 
telescopes,  when  presented  edgeways. 

2818.  Stability  of  the  rings.  —  One  of  the  circumstances  tl 
tending  this  planet,  whichh  as  excited  most  general  astonishment 
is  the  fact  that  the  globe  of  the  planet,  and  two,  not  to  say  more 
stupendous  rings,  carried  round  the  sun  with  a  velocity  of  22,00 
miles  an  hour,  subject  to  a  periodical  variation  not  inconsiderabl( 
due  to  the  varying  distance  of  the  planet  from  the  sun,  shoul 
nevertheless  maintain  their  relative  position  for  countless  ages  ui 
disturbed;  the  globe  of  the  planet  remaining  still  poised  in  th 
middle  of  the  rings,  and  the  rings,  two  or  several  as  the  case  ma 
be,  remaining  one  Within  the  other  without  material  connection  o 
apparent  contact ;  no  one  of  the  parts  of  this  marvellous  oombinatio 
having  ever  gained  or  lost  ground  upon  the  other,  and  no  apptreo 
approach  to  collision  having  taken  place,  notwithstanding  the  inno 
merable  disturbing  actions  of  bodies  external  to  them. 

2819.  Cause  assigned  for  this  stability, — The  happy  thought  ol 
bringing  the  rings  under  the  common  law  of  gravitation,  whicl 
gives  stability  to  satellites,  has  supplied  a  striking  and  beautifol  so 
iotion  for  this  question.     The  manner  in  which  the  attraction  ol 


Lib . 


'\ 


N  D 


,    ♦J^ 


TOTAL   SOLAR  ECLIPSK    OF  IHM 


^;*. 


THB  MAJOB  PLANBTS.  iOO 

gnfiiatimi,  eomlnoed  with  e^Dtrifogal  force,  Oansetf  the  moon  to 
keep  reTolving  round  the  earth  without  falling  down  upon  it  by  ite 
griTity  on  the  one  hand,  or  receding  indefinitely  from  it  by  the  cen- 
irifoal  force  on  the  other,  la  well  understood.  In  virtue  of  the 
eqoality  of  these  forces,  the  moon  keeps  continually  at  the  same 
mean  distance  from  the  earth  while  it  accompanies  the  earth  round 
tbe  sun.  Now  it  would  be  easy  to  suppose  another  moon  revolving 
bj  the  same  law  of  attraction  at  the  same  distance  from  the  earth. 
It  would  revolve  in  the  same  time,  and  with  the  same  velocity,  as 
the  first  We  may  extend  the  supposition  with  equal  facility  to 
three,  four,  or  a  hundred  moons,  at  the  same  distance.  Nay,  we 
my  suppose  as  many  moons  placed  at  the  same  distance  round  the 
euth  as  would  complete  the  circle,  so  as  to  form  a  ring  of  moons 
touching  each  other.  They  would  still  move  in  tbe  same  manner 
and  with  the  same  velocity  as  the  single  moon. 

If  such  a  ring  of  moons  were  beaten  out  into  the  thin  broad  flat 
lings  which  actually  surround  S^^turn,  the  circumstances  would  be 
KMiewhat  changed,  inasmuch  as  the  periods  of  each  concentric  lone 
would  vary  in  a  certain  ratio,  depending  on  its  distance  from  tbe 
ientre  of  oatum,  so  that  each  such  zone  would  have  to  revolve  more 
lapidly  than  those  within  it,  and  less  rapidly  than  those  outside  it 
Bot  if  the  entire  mass  were  coherent,  as  the  component  parts  of  a 
lolid  body  are,  tbe  complete  ring  might  revolve  in  a  periodic  time 
less  than  that  due  to  its  exterior  and  longer  than  that  due  to  its  in- 
terior parts.  In  (act,  the  period  of  its  revolution  would  be  the 
period  due  to  a  certain  sone  lying  near  the  middle  of  its  breadth, 
exactly  as  the  time  of  oscillation  of  a  compound  pendulum  is  that 
which  is  proper  to  the  centre  of  oscillation  (543).  Indeed,  the  case 
eC  tbe  oedllation  of  a  pendulum  and  the  conditions  which  determine 
the  centre  of  oscillation  afibrd  a  vei^  striking  illustration  of  the 
physical  phenomena  here  contemplateo. 

2820.  Rotation  of  the  ringt. — Now  the  observations  of  Sir  WiU 
liim  Herschel  on  certain  appearances  upon  the  surface  of  the  rings 
led  to  the  discovery  that  they  actually  have  a  revolution  round  their 
common  centre  and  in  their  own  plane,  and  that  the  time  of  such 
Isolation  is  very  nearly  equal  to  the  periodic  time  of  a  satellite 
those  distance  from  the  centre  of  the  planet  would  bo  equal  to  that 
of  the  middle  point  of  the  breadth  of  the  rings. 

But  if  the  principles  above  explained  be  admittrd,  it  would  follow 
tkat  each  of  the  concentric  zones  into  wliicb  the  ring  is  divided 
toold  have  a  different  time  of  revolution,  just  as  satellites  at  dif-  ^ 
ferent  distances  have  different  periodic  times ;  and  it  is  extremely 
probable  that  such  may  be  tbe  case,  because  no  observations  hitherto 
(iiade  affurd  results  sufficiently  exact  and  conclusive  as  to  either 
Establish  or  overturn  such  an  hypothesis. 

31  • 


WW  Asntmoiir. 

'  D  ippatt%  dienfhn^  b  ibe.  ifaik  the  ildbi^  «r  t^ 
pliciibla  upon  tiM  MUM  priBoiplo  M  the  ■yU  <« 

lin^  18  not  oonoentnoil  with  the  idansli  nnihad  ItaM 
lioni  made  by  Mean.  Haiding  and  Bohvibe;  after  vUeh  Ae 
jeot  waa  taken  up  by  IVofcaaor  Stntfe,  wIm^  bf  daliaala  ■Ihmi 
obeervatione  and  meaaaiementa  ezeooled  mfk  tha  gnat  Doipilit 


atniment,  folly  eatabliehad  the  ft0i»  thai  the  eantn  ef  fta  Urn 
moTea  in  a  anmll  oriul  round  the  oentve  of  the  plaiMl^  beimeBBMi 
lound  bj  the  rotation  of  the  ringi. 

2822.  ArgumeiUM/n'ikstUMMi^JamUUcmAq 
Sir  John  Henohel  haa  indioated,  in  thia  deriatioii  of  the 
the  rinn  from  the  oentie  of  the  planet^  another  aoone  of 
bility  of  the  Satomian  ayatem.    If  the  rings  were  <' 
perfect  m  their  ciioulart<mny  and  einetlyooDoentrioviA  the  fkiiii 
at  ia  demonstrable  that  they  would  form  ^n  apite  of  thmr  oanmi|pH 
foree)  a  ajatem  in  a  state  of  unttahie  equilibrium^  whieh  dm  tlif|Mi 
external  power  would  subvert — not  by  causing  a  rupture  in  the  ai^ 
stance  of  tbo  rings  -:—  but  by  precipitating  them,  unbroken,  oo  tk 
surface  of  the  planet.    For  the  attraction  of  such  a  ring  or  riagi  m 
a  point  or  sphere  eccentrically  situate  within  them  is  not  the  suae 
in  all  directions,  but  tends  to  draw  the  point  or  sphere  toward  Ae 
nearest  part  of  the  ring,  or  away  from  the  centre.     Hence,  aappv- 
ing  the  body  to  become,  from  any  cause,  ever  so  little  ecoeatris  to 
the  ring,  the  tendency  of  their  mutual  gravity  ia,  not  to  ooneot  hit 
to  increase  this  eccentricity,  and  to  bring  the  nearest  parte  of  tbaa 
together.     Now,  external  powers,  capable  of  producing  audi  eeni- 
tricity,  exist  in  the  attractions  of  the  satellites;  and  in  eider  te 
the  system  may  be  stable,  and  possess  within  itself  a  power  of  n- 
aisting  the  first  inroads  of  such  a  tendency,  while  yet  naaeent  aad 
feeble,  and  opposing  them  by  an  opposite  or  maintaining  power,  it 
has  been  shown  that  it  is  sufBcient  to  admit  the  rings  to  be  ioadd 
in  some  part  of  their  circumference,  either  by  some  minute  ii- 
equality  of  thickness,  or  by  some  portions  being  denser  than  othen. 
Such  a  load  would  give  to  the  whole  ring  to  which  it  waa  attached 
somewhat  of  the  character  of  a  heavy  and  sluggish  satellite,  mttB- 
taining  itself  in  an  orbit  with  a  certain  energy  sufficient  to  oveitoae 
minute  causes  of  disturbance,  and  establish  an  average  bearing  on 
its  centre.     But  even  without  supposing  the  existence  of  any  such 
load  —  of  which,  after  all,  we  have  no  proof —  and  granting,  the^^ 
fore,  in  its  full  extent,  the  general  instability  of  the  equilibrium,  we 
think  we  perceive,  in  the  periodicity  of  all  the  causes  of  disturbance, 
a  sufficient  guarantee  of  its  preservation.     However  homely  be  the 
illustration,  we  can  conceive  nothing  more  apt  in  every  way  to  gire 
a  general  conception  of  this  maintenance  of  equilibrium,  und^  t 
constant  tendency  to  subversion,  than  the  mode  in  which  a 


THE  MAJOR  PLANETS.  867 

band  will  sostun  a  long  pole  in  a  perpeodionlar  position  restiDg  on 
the  finger,  by  a  coDtional  and  almost  imperceptible  variation  of  the 
poini  of  support  Be  that,  however,  as  it  may,  the  observed  oscil- 
latioa  of  the  centres  of  the  rinss  about  that  of  the  planet  is  in  it- 
self the  evidence  of  a  perpetuiQ  contest  between  conservative  and 
destmctiye  powers — ^both  extremely  feeble,  but  so  antagonising  one 
another  as  to  prevent  the  latter  from  even  aoquiring  an  unoon- 
tiollAble  ascendancy,  and  rushing  to  a  catastrophe.'' 

Sir  J.  Herschel  further  observes,  that  since  '^  the  least  difference 
(4  velocity  between  the  planet  and  the  rings  must  infallibly  precip- 
itate the  one  upon  the  other,  never  more  to  separate  ^for,  once  in 
eoofcaot,  they  would  attain  a  position  of  stable  equilibnum,  and  be 
hdd  together  ever  after  by  an  immense  force),  it  follows  either  that 
Ikeir  motions  in  their  common  orbit  round  the  sun  most  have  been 
adjusted  to  each  other  by  an  external  power  with  thcf  minutest  prc- 
dsioD,  or  that  the  rings  must  have  been  formed  about  the  planet 
vhile  subject  to  their  common  orbital  motion,  and  under  the  full 
and  free  influence  of  all  the  acting  forces." 

2823.  Satellites,  —  Saturn  is  attended  by  eight  satellites,  seven 
of  which  move  in  orbits  whose  planes  coincide  very  nearly  with  that 
of  the  equator  of  the  planet,  and  therefore  with  the  plane  of  the 
iiDga.  The  orbit  of  the  remaining  satellite,  which  is  the  most  distant, 
is  inclined  to  the  equator  of  the  planet  at  an  angle  of  about  12^  14', 
and  to  the  plane  of  the  planet's  orbit  at  nearly  the  same  angle. 

2824.  Their  noTnenciature. — In  the  designations  of  the  satellites, 
much  confusion  has  arisen  from  the  disagreement  of  astronomers  as 
to  the  principle  upon  which  the  numerical  order  of  the  satellites 
dioald  be  determined.  Some  name  them  first,  second,  third,  &c., 
in  the  order  of  their  dipcovery ;  while  others  designate  them  in  the 
order  of  their  distances  from  Saturn.  It  has  been  proposed  to  remove 
til  confusion,  by  giving  them  names,  taken,  like  those  of  the  planets, 
from  the  heathen  divinities.  The  following  metrical  arrangement  of 
theve  names,  in  the  order  of  their  distances,  proceeding  from  the 
most  distant  inwards,  has  been  proposed,  as  affordiDg  an  artificial  aid 
to  the  memory  : — 

Ia[>eta8,  Titan ;  Rhea,  Dione,  Tethjs  * ; 
EneeladoB,  Mimas . 

2825.  Order  of  their  fitsrovery.  —  Since  this  was  suggested,  the 
eighth  satellite,  situate  between  lapctus  and  Titan,  has  been  discov- 
ered, and  called  Hyperion. 

*  Pronounced  TStbjs. 


S08 


imioiroift. 


The  order  of  their  discorery  was  fts  follows  :-^ 


*«■«. 


lapetui. 

liUn. 

Rhea. 

Dioite. 

ICnraUdof. 

Idlmaa. 

Hyperion. 


HuTgens. 
D.Gw«iiiL 

Do. 

Do. 
8iy  W«  HflfwBw* 

Do. 
Mem.  I«MdI  tnd  Bond. 


HMMfl 


— «* 


Hyperion  was  disooyered  on  the  same  nighty  19th  Stpt.  3 
by  Mr.  Lassell  of  Liverpool,  and  Professor  Sond  of  the  UMM 
of  Cambridge  in  the  United  States. 

2826.  Their  distances  and  periods,  — The  periodio  tioMfe 
mean  distances  of  these  bodies  from  the  centre  of  SatiinL'>i 
tained  by  the  same  kind  of  observations  as  already  ezplaiiM&t 
case  of  the  satellites  of  Jupiter,  are  as  follows :  —  e 


Mimaii 
Kneel  ad  us 

T.'thvM 

Dione 

r.hen 

Titan  

Hypvrlon . 
InpetuH .... 


TtMUit. 

m 

D. 

H. 

M. 

B. 

n»»* 

•a* 

■ .  -^ 

0 

23 

87 

22-« 

2-16 

U 

1 

8 

63 

fi-7 

8-14 

«• 

1 

21 

18 

267 

4-32 

t« 

2 

17 

41 

B-9 

6-26 

M 

4 

12 

25 

10-8 

10*60 

tfl 

15 

22 

41 

26-2 

36-48 

ttk 

22 

12 

f 

f 

61-    f 

» 

79 

7 

63 

40-4 

165- 

64« 

2827.  Harmonic  law  observed.  —  By  compariDg  the  nan 
expressing  the  ratio  of  the  periods  and  distances,  it  will  be  f 
that  the  numbers  expressing  these  fulfil  the  harmonic  law,  sn 
to  such  deviations  from  its  rigorous  observance  as  arc  due  to  th 
fluence  of  small  disturbing  causes  already  noticed.  Thus,  if  l 
press  the  mean  distance  of  any  satellite  from  the  centre  of 
planet,  and  P  its  period,  it  will  be  found  that  the  relation 


jy' 


=  74 


will  be  very  nearly  true  for  all  the  satellites. 

2828.  Elongations  and  relative  distances. — The  greatest  « 
gations  of  the  satellites  from  the  primary,  and  the  scale  of  tbcir 
tances  in  relation  to  the  diameters  of  the  planet  and  it^  rings 
represented  iny?//.  770. 

It  appears,  therefore,  that  the  oibit  of  the  most  remote  of 
satellites  subtends  a  visual  angle  of  only  128G''  at  the  earth,  b 
about  two-thirds  of  the  apparent  diameter  of  the  sun  or  moon, 
within  this  small  visual  space  all  the  vast  physical  machinery 


THB  MAJOR  PLAKET&  809 

{dienomena  whioh  we  have  here  noticed  are  in  opera- 
tion, and  witliin  such  a  space  havo  these  extraordinary 
diaooTeries  been  made.  The  apparent  diameter  of  the 
external  edge  of  the  rings  is  only  44",  or  the  fortieth 
part  of  the  apparent  diameter  of  the  sun  or  moon ;  yet 
within  that  small  circle  have  been  observed  and  mea- 
snred  the  planet,  its  belts,  atmosphere,'  and  rotation, 
and  the  two  rings,  their  magnitude,  rotation,  and  the 
lineaments  of  their  surface. 

2829.  Yariaui  pTuues  and  appearances  of  the  taUHr 
lites  to  observers  on  the  planet.  —  All  that  has  been 
said  of  the  phases  and  appearances  of  the  moons  of 
Jnpiter,  as  presented  to  the  inhabitants  of  that  planet, 
ia  equally  applicable  to  the  satellites  of  Saturn,  with 
this  difference,  that  instead  of  four  there  are  eight 
moons  continually  revolving  round  the  planet,  and 
exhibiting  all  the  monthly  changes  to  which  we  are 
accustomed  in  the  case  of  the  solitary  satellite  of  the 
earth. 

The  periods  of  Saturn's  moons,  like  those  of  Jupi- 
ter, are  short,  with  the  exception  of  those  most  remote 
from  the  primary.  The  nearest  passes  through  all  its 
phases  in  22^  hours,  and  the  fourth,  counting  upwards, 
in  less  than  66  hours.  The  next  three  have  months 
varying  from  4  to  22  terrestrial  days. 

These  seven  moons  move  in  orbits  whose  planes  are 
nearly  coincident  with  the  plane  of  the  rings.  The 
consequence  of  this  arrangement  is,  that  they  are 
7ff.  always  visible  by  the  inhabitants  of  both  hemispheres 
when  they  are  not  eclipsed  by  the  shadow  of  the  planet, 
two  inner  satellites  are  seen  making  their  rapid  course  along 
«mal  edge  of  the  ring,  within  a  very  small  apparent  distance 
The  motion  of  the  nearest  is  so  rapid  as  to  be  perceivable, 
lat  of  the  hour-hand  of  a  colossal  time-piece.  It  describes 
Q  22^  hours,  being  at  the  rate  of  16^  per  hour,  or  16'  per 
) ;  so  that  in  two  minutes  it  moves  over  a  space  equal  to  the 
Qt  diameter  of  the  moon. 

eighth,  or  most  remote  satellite,  b  in  many  respects  excep- 
and  different  from  all  the  others.  Unlike  these,  it  moves  in 
t  inclined  at  a  considerable  angle  to  the  plane  of  the  rings, 
exceptional  also  in  its  distance  from  the  primary,  being  re- 
to  the  distance  of  64  semidiameters  of  Saturn.  The  only 
Alogous  to  this  presented  in  the  solar  system  is  that  of  the 
moon,  the  distance  of  which  is  60  semidiameters  of  the 

IT. 

).  Magnitudes  of  the  satellites,  —  Owing  to  the  great  distanof 


i 


ST9  ABTBOHMir. 

oT  BMite,  ttifl  dimennotai  of  tt*  rtfciTllfcs  Ihtc'd „ 

ltfD«d.  Ilie  rizth  hi  ordor,  prooBailiBg  nuiwards,  is,  hcrweTer. 
ksowB  to  be  the  largsBt,  aod  it  ■ppnn  Mriaio  that  iu  Totame  is 
Elth  I«Bi  tluB  thst  of  the  pinwt  Han.  Tbe  three  ^tellitea  im- 
ttediately  vithiD  this,  Rhc*,  Dlone,  tad I^h j>,  are  smaller  bodies, 
md  ctn  ooly  ^  seen  with  toIsBoopM  of  giM  power.  Tbe  oih«r 
two,  HimM  and  Sneekdm,  raqvin  inlmuiMBor  tbe  wry  highest 
power  Mid  peribetion,  and  atm<npb«rioeoAdWoi»  of  the  roost  ftvour- 
«blfl  nature,  to  be  obaemble  at  all.  Sir  S.  Hersehel  u^,  tbnt  at 
the  time  thejr  were  diaoarerad  b;  hii  fkther  "they  were  Been  to 
thread,  like  beads,  die  almoat  infiDiMT  Ain  fibre  of  light  to  ithich 
Ae  rin^  then  eeen  edgewan,  was  redneed,  and  for  a  short  time  to 
advatioe  off  it  at  either  end,  speedilj  to  return,  and  bastcDiog  (o 
their  habitoal  eoncealinent  behind  the  bodj." 

S831.  A^Mrent  tnagnihidtt  <m  leat  Jrom  Saturn.  —  The  tea] 
BBgnltodea  of  the  ntellitea,  the  eighA  excepted,  being  iiBucer- 
tattled,  nothing  can  be  inferred  with  any  eertainty  r^epectiDg  their 
apparent  raagnitndes  as  seen  from  the  BDrf»cc  of  SuCura,  exMpl 
what  may  be  reafonably  eoqjeotared  upon  aaalogies  to  other  tike 
bodies  of  the  ayatero.  The  Mtallites  of  Jupiter  being  all  greater 
than  the  moon,  while  one  of  them  ezeeeds  Mcroury  ia  magnitiide, 
•od  another  is  but  little  ioEetior  in  volume  to  that  planet,  it  may  b« 
assumed  with  great  probability  of  truth  that  the  &aiel!ites  of  SaRm 
an  at  least  sereraUy  greater  in  their  aotoal  dimcDsioQs  Uian  our 
moon. 

If  this  be  admitted,  their  probable  apparent  magaitudea  at  hean 
from  Saturn  maybe  inferred  from  their  distances.  The  diatuBO  rf 
the  first,  Slimaa,  from  the  nearest  part  of  the  surikoe  of  the  planet, 
is  only  94,000  miles,  or  about  2  j  timcB  less  than  the  distanoe  of 
the  moon ;  the  distance  of  the  second  is  about  half  that  of  the 
moon ;  that  of  the  third  about  two-lbirda,  and  that  of  the  fourth 
about  fiTe-sixtbs,  of  the  moon's  distance.  If  these  bodies,  therefore, 
exceed  the  moon  in  their  actual  dimeosioos,  their  apparent  magni- 
tudes as  seen  from  Saturn  will  exceed  the  apparent  magnitude  of 
the  moon  in  a  still  greater  ratio  than  that  in  which  the  aistanoe  of 
tbe  moon  from  the  earth  exceeds  their  sevenl  distances  from  the 
surface  of  Saturn.  Of  the  remaining  satellites,  little  is  as  yet 
known  of  the  Beventh,  Hyperion,  which  has  only  been  noeotly  dis- 
ooYcred ;  and  the  great  magnitude  of  the  sixth,  Titan,  Koders  i( 
probable  that,  notwithstanding  its  great  distance  from  Saturn,  it 
may  still  appear  with  a  disk  not  very  much  less  than  that  of  the 

2882.  Horizonfal  paraUax  of  the  taUBitet. —  Tha  horiaoDtel 
parallax  is  detcrmiDCii  in  the  same  manner  as  for  the  wti^llihw  of 
Jninler  (2767).     Let  the  Tslues  of  it,  for  the  eight  i 


IBS  MAJO&  PLANETS.  871 

oeeding  oiitward%  be  ezpreaaed  by  Hi,  h^  h^  &o.,  and  wc  shall 
haTe 

•.-^-»»-        -.-'^->3-        '.-5^-^'         •.-•-^-«^« 

-.-^-•^     '.-^-«^      '.-!^-^     '.-^-«^- 


2tlA  «         28  "       M-aO 

2888.  Apparent  magnitudes  of  Saturn  seen  from  the  sateUite^, 
— It  follows,  therefore^  that  the  disk  of  Satarn,  seen  from  the 
Mtellites  respectively,  subtends  visual  angles  varying  from  34^  sub- 
tended al  the  nearest,  to  2^  at  the  most  remote. 

2884.  Satellites  not  visible  in  the  circumpolar  regions  of  the 
flanet  —  From  what  has  been  explained  in  (2769),  combined  with 
the  obeerved  fact  that  all  the  satellites  except  lapetus  move  in  the 
pbuw  of  the  equator  of  the  planet,  it  follows  that  they  are  severally 
bvinble  within  distances  of  the  poles  of  the  planet  expressed  by 
tkeir  horiiontal  parallaxes.  Thus,  the  first  cannot  be  seen  at  lati- 
tadM  higher  than  78<^;  the  second,  IQ^'i;  the  third,  79''-8,  and 


2885.  Remarkable  relation  between  the  periods,  —  The  periods 
of  the  four  satellites  nearest  to  the  planet  have  a  very  remarkable 
oamerical  relation.  If  they  are  expressed  by  P,  p',  p",  and  p"',  we 
ikall  fiod  that 

p"=2p,  p'"=2p'; 

that  ]«y  the  periods  of  the  third  and  fourth  are  respectively  double 
those  of  the  first  and  second. 

2886.  Rotation  on  their  axes,  —  The  case  of  the  moon,  and  the 
obserratioDB  made  on  the  satellites  of  Jupiter,  raise  the  presumption 
that  it  is  a  general  law  of  secondary  planets  to  revolve  on  their 
izes  in  the  times  in  which  they  revolve  round  their  primary.  The 
great  distance  of  Saturn  has  deprived  observers  hitherto  of  the 
power  of  testing  this  law  by  the  Satumian  system.  Certain  ap- 
pearanoes,  however,  which  have  been  observed  in  the  case  of  the 
great  latellite  l^tan,  indicate,  at  least  with  regard  to  it,  such  a  rota- 
tion. The  variation  of  its  apparent  brightness  in  different  parts  of 
its  orbit  is  very  eonspicuous,  and  the  changes  have  a  fixed  relation 
to  its  elongation,  the  same  degree  of  brightness  always  correspond- 
ing to  the  same  position  of  the  satellite  in  relation  to  its  primary. 
Now  this  is  an  effect  which  would  be  explicable  on  the  supposition 
that  different  sides  of  the  satellite  reflect  light  with  different  degrees 
of  intensity,  and  that  it  revolves  on  its  axis  in  the  same  time  that 
it  revolves  round  its  primary.  It  has  been  observed  that,  when  the 
satellite  has  eastern  elongation,  it  has  ceased  to  bo  visible,  from 
which  it  has  been  inferred  that  the  hemisphere  then  turned  to  the 
earth  has  so  feeble  a  reflective  power  that  the  light  proceeding  from 
it  ii  intoflkieot  to  affect  the  eye  in  a  sensible  degree.   The  improve- 


871  ABnoKom. 

nfl&t  of  telescopes  Iiu  MiaUed  olMrfeni  to  ftUov  ft  a|  fnmit 
through  the  entire  extent  (tf  its  orbit^  but  the  dininwtioD  of  ill 
Instxe  on  the  eastern  side  of  the  plmt  is  stiU  so  gna^  thai  il  is 
only  seen  with  the  grestest  diffioaltj. 

2887.  Mom  of  Saium.—Th»  mass  of  Sstnm  is  aseertsinaa  hj 

the  motion  of  hu  satellites  by  the  method  abeadj  eEphnwd  (2686). 
If  r  express  the  distance  of  the  pbuset  from  the  aim  in  semi* 
diameters  of  the  orlnt  of  a  satdlitej  P  the  period  of  the jdapat  taking 
that  of  the  satellite  for  the  onit^  and  H  the  mass  of  tao  ana  taking 
that  of  the  pUnet  for  the  anit|  we  shall  have 

By  snhstitQting  for  these  symbols  the  nnmbers  whioli  they  lepv^ 
sent  in  the  case  of  Saturn  and  his  satellites,  values  will  m  ftm 
for  M,  a  mean  of  which  is  about  8500,  showing  that  tk  maas  of 
Saturn  is  the  8500th  part  of  the  mass  of  the  sun. 

Since  the  earth  is  the  855,000th  pert  of  the  mass  of  the  saB|  it 
^follows  that  the  mass  of  Saturn  is  100  times  that  of  the  earth. 

2838.  Dermfy.  —  Since  the  mass  of  Saturn  is  only  100  tinei 
that  of  the  earth,  while  his  volume  is  about  1000  times  greater,  it 
follows  that  this  planet  is  composed  of  matter  whose  moan  densitj 
is  about  ten  times  less  than  thai  of  the  earth ;  and  since  the  densitj 
of  the  earth  is  five  and  a  half  times  greater  than  that  of  water,  it 
follows  that  the  density  of  Saturn  is  a  little  more  than  half  that 
of  water.  This  is  the  density  of  the  light  sorts  of  wood,  snch  u 
cedar  and  poplar,  and  is  about  twice  the  density  of  cork  (787). 

2839.  Superficial  gravitt/,  —  The  gravity  by  which  bodies  on 
the  surface  of  Saturn  are  attracted,  omitting  for  the  moment  all  con- 
sideration of  the  effects  of  the  spheroidal  form  and  rotation,  may  be 
computed  by  the  principles  already  explained  by  its  mass  and  meta 
diameter. 

Let  m'  =  the  mass,  that  of  the  earth  being  1 ; 

/  =  the  mean  semidiameter,  that  of  the  earth  being  1 ) 
^  =  superficial  gravity,  that  of  the  earth  being  1. 

We  shall  then  have 

,       m       101-6       ,  -„ 

Superficial  gravity,  therefore,  on  Saturn  exceeds  that  upon  the 
earth  by  thirteen  per  cent ,  omitting  the  effects  of  form  and  rotation. 

2840.  Centrifugal  force  at  Saturn* s  equator,  —  The  force  of 
^vity  on  Saturn,  as  on  Jupiter,  is  subject  to  considerable  vaiia- 
tiou;  arising  from  the  counteracting  effects  of  centrifugal  force. 


THS  MAJOR  PLANETS.  373 

Lei  0  =  oentrifagal  force  at  the  planet's  equator  related  to  ter- 
restrial gravity  as  the  unit ; 
g  =:  16*08  feet; 
V  =  yeloeity  of  Saturn's  equator  in  feet  per  second. 

We  shall  then  have  (813) 

_     y* 

The  Talne  of  y  deduced  from  the  equatorial  diameter  of  the 
planet  and  the  time  of  its  rotation  is  34^775,  and  it  follows,  there- 
fatt,  that  0  =  01799. 

Deducting  this  from  the  superficial  CTavity,  undiminished  by 
rotation  alrndy  computed  (2839),  we  shall  have 

y  —  0  =  1-13  —  01799  =  0-9501 ; 

which  i8|  therefore,  the  efiective  gravity  of  Saturn's  equator  related 
to  terrestrial  gravi^  as  the  unit 

2841.  Variaium  of  gravity  from  equator  to  pole.  —  Let  e,  w, 
aad  c  retain  their  former  significations  (2777)  (2384),  and  by  the 
tkenem  of  Clairanlt,  already  noticed,  we  shall  have 

e  -f  10  =  2-6  c. 

Bat,  by  what  has  been  proved,  we  have 

^—0     0-9501  ' 

from  which  it  follows  that 

w=2  5  X  0189  —0097  =  0-3755. 

It  follows,  therefore,  'that  a  body  which  weighs  10,000  lbs.  at 
Saturn's  equator  would  weigh  13,755  lbs.  if  traosported  to  his  pole ; 
ind  a  body  which  weighs  100  lbs.  placed  upon  tbe  earth  would 
Weigh  9o  lbs.  on  Saturn  s  equator. 

The  height  through  which  a  body  would  fall  in  a  second  upon 
Satom  will  be 

1608  X 0-95  =  15-28  feet  at  the  equator; 
15-28  X  1-375  =  2501  feet  at  the  pole. 

The  relative  heights  through  which  bodies  would  fall,  and  the 
lengths  of  pendulums,  may  be  determined  in  the  same  manner  as 
already  exnlained  (2777). 

2842.  Prevailing  errors  respecting  the  tiranographg  of  Saturn,'—' 
The  rings  must  obviously  form  a  most  remarkable  object  in  the 
firmament  of  observers  stationed  upon  Saturn,  and  must  play  an 
important  part  in  their  uranography.  The  problem  to  determine 
their  apparent  magnitude,  form,  and  position,  in  relation  to  the  fixed 
Stan,  the  snn,  and  Satumian  moons,  has,  therefore,  been  Te^gtt^*^^ 

VLL  32 


S74  AffiEBOvoifr. 

■•  a  quflstion  of  .mterastuiff  wpmiM&m,  if  noft  of  gml  wamSM  !»• 
porfeanoe ;  and  has,  aoooran^T,  mora  or  Ia«  onmged  Iho  attotttiaa 
of  aatroDomers.  It  is  neTortheleM  a  abgular  frel^  flttl^  dthwij^ 
the  Bulject  has  been  dwoiMwed  and  oxaminnd  hj  Tarioot  aiMboritMi 
for  three-qnarten  of  a  oentniyi  the  eonolnaiona  at  wUdi  thej  ham 
arrived,  and  the  viewa  whioh  have. been  genendlf  ejrtreMed  and 
adopted  respecting  it,  are  oompletelj  erroneooa. 

In  the  IBerlin  Jahrimeh  for  1786,  Pkofeaaor  Bode  pabBdied  aa 
eaaay  on  this  aubjeot^  whioh,  inb|eot  to  the  imperfeot  kixnrled|gs  of 
the  dimensione  of  the  ringa  whrah  had  then  resolted  firom  the  eb- 
■ervatioDB  made  npon  them,  does  not  seem  to  differ  inalmall|j  fa 
principle  firom  the  Yiews  adopted  bj  the  most  eminenl  aalraiioaua 
of  the  prssent  daj. 

2848.  Views  of  Sir  J.  BenckeL  —  Sr  John  Henbhd,  in  Ui 
Outlines  of  Astronomy,  edit  1849,  states  that  the  linai  as  sees 
from  Satnm  appear  as  vast  arches  spanning  the  skj  £rom  Jmina  to 
horiion,  holding  an  almost  invariable  sitoation  among  the  stars;  anl 
that,  in  the  hemisphere  of  the  planet  whioh  is  on  their  dark  mS|  a 
solar  eclipse  of  fifteen  gears'  doration  tskes  pboe. 

This  statement,  which  has  been  reprodncea  by  almost  all  wiiIbs 
both  in  England  and  on  the  Continent,  is  incorrect  in  both  the  pa^ 
ticulars  stated.  First,  the  rings  do  not  hold  an  almost  invariaUe 
position  among  the  stars.  On  the  contrary,  their  position  with  n- 
lation  to  the  fixed  stars  is  subject  to  a  change  so  rapid  that  it  must 
be  sensible  to  observers  on  the  planet,  the  stars  seen  on  one  side  of 
the  rings  passing  to  the  other  side  from  hour  to  hour.  Secand^f 
no  such  phenomenon  as  a  solar  eclipse  of  fifteen  years'  dnration,  or 
any  phenomenon,  bearing  the  least  analogy  to  it,  can  take  place  oo 
any  part  of  the  globe  of  Saturn. 

2844.  Theory  of  Mddler.  —  Among  the  continental  astronomen 
who  have  recently  reviewed  this  question,  the  most  eminent  is  Dr. 
Madler,  to  whose  observations  and  researches  science  is  so  lamlj 
indebted  for  the  information  we  possess  respecting  the  physical  ofiar> 
acter  of  the  surface  of  the  Moon  and  Mars. 

This  astronomer  maintains,  like  Herschel,  that  the  rings  hold  i 
fixed  position  in  the  firmament,  their  edges  being  projected  on  par- 
allels of  declination,  and  that,  consequently,  all  celestial  objects  are 
carried  by  the  diurnal  motion  in  circles  parallel  to  them,  so  that  in 
the  same  latitude  of  Saturn  the  same  stars  are  always  covered  by 
the  rings,  and  the  same  stars  are  always  seen  at  the  same  distance 
from  them. 

This  is  also  incorrect.  The  zones  of  the  firmament  covered  bj 
the  rings  are  not  bounded  by  parallels  of  declination,  but  by  curves 
which  intersect  these  parallels  at  various  angles. 

Dr.  Madlcr  enters  into  elaborate  calculations  of  the  solar  eclipses 
which  take  place  during  the  winter  half  of  the  Satoroiaa  year. 


THB  MAJOR  PLANETS.  875 

Aocording  to  him,  at  a  certain  epoch  after  the  autumnal  equinox  in 
each  latitude,  the  sun  passes  under  the  outer  ring  and  is  eclipsed  by 
it,  and  continues  to  be  thus  eclipsed  until,  by  its  increasing  declina- 
tion, it  emerges  from  the  lower  edge  of  that  ring  and  passes  into  the 
opening  between  the  rings,  where  it  continues  to  be  visible  for  an 
iDterval  greater  or  less  according  to  the  latitude  of  the  observer, 
DDtil  the  further  increase  of  its  declination  causes  it  to  pass  under 
the  edge  of  the  inner  ring,  where  it  is  again  eclipsed.  The  further 
increase  of  its  declination  in  certain  latitudes  would,  according  to 
this  astronomer,  carry  it  beyond  the  lower  edge  of  the  inner  ring, 
after  which  it  would  be  seen  below  the  ring  uneclipsed.  Afler  the 
solstice  in  such  latitudes,  when  the  sun  returns  towards  the  celestial 
equator,  its  decreasing  declination  would  carry  it  successively  first 
under  the  inner  and  then  under  the  outer  ring.  There  would  thus 
be,  according  to  Madler,  in  such  latitudes  two  solar  eclipses  of  long 
doration,  one  by  each  ring  before  the  winter  solstice ;  and  two  others 
of  like  duration,  but  in  a  contrary  order,  after  the  winter  solstice. 
In  certain  latitudes,  however,  the  declination  of  the  lower  edge  of 
the  inner  ring  beiuf  greater  than  the  obliquity  of  the  orbit  to  the 
Satumian  equator,  the  sun  would  not  emerge  from  the  inner  ring, 
ind  in  this  case  there  would  be  only  one  eclipse  by  the  inner  ring, 
tnd  that  at  mid-winter ;  but,  as  before,  two,  one  before  and  the  other 
ifter  the  solstice,  by  the  outer  ring,  separated  from  the  former  by  the 
time  during  which  the  sun  passes  across  the  interval  between  the  rings. 

Dr.  Midler  computes  the  duration  of  these  various  eclipses  in  the 
diflferent  latitudes  of  Saturn,  and  gives  a  table,  by  which  it  would 
ippear  that  the  solar  eclipses  which  take  place  behind  the  inner 
ring  vary  in  length  from  three  months  to  several  years,  that  the  du- 
ration of  the  eclipses  produced  by  the  outer  ring  is  still  greater,  and 
that  the  duration  of  the  appearance  of  the  sun  in  the  interval  be- 
tween the  rings  varies  in  different  latitudes  from  ten  days  to  seven 
and  eight  months.* 

2845.  Correction  of  the  preceding  vieics.  —  These  various  con- 
elusions  and  computations  of  Dr.  Sladler,  and  the  reasoning  on 
which  they  are  based,  are  altogether  erroneous ;  and  the  solur  phe- 
nomena which  he  describes  have  no  correspondence  with,  nor  any 
resemblance  to,  the  actual  uranographical  phenomena. 

We  shall  now  explain,  so  far  as  the  necessary  limits  of  the  present 
Tolome  will  admit,  what  the  actual  phenomena  arc  which  would  be 
witnessed  by  an  observer  stationed  at  different  parts  of  the  surface 
of  Saturn.  It  will  not,  however,  be  possible  to  enter  into  the  de- 
tails of  the  reasoning  upon  which  the  conclusions  are  based.  For 
this  we  must  refer  to  a  memoir  by  the  author  of  this  voluiuc,  read 
K-forc  the  Royal  Astronomical  Society  of  Loudon,  and  which  will 
be  been  io  their  Transactions. 

*  See  Popnl&re  Aitronomie,  von  Dr.  J.  H.  Madler.    Barlln,  X^l. 


S7ft 


ASTEOKoirr. 


2846.  Phencmena  preBenUd  io  am  obmrmt  9kifimml  gt  Sakm/9 
emtaior. —  Zone  o/thejirmammt  covered  Im  Ae  rkiaj^^iim  iMioB 
Of  the  oheerver  in  this  case  being  in  die  pltne  of  ue  A^  and  the 
heavens  hiving  the  charaoter  of  a  li^ht  apWrei  the  iiiij|  wl  oovnr  ft 
lone  of  the  fimament  coinciding  with  the  nrime  mCnal^  vUbb,  in 
thia  case,  is  alao  the  oelesdal  eqnator.  It  will  ttenpfim  pan  lihiOB|^ 
the  zenith  of  the  observer  at  riffht  anglea  to  hif  miffMian,  daNamfing 
to  the  horiion  at  the  east  ana  west  fointa.  Ihe  tmb/  pvt  of  Hm 
ratem  of  rinn  expoeed  to  view  ia  th^  inner  edge  of  t&  nmr  n^g. 
This  ed^  ia  ulnminated  at  nigM  bj  the  nn  aft  III  tim%  mepC  a(t 
the  eqoinoz,  when  the  ann,  neing  in  the  phne  pf  Ae  xn^  em 
aemicirole  of  the  ring  throws  its  ^hiSbw  oo  the  other:  and  «impCij|fc 
alao^  that  arc  of  the  ring  on  which  the  shadow  of  ue  plaiMt  mEi 
In  the  day-time  the  edge  of  the  ring  ia  rather  atrani^j  flhunnaftad 
bv  light  reflected  from  the  extensive  and  not  Tory  zttBMrile  sn&ea 
m  tte  planet 

The  thickness  of  the  ring  not  b^ng  exactly  aaoertaiiiady  tlia  sf- 
parent  width  of  the  aone  of  the  firmament  whim  it  coren  eanaoft  oa 
determined  with  precision. 

Ifi  howeveri  the  migor  limit  of  260  miles,  assigned  to  the  dusk 
ness  by  Sir  J.  Herschel,  be  adopted^  the  corresponding  limit  of  the 
apparent  width,  obtained  by  the  usual  method  of  calcalationy  by 
comparing  this  thickness  with  its  distance  from  the  observer,  wiU 
give  45'  as  the  apparent  breadth  of  the  zone  occupied  by  the  ring  at 
the  zenith ;  and  since  the  observer,  being  stationed  at  the  point  0 
(Jig.  780)  considerably  removed  from  the  centre  o  of  the  rinff,  is  at 

a  greater  distance  oi^  oir  from 
those  points  of  the  ring  which  meet 
the  horizon  than  from  that  which  ia 
at  the  zenith,  the  apparent  breadth  of 
the  ring  will  gradually  decrease  from 
the  zenith  z  to  the  horiion  in  the 
same  proportion  as  the  distance  of 
successive  points  P,  p^,  &c.,  of  the  ring 
from  the  station  of  the  obeerver  in- 
creases. From  the  known  valnea  of 
the  diameters  of  the  planet  and  the  ring  already  ffiven,  it  ia  easy  to 
show  that  the  apparent  breadth  of  the  rin^  at  the  horiion  will  be 
less  than  its  apparent  breadth  at  the  zenith  in  the  ratio  of  9  to  4 
very  nearly,  that  being  the  inverse  ratio  of  the  distance  of  the  two 
points  from  the  observer.  If,  therefore,  the  apparent  breadth  of  the 
ring  at  the  zenith  z  be  45',  its  apparent  breadth  at  the  horiion  F^p" 
wUI  be  2(y.  ^ 

It  appears,  therefore,  that  a  zone  of  the  firmament  is  in  this  case 
covered  by  the  ring  extending  22}'  N.  and  S.  of  the  equator  at  the 
lenithj  and  10'  N.  and  S.  of  it  at  the  horizon,  and  gradnally  deorsaa- 


Fig.  780. 


THB  MAJOR  PLANETS.  S77 

mg  iQ  width  from  the  one  point  to  the  other.  It  follows  that  two 
parBlIels  of  decliofttion  at  22}'  N.  and  S.  touch  this  zone  at  the 
pduts  where  it  intersects  the  meridian,  and  lie  elsewhere  altogether 
clear  of  it ;  and  two  other  parallels,  whose  declination  N.  and  S.  is 
1(K,  meet  it  at  the  horizon,  and  lie  elsewhere  altogether  within  it. 
The  intermediate  parallels  intersect  the  edges  of  the  zone  at  certain 
pdots  hetween  the  zenith  and  the  horizon,  and  pass  oatside  it,  helow 
and  under  it^  ahove  thoee  points.  It  follows  from  this,  that  all 
objects  situate  in  such  parallels  rise  clear  of  the  ring,  pass  under  it 
at  a  oertaio  altitude,  and  culminate  occulted  by  it.  AH  parallels  of 
declination,  whose  distance  from  the  equator  is  less  than  ICK,  are 
entirely  eovered  by  the  ring  from  the  horizon  to  the  zenith ;  and  all 
objeets  placed  on  such  parallels  are,  consequently,  occulted  by  the 
ring  throuffh  the  whole  period  of  their  diurnal  motion. 

2847.  S(fiar  tdiptet  at  Saturn's  equator,  —  These  observations 
are  applicable,  of  course,  not  only  to  the  sun,  but  to  all  objects  of 
changeable  declination.  As  to  the  sun,  its  apparent  diameter  at 
Saturo  being  3''3,  its  disk  will  be  in  external  contact  with  the  ring 
at  the  zenith,  when  the  declination  of  its  centre  is  24 i',  and  in  in- 
ternal contact  with  it  when  its  declination  is  21'. 

From  a  calculation  of  the  rate  at  which  the  sun  changes  its  decli- 
nation at  and  near  Saturn's  equinox,  derived  from  the  ascertained 
obliquity  of  his  equator  to  his  orbit,  it  may  be  shown  that  it  will 
have  the  declination  24  i'  at  twenty-two  days  before  the  equinox,  and 
the  declination  21'  at  nineteen  days  before  it.  At  twenty-two  days 
before  the  equinox,  therefore,  a  partial  eclipse  of  the  sun  by  the  ring 
at  the  lenith  will  oommence,  which  will  become  total  at  nineteen 
days  before  it. 

But  though  total  at  the  zenith,  it  will  still  be  only  partial  at  lower 
altitudes,  and  the  sun's  disk  will  be  clear  of  the  ring  altogether  when 
itill  nearer  to  the  horizon. 

When  the  sun's  declination  still  decreasing  becomes  11''65,  its 
disk  will  be  in  external  contact  with  the  ring  at  the  point  where  it 
rises  and  sets;  and  when  its  declination  becomes  8''35,  it  will  be  in 
internal  contact,  and  therefore  totally  eclipsed.  The  sun  will  have 
the  former  declination  at  ten  days  and  a  half,  and  the  latter  at  seven 
days  and  a  half,  before  the  equinox. 

It  follows,  therefore,  that  the  sun  will  be  totally  eclipsed  from 
rising  to  setting,  seven  days  and  a  half  before,  and  seven  days  and 
a  half  after,  the  equinox,  to  an  observer  stationed  on  the  equator  of 
the  planet. 

2848.  Eclipses  of  the  satellites.  —  The  orbits  of  the  six  inner 

satellites,  being  exactly  or  nearly  in  the  plane  of  the  ring,  they  will 

be  permanently  eclipsed  by  the  ring  to  an  observer  stationed  on  the 

planet's  equator,  unless,  indeed,  the  apparent  magnitudes  of  their 

disks  exceed  the  apparent  width  of  the  ring.     The  real  magnitude 

?io* 


878  ABTROHomr. 

■ 

of  di6  wtellitet  being  iiiuunertaiiM|l,  if  b  impoaBSl^  fi^4iHtmtJaB 
their  apparent  magnitodes ;  from  tnalogj  it  wodm  appear  iirttolMiHa 
that  they  should  be  so  great  as  the  apparent  width  of  the  nay  eim 
at  the  horizon,  and  nnl^  thev  depart  to  aoqu  eztpiil  bj  reaaoB  df 
email  obliqoitiea  in  their  orbits,  firom  the  J^tob  of  1M  liqL  dl 
mw  of  them  mnst  be  permanentlj  iytereeptea  ftoni  aa  6b&ufmhm 
atationed. 

ne  eighth  satellite,  howeTer,  whoa^  oibit  b  ineliiied  to  tba  ptaae 
of  the  ring  at  an  ang^e  of  aboat  18^,  denarta  N.  and  8.  of  Oa  li^ 
to  thb  extent,  and  b  anbjeot  to  eelipaea  mmilar  to  tlioaa  of  &a  an 
already  desoribed. 

2849.  Phenomena  pmenfed  to  an  ehmrver  at  oO^  Jhftif&m 
lalti^ei.  —  If  an  observer  be  station^  at  any  point  oa  ooa  of  dbe 
meridians  of  the  planet,  on  the  same  nde  of  the  lingai  &a  iBBylhe 
ring  will  present  to  him  the  appeeranee  of  an  anh  m  Ao  heami^ 
beuingaome  resemblanoe  in  its  form  toa  runbow;  the  mrflMM^  how- 
ever, £iving  an  appearanoe  resembling  that  of  the  moon. 

The  vertex  or  highest  point  of  thb  aroh  will  be  npon  hb  meridian, 
and  the  two  portions  into  which  it  will  be  divided  by  the  neridiaa 
will  be  eq|aal  and  simikr,  and  will  deseend  to  the  horiaoo  at  points 
equally  distant  from  the  meridian.  The  apparent  breadth  A  tiiu 
illuminated  bow  will  be  greatest  upon  the  meridian,  and  it  will  de- 
crease in  descending  on  either  side  towards  the  horiaon,  where  it 
will  be  least.  The  divisioo  between  the  two  rings  will  be  apparent, 
and,  except  at  places  within  a  very  short  distance  of  the  equator, 
the  firmament  will  be  visible  through  it. 

2850.  Edges  of  the  rings  seen  at  variable  distances  from  cdes- 
tial  equator.  —  The  distance  of  the  edge  of  the  bow  from  the  celes- 
tial equator  will  not  be  every  where  the  same,  as  it  haa  been  erro- 
neously assumed  to  be.  That  part  of  the  bow  which  b  upon  the 
meridian  will  be  most  remote  from  the  celestial  equator;  and  in 
descending  from  the  meridian  on  either  side  towards  the  horiion, 
the  declination  of  its  edce  will  gradually  decrease,  so  that  those 
points  which  rest  upon  the  horizon  will  be  nearer  to  the  equator 
than  the  other  points. 

2851.  Parallels  of  declination^  therefore^  intersect  them.  —  It 
follows  from  this,  that  the  parallel  of  declination  which  passes 
through  the  points  where  the  upper  edge  of  the  bow  meets  the 
horizon  will  lie  every  where  above  it,  and  the  parallel  which  passes 
through  the  point  where  the  upper  edge  crosses  the  meridian  will 
lie  every  where  below  that  edge.  This  necessarily  follows  from 
the  fact,  that  the  declination  of  the  points  whei'e  the  edee  meets  the 
horizon  is  less,  and  that  of  the  point  where  it  meets  l£e  meridian 
greater,  than  that  of  any  other  point  upon  it 

It  appears  from  this,  that  all  parallels  whose  declinations  are 
greater  than  those  of  the  points  where  the  edge  meets  the  horiion, 


THE  HAJOR  PLANETS. 


879 


ud  len  thu  that  of  tbe  point  where  it  croesea  the  meridian,  most 
interaect  the  edge  between  the  horison  and  the  meridiaD,  and  must 
therefore  lie  below  it  under  the  point  of  intersection,  and  above  it 
orer  the  point  of  intersection. 

Theae  conditions  are  eqaall;  applicable  to  each  of  the  edges  of 
caeh  of  the  rings,  and  will  servo  to  determine  in  all  cases  those 
puallelfl  which  will  intersect  them  respectively. 

2852.  Edgetpiaeed  tymmetrieaSi/  tn  relation  to  meridian  and 
luirixo*.  —  From  tbe  ajmrnetrical  position  of  each  of  the  edges,  with 
relation  to  the  meridian  and  horison,  it  will  be  apparent  that  tbe 
points  at  «rbich  each  parallel  intersects  them  will  be  similarlj  placed 
on  each  side  of  the  meridian,  baviog  equal  altitudes  and  equal  ari- 
unths  EL  and  W- 

2853.  Ibrm  of  Ae  prq/tetion  at  dijerent  latiludei.  —  The  geae- 
tal  form  and  poeition  of  the  bow  formed  b;  the  projection  of  the 
rings  upgo  the  firmament  in  each  latitude  may  be  easily  determined 
by  elemfstu;  geometrioal  prindplea.    Let  te  (Jig.  781)  be  the 


qnaihaiit  of  the  merilian  of  the  pluwt  jMring  thnBcb  thv  riiiias 
of  this  obBeirer  o,  snd  let  b  a'  r  raprewnt  one  ot  tha  niljM  «f  dta 
liop  reduoed  by  penpeetive  to  an  oval,  bnt  ahovD  aa  a  cin^l«  io  the 
loirer  figure.  It  will  be  eanly  ponaiTed,  that  tha  visual  raj  pasting 
fhraogb  O  to  R  carried  nHrnd  tha  <Mi»  B,  a',  a^,  &c  ,  will  describe 
the  lurfaoe  of  an  oblit^ne  o(»ie,  vhoae  baae  ia  tbt  plaac  of  ihc  ring, 
and  whoiQ  axis  o  0  ia  inoliaed  to  the  base  at  aa  angle  o  c  R,  equ&l 
to  tha  latitnde  of  the  statioii.  The  projeotioa  cf  the  edge  of  ihe 
bow  upon  the  finuamantwill  then  be  the  inlatMttioD  of  the  earface 
of  thia  okJiqne  eooe  with  the  celestial  aphen ;  and  it  can  be  demoe- 
■ttatad,  that  the  poiat  of  this  which  ia  most  nmote  from  the  cele^ 


THE  MAJOR  PLANETS.  881 

titi  equator  is  the  projection  of  the  point  r,  where  the  plane  of  the 
meridian  intersects  the  plane  of  the  ring;  th:it  the  other  points  of 
tie  pnjffctiun  approach  nearer  to  the  celestial  equator  as  their  dis- 
taDCC  from  the  meridian  increases ',  and  that  they  have  equal  decli- 
Ditions  at  e<(ual  distances  east  and  west  of  the  meridian. 

To  illustrate  this  still  more  fully,  let  N  c  E,  Jif/.  782,  he  a  quad- 
rant of  a  meridian  of  the  planet,  c  being  its  centre  and  c  £  its  semi- 
diameter.  Let  R  r'  be  a  section  of  the  inner  ring,  made  by  the 
plane  of  the  meridiaa  continued  through  the  ring,  and  let  r  r'  be  a 
Hke  section  of  the  exterior  ring. 

2854.  Ringt  invinUe  above  lat.  GS""  20^  38".— If  we  suppose  an 
observer  to  tnvel  upon  the  meridian  from  the  pole  n,  towards  the 
equator,  it  is  evident  that  at  first  all  view  of  the  rings  will  be  inter- 
cepted by  the  conTezity  of  the  planet  If  a  line  be  drawn  from  r, 
the  external  point  of  the  external  ring,  touching  the  planet,  it  can 
be  proved  that  the  point  of  contact  will  be  at  the  latitude  of  63^ 
'2(y  38" ;  and  it  ia  evident,  that  when  the  observer  has  descended  to 
this  latitude  the  point  r  will  be  in  his  horizon,  and  consequently  at 
all  higher  latitudes  it  will  bo  below  his  horizon,  and  therefore  in- 
Tisible.  It  appears,  therefore,  that  no  part  of  the  outer  ring  is 
visible  from  any  latitude  above  63^  20'  38  ,  and  that  at  this  latitude 
1  single  point  of  the  exterior  ring  is  visible  just  touching  the 
Eouthem  point  of  the  horizon. 

2855.  Appearance  at  lat.  69°  20'  25". — If  the  observer  now  de- 
Kend  to  lower  latitudes,  the  exterior  ring  will  begin  to  rise  above 
his  horizon  at  the  southern  point ;  and  it  can  be  shown  that  when 
he  has  descended  to  the  latitude  59°  20'  25",  his  horizon  will  just 
touch  the  inner  edge  /  of  the  exterior  ring,  cutting  off  a  segment 
of  that  ring,  which  will  be  seen  above  the  horizon. 

The  position  of  the  ring  thus  visible  above  the  horizon,  will  have 
the  appearance  of  a  lunar  segment. 

2856.  Appearance  ai  laL  58°  32'  20".— If  the  observer  continue 
to  descend  to  a  lower  latitude,  the  ring  will  condnue  to  rise  to  a 
greater  elevation,  and  the  interval  between  the  rings  will  become 
visible.  When  he  has  descended  to  the  lat  58°  32'  20"  his  horizon 
will  just  tonok  the  outer  edge  of  the  inner  ring,  and  a  segment  of 
the  interval  between  the  rings  will  be  visible  under  the  arch  of  the 
outer  ring,  which  will  appear  projected  upon  the  southern  firma- 
ment 

The  outer  ring,  therefore,  b  presented  to  the  observer  in  this  case 
as  a  lunar  bow  spanning  the  southern  firmament  It  must  be  re- 
membered that  the  declinations  of  the  points  at  which  each  of  tho 
edges  intersect  the  meridian  being  greater,  and  the  declination  of  tho 
points  where  they  meet  the  horizon  less,  than  that  of  any  interme- 
diate points,  all  parallels  having  declinations  between  these  will  inter- 
lect  the  edges  severally,  while  all  parallels  whose  declination  is  be- 


•B  AeTKONUMY. 

Mid  IhtM  limits  will  puis  alu^ther  above  jr  altngetber  («In  i 
nun,  wptutivplv,  us  the  miae  niay  b«.  I 

2867.  Jj.i.r',riifue  ul  lal.  47°  33' 51".  — When  the  oWmt  | 
hu  dnoendcd  to  this  latitude,  ibe  boriion  will  jusl  tovrli  the  i 
adga  of  tho  inner  ring,  cutting  off  n  Bcgiiicnt  of  it,  of  wliicli  ibt  1 
horaan  ii  tLe  base,  the  outer  ring  appvariDg  &s  a  bow  sIktc  ' 
njnMDled  iu  ^.  783.     The  tamo  obeerratioD  u  to  iJie  ti 


Pig.  TS3. 

decUnstaon  of  the  edges  of  both  rings  trill  be  applicsbl?  ia  (hit  m 
ID  the  former  case,  and  certuia  psmllels  will  acoordiagl;  taUnect 
each  of  the  tdges  of  tbe  rings,  and  olhera  will  be  eotirelj  coTeicd 
by  theiD. 

2858.  Appearance  at  lower  latitudrn.  —  In  descending  lo  ifill 
lower  latjludea,  the  cleTation  of  iho  bow  formed  by  the  projectini 
at  tbe  rings  increases ;  and  the  lower  ring,  which  hitherto  has  pn- 
Knted  itself  as  a  mere  scgmCDt,  having  the  homon  as  a  hue,  w* 
anames  tbe  form  of  a  bow,  iuclosing  below  it  a  plane  Kgment  of 
(he  firmament,  as  represented  in^^.  784. 


Ai  tbe  latitado  decreases,  tbe  amplitade  and  elevation  of  tUi 
bow  also  iDcreaBe,  but  its  apparent  breadth  diminisbeB,  aa  in  Jlg>- 
785,  786,  787.  The  obliquity  of  ita  several  edgra  to  the  ditMkS 
of  the  parallels  of  declinatioD  still  continacB,  and  it  ia  conaeqMDdy 


THB  MAJOB  PLANETS. 


[  bj  them  Kt  every  point,  bo  tbat  the  pumllels  whioli 
tideee  it  will  lie  altemalel;  above  uid  below  its  edges  u  aljraftd; 


rig.  m. 

cMribed ;  Kiine  parallels,  however,  lying  entirely  above  and  othen 
idtelj  below  it,  aa  represented  in  /?//.  788.  It  will  be  easy  to 
meive  by  tbia,  without  rendering  the  diagrams  complicated  by 
nhipljiiig  upon  tbem  the  arcs  of  iho  paralk-Ia,  that  they  will  be 
irioDsly  interlaced  by  these  parallels,  whicb  will  pss  alternately 
ove  and  below  the  rings,  being  at  one  phice  covered  by  tbem,  and 
anotber  iiocovend;  at  ooo  {Hjint  crwH^illg  the  interval  between 


AfiTKONOHT. 


the  rings,  Mid  ftt  «Dottier  lying  abore  or  below  it;  aome  nml 
lying  entirel;  above,  othen  entirely  below,  either  ring,  while  m 


may  be  altogether  covered  by  the  one  ring  or  the  other.     I  h 

ascertained,  by  an  investigatioQ  of  the  diinenatons  nod  form 
the  bow  ID  different  latitudes,  that  the  only  latitudeK  in  vhii 
parallel  lies  altogether  within  the  interval  between  the  ringH, 
those  included  between  the  latitudes  58°  and  50°.  At  all  01 
ktiludcs  of  tlie  planet  from  which  the  interval  between  the  ring 
visible,  (he  parallels  which  pass  between  the  ring  will  lie  pi 
within  the  interval,  and  partly  above  or  below  it. 

I2S59.  Occullatiom  of  ccleilial  ohjecli  6j  ihe  ringt.  — It  follt 
from  all  this,  that,  in  general,  celestial  objecta  arc  carried  by  tl 
diurnal  motion  alternately  above  and  below  each  of  the  edges  of 
ringa;  and  if  a  parallel  ioterscetB  all  the  edged,  which  happen! 
many  cases,  then  the  object  in  such  a  parallel  will  rise  below 
rings,  will  pass  successively  under  them,  will  ho  occulted  by  e 
of  theni,  will  he  \-iaiblc  in  crossing  the  interval  between  them,  1 
will  culminate  above  them  ;  and  this  will  take  place  in  precisely 
Banic  manner,  and  at  precisely  the  same  ahitudes  and  azimntbs 
and  W.  of  the  meridian,  so  thot  such  an  object  will  be  occulted  ( 
times  by  the  rings  between  rising  and  setting;  that  is  to  say,  tv 
between  the  horizon  and  meridian  east  and  west  of  the  latter. 
rising,  it  will  be  first  occulted  by  the  inner  ring,  then  passing  an 
the  interval  will  be  occulted  by  the  outer  ring,  after  which  it  1 
culminate  clear  of  the  rings;  and  in  descending  on  the  west  tows 
the  horiion,  it  will  be  successively  occulted  by  the  outer  and  in 
rings  in  the  same  manner  and  at  the  same  allitndes  as  it  was 
cultcd  before  culininatiou,  and  will  finally  set  clear  of  the  rings. 


THB  MAJOR  PLANETS.  885 

When,  as  happens  in  some  esses,  the  parallel  which  comes  under 
tiiese  conditions  fidls  within  the  range  of  the  sun's  declination,  that 
is  to  sajy  when  its  declination  is  less  than  26^  48'  40",  the  sun,  at- 
taining this  particular  declination,  will  suffer  four  such  eclipses  he- 
tween  rising  and  setting, — ^two  before  and  two  after  culmination. 

In  some  cases  a  parallel  of  declination  will  be  covered  by  the 
lower  ring  at  the  meridian,  but  will  be  clear  of  it  near  the  horizon. 
This  will  take  place  when  the  declination  of  the  parallel  is  greater 
than  that  of  the  points  where  the  lower  edg^  of  the  ring  meets  the 
horizon,  and  less  than  that  of  the  point  where  it  meets  the  me- 
ridian. In  that  case,  an  object  in  such  a  parallel  will  rise  and  set 
dear  of  the  ring,  but  will  be  occulted  by  it  at  culmination.  Such 
an  objeet^  therefore,  will  be  occulted  only  once  between  rising  and 
letting. 

An  object  may  in  like  manner  be  occulted  at  or  a  little  above  the 
horiioD  by  the  inner  ring,  and  may  culminate  in  the  interval,  or  it 
may,  afker  being  occulted  by  the  inner  ring,  pass  under  the  outer 
ring  and  culminate  occulted  by  it. 

In  fine,  all  these  various  phenomena,  and  many  others  too  nume- 
rous and  complicated  to  be  explained  here,  are  manifested  in  the 
Satumian  firmament,  and  the  sun  itself  is  subject  to  most  of  them. 
It  happens,  in  some  cases,  that  a  certain  number  of  parallels  of  de- 
clination are  entirely  covered  by  the  outer,  and  others  by  the  inner 
ring;  and  when  the  sun  is  found  at  any  one  of  these  parallels  it  will 
be  eclipsed  constantly  from  rising  to  setting  by  one  or  the  other 
ring. 

2^60.  Zone  vhibh  leticccn  the  rings,  —  The  zone  of  the  heavens 
visible  between  the  rings  is  found  by  calculating  the  vbual  angle 
subtended  at  the  station  of  the  observer  by  lines  drawn  to  the  inner 
edge  of  the  outer  and  to  the  outer  edge  of  the  inner  ring,  supposing 
that  the  thickness  of  the  outer  ring  bears  an  inconsiderable  propor- 
tion to  the  width  of  the  space  which  separates  them ;  and  it  is 
erident  that  the  magnitude  of  this  visual  angle  will  gradually  and 
indefinitely  decrease  as  the  obser^'er  approaches  the  equator,  inas^ 
DiQch  as  the  obliquity  of  the  visual  ray  to  the  plane  of  the  rings 
indefinitely  increases. 

2861.  Effect  of  the  thickness  of  the  rings  on  this  zone. — If,  how- 
ever, the  thickness  of  the  outer  ring  be  supposed  to  bear  any  con- 
siderable ratio  to  the  width  of  the  space  between  the  rings,  it  will 
iutercept  a  portion  of  the  visual  rays  included  within  the  angle 
formed  by  the  rays  drawn  to  the  edges  of  the  two  rings,  and  tho 
efiectivc  opening  will  be  found  by  subtracting  the  visual  angle  sub- 
tended by  the  thickness  of  the  outer  nog  from  the  visual  angle  sub- 
tended by  tho  space  between  the  rings ;  and  since  the  obliquity  of 
the  visual  rays  bounding  the  former  gradually  diminish  .^  in  ap- 
proaching the  equator,  while  the  obliquity  of  the  visual  rav>  Uoui^ie- 

ui.  3o 


886  ASTRONOHT. 

bg  Iha  Uttv  Riduall J  iDCreaam,  it  u  enrideat  thkt  the  iwo^  iiig|(  J 
nUanded  by  tta  thicknen  of  tlie  outer  ring  eontuiiwllj  ituitMiMfl 
iriU,  tt  maao  oertain  ktJtude,  beeome  equal  ta  the  Tisokl  angbsO)'] 
tended  by  the  ipue  between  the  rtngB ;  uid  at  that  latitwia  iMt 
iogly,  u  well  aa  at  all  iofenor  ladtades,  the  tbtokneM  of  tbc  « 
ring  will  altogether  intercept  the  evening,  and  no  nme  of  fll  I 
haaTena  will  m  lieible  tbroo^  it  I  have  fbuod  byc^ieaUinl 
that  if  260  milea  be  ftd[iiitt«d  as  the  major  limit  d  the  nimill 
view  of  the  heaTeuB  tbroagb  the  opening  will  be  intercepted  at  !■%  1 
tndea  bdow  8°;  and  if  the  probable  minor  limit  of  150  miles  bi  1 
amimed>  all  view  will  be  intercepted  aland  below  tbe  latitude  (^5°.  [ 

2862.  Solar  eelipui  by  the  ringt. — The  principles  npao  vtiidi 
■alar  mUmcs  I^  the  rings  in  each  latitude  are  calculated  are,  thotk  | 
fbre,  caolj  nnderetood.     B;  comparing  tbe  p^sUel  «C  4 
of  UK  nn  at  anj  time  with  tbe  parallels  of  deeliaatiog  <" 
where  each  of  the  edgex  of  each  of  tbe  rings  rooeta  tta 
the  meridian,  the  conditions  under  which  it  will  intoiMl  __ 

aevetally  will  be  determined,  and  hence  it  will  appear  that  aa 
onrions  and  interastinB  body  of  nolar  pheoomcoa,  not  antioipalod  i> 
anj  of  the  worlia  in  which  tbe  uranogmphy  of  Saturn  haa  been  in- 
vestigated,  are  broagbt  to  light.  In  tbe  lower  latitudes  tbe  aan  gfr 
dergoes  at  certain  epochs  four  eclipses  per  day,  two  in  the  foreiuiw 
and  two  in  tbe  afternoon,  and  between  each  pair  of  eclipses  it  Ma 
Bbining  through  tbe  space  between  tbe  rings.  In  higher  latatndM, 
at  certain  seasons,  it  does  not  emerge  from  one  or  other  of  tin  | 
rings,  and  suffers  only  three  eclipses,  two  by  one  ring  and  on*  bj 
tbe  other.  At  other  latitudes,  at  certain  times,  it  is  only  edipied  ' 
at  rising  and  setting,  and  at  others  only  in  culminating. 

Our  limits,  hawever,  preclude  us  from  giving  these  detaili,  ml 
others  not  loss  curious,  for  which  the  reader  is  referred  to  tbe  p^S 
already  mentioned. 

2863.  Eclipaet  of  the  iateaiUt.  —  T\ie  inner  satellites  beinf  b 
the  plane  of  the  ring^  th^ 
will  necessarilj  be  pro- 
jected on  a  lone  of  Iht 
heavens  outaide  the  ex- 
terior ring,  and  can  neier 
be  intcrct  pled  or  eelipied 
by  the  rings  (fig.  789). 

The     eightb     ntellile, 

however,  whose  orbit  bis 

an  obliquity  of  12"  or  IS' 

Fig.  Tse.  to  the  plane  of  the  nop, 

will  be  eclipsed  at  than 

latitudes  at  which  tbe  edges  of  tbe  rings  have  declinations  len  ikso 

thoae  which  it  attaina.     These  eclipses  are  calculated  and  cxpUiiMl 


THE  MAJOR  PLANEXa  387 

M  the  Bame  principles  exactly  as  those  of  the  sun,  mutatis  mu- 
tandis. 

2864.  Satumian  seasons.  —  It  has  been  shown  (2795)  that  the 
uis  of  the  pLmet  is  inclined  to  the  piano  of  its  orbit  at  an  angle  of 
26®  48'  40",  and  is,  like  the  axis  of  the  earth,  carried  parallel  to 
itself  round  the  sun.     The  obliquity  therefore  which,  so  far  as  the 
lao  is  concerned,  determines  the  extremes  of  the  Satumian  seasons, 
difSen  by  no  more  than  3®  from  that  of  the  ecliptic.     The  tropics 
ire  parallels  of  latitude  26®  48'  40"  north  and  south  of  the  equa- 
tor.   The  parallels  within  which  the  sun  remains  in  winter  below 
the  horiion  during  one  or  more  revolutions  of  the  planet  are  at  the 
ktitnde  63®  11'  20".     These  circles,  therefore,  afifect  the  Satumian 
dimatology  in  the  same  manner  as  the  tropics  and  polar  circles 
ilfect  that  of  the  earth.     The  slow  motion  of  the  sun  in  longitude, 
•nd  its  rapid  diurnal  motion,  however,  must   produce  important 
diierenccs  in  its  effects  as  compared  with  those  manifested  on  the 
(nth.     While  the  sun,  as  seen  from  the  earth,  changes  its  longitude 
It  the  mean  rate  of  very  nearly  1®  per  day,  its  change  of  longitude 
tor  Satara  is  little  more  than  2'  per  day ;  and  while,  as  seen  in  the 
tonestrial  firmament,  it  is  carried  by  the  diurnal  motion  over  1®  in 
;     four  minntes,  a  Satumian  observer  sees  it  move  over  the  same  space 
:    b  less  than  two  minutes.     If  the  heating  and  illuminating  power 
^.    tf  the  snn  be  diminished  in  a  high  ratio  by  the  greater  distance  of 
t   tfist  lominary,  some  compensation  may  perhaps  arise  from  the  rapid 
'    iUeroations  of  light  and  darkness. 

III.  Uranus. 

■_      2865.  Ducovery, — "While  occupied  in  one  of  his  surveys  of  the 

kiTens  on  the  night  of  the  13th  of  March,  1781,  the  attention  of 

&r  William  Herschel  was  attracted  by  an  object  which  he  did  not  ^ 

'   iad  registered  in  the  catalogue  of  stars,  and  which  presented  in 

*  \   tti  telescope  an  appearance  obviously  different  from  that  of  a  fixed 

\'-   Mir.    On  viewing  it  with  increased  magnifying  p<}wers, it  presented 

iiensible  disk;  and  after  the  lapse  of  some  days,  its  place  among 

^^    Aft  fixed  Stan  was  changed.     This  object  must,  therefore,  be  either 

|.    teonet  or  a  planet;  and  Sir  W.  Herschel,  in  the  first  instance, 

nsooQced  it  as  the  former.     When,  however,  submitted  to  further 

,^    ttd  more  continued  observation,  it  was  found  to  move  in  an  orbit 

Scvly  circular,  inclined  at  a  small  angle  to  the  plane  of  the  ecliptic, 

Od  to  have  a  disk  sensibly  circular. 

It  appeared,  therefore,  to  have  the  characters,  not  of  a  comet,  but 
Bplaoet  revolving  outside  the  orbit  of  Saturn.  It  was  named  the 
^Georgium  Sidus"  by  Sir  W.  Herschel,  in  compliment  to  his  friend 
nd  patron  George  III.  This  name  not  being  accepted  by  foreign 
MtroQomen,  that  of  "  Herschel "  was  proposed  by  LaplaGe,  aiid  U) 


ASTRONOUT. 

for  a  time  adopted.     Dcfiaitively,  however,  tbe 

lina  agreed  upon  the  name  "Uranus,"  by  whicL  thia 

(11  tlic  Bjetcm  ia  noir  universally  dcEigniit^d. 

Period,  iy  ti/nodic  molwa.  —  Owing  to  tbe  great  lengli 

jjcriod  of  tbis  pknet,  thoee  methods  of  determination  which 

re  tbe  obMrvatioD  of  one  or  more  complete  revoluiions  could 

applied  to  iL     The  eynodio  period,  however,  or  the  interval 

I  two  Eucoessive  oppositions,  being  only  3I}9'4  days,  supplied 

as  of  obtaining  a  first  jinnrnTimntlon.     Tbis  gives 

j___l 1       _      1 

p  ~  365-25      3ti9-40~30ti43' 
period  of  30,643  days. 

the  apparent  motum  in  qwiilrature.  —  When  a  planat 
^uaurature,  its  visual  direction  being  a  tangent  to  tbe  eardi'i 
its  apparent  place  is  not  affected  by  the  earth's  orbital  motion. 
^e  quadrature  which   precedes    opposition,  tbe   earth   mov«a 
Btly /owarrf*  the  planet;  and  in   the  quadrature  w Li ch   follom 
nsiUon,  it  moves  directly  from  the  planet     in  neither  cue, 
afore,  would  its  motion  produce  any  apparent  change  of  plaeg 
ID  uie  pknet.      It  follows,  therefore,  that  wlien  a  planet  is  in  quad- 
ntare,  its  apparent  motion  is  due  exclusively  to  its  own  motion, 
and  not  at  all  to  that  of  the  earth,     Tbe  daily  motion  of  tbe  planet 
■s  tlicn  observed  is,  therefore,  the  actual  daily  increment  of  its  geo- 
centric longitude. 

Bat  in  the  case  of  a  planet  sucli  as  Uranus,  or  even  Satam, 
whose  distance  from  tbe  aun  bears  a  large  ratio  to  the  earth's  dis- 
tance, the  geocentric  motion  of  the  planet  will  not  differ  sensibly 
from  the  heliocentric  motion ;  and,  therefore,  tbe  geocentric  daily 
inorcment  of  tbe  planet's  longitude  observed  when  in  quadrators 
nuif,  to  obtain  an  approximative  value  of  the  period,  be  taken  u 
*  tbe  daily  increment  of  tbe  heliocentric  longitude.  If  this  iocro- 
ment  be  expressed  by  I,  we  shall  have 
360° 


Now,  it  is  found  that  tbe  apparent  daily  increment  of  the  ptanel'i 
longitude  when  in  quadrature  is  42"-23.  If  360°  be  reduced  to 
aeoonds  wc  shall  then  have 

P  =  1?|?  =  30689. 

By  more  accurate  calculation,  the  periodic  time  has  been  detmnuaed 

ftt  30,686-82  days,  or  81  years. 

2868.  Beliocentric  moti<m. — The  mean  heliocentrio  motioD  rf 
ths  planet  b  therefore,  more  exactly, 


THK  MAJOR  PLASET8.  889. 

^  =  4°  17'  8"-5  yearly; 

^i^=  21' 25"-7  monthly; 

1296000      ^„„„„„  ^  ., 
-SOesT  =  ^2  238  dady. 

2669.  Synodic  motion.  —  The  mean  daily  apparent  motion  of 
the  san  being  0^*9856,  or  3548"'16,  the  mean  daily  synodic  motion 
or  increment  of  elongation  of  Uranus  will  be 

3548-16 —42"-23  =  3505"-93  =  58'-43  =  0°-975. 
The  synodic  period  is  therefore,  more  exactly, 

^5  =  ^^^  23  days. 

The  eertb,  therefore,  in  4 J  days  overtakes  the  planet,  after  com- 
pleting each  sidereal  revolution. 

2870.  Distance.  —  The  mean  distance  r  of  the  planet  from  the 
snn^  determined  by  the  harmonic  law,  is  therefore 

f^  =  84«  =  7056, 
r  =  1918. 

The  mean  distance  is  therefore  19-18  times  that  of  the  earth,  and, 
eoDseqiiently,  the  actual  distance  is 

95,000,000  X 1918  =  1,822,100,000  miles. 

The  Stance  of  Uranus  from  the  sun  is  therefore  1822  millions  of 
ttfles,  and  its  distance  from  the  earth,  when  in  opposition,  is  there- 
§ate  1727  millions  of  miles. 

The  eccentricity  of  the  orbit  of  Uranus  being  0*046,  these  distances 
lie  liable  to  only  a  very  small  variation.  The  distance  from  the 
nm  is  increased  in  aphelion,  and  diminished  in  perihelion  by  less 
than  a  twentieth  of  its  entire  amount.  The  plane  of  the  orbit  coin- 
cides very  nearly  with  that  of  the  ecliptic. 

2871.  Relative  orbit  and  distance  from  the  earth. — The  relative 
proportions  of  the  orbits  of  Uranus  and  the  earth  are  represented  in 
Jig,  790,  where  E  e'  e''  is  the  orbit  of  the  earth,  and  s  u  the  distance 
of  Uranus  from  the  snn.  The  four  positions  of  the  earth,  corre- 
sponding to  the  opposition,  conjunction,  and  quadratures  of  the 
jAanet,  are  represented  as  in  the  former  cases. 

2872.  Annual  parallax,  —  Since  su  is  19*18  times  SE,  we  shall 
have  for  the  angle 

,      57°-30      _ 

^""=1918-  =  ^- 
33* 


I  Hk  diameter  of  tbe  evth'n  oiint,  meamring  u  it  ioet 
I  BaKrljr  200  miUions  of  miles,  therofate  subteodj,  »t 
I  UlMos,  a  Tisoal  ugle  of  ool;  6° ;  *nd  a  elobe  whi^ 
I  mold  fill  it,  Been  firom  tbe  plkiiet,  would  dstb  an  i^ 
I  pwent  diameter  only  tvelve  times  greater  tfaia  Aal 
I  of  the  mooD. 

I  &8T3.  Vatt  tcale  of  the  orbital  mofibn.  —  The  di» 
I  (woe  of  UranoB  from  the  son  being  above  aincteM 
I  timeg  that  of  the  earth,  and  the  eaitC  being  at  >oc&  « 
I  distance  that  light,  moving  at  the  rate  of  Dcajj 
I  SOOjOOO  miles  per  second,  takes  kboat  eidit  matim 
I  to  come  from  the  son  to  the  eartb;  U  MMi  Allk 
I  will  take  10x8  =  152  miiint0«,(«t«D  bwBi  ai  « 
I  half,  Co  move  from  the  sun  to  nruras.  SmniMl 
I  BD&^t  arc,  therefore,  not  peroeiTed  bj  tfw  inbtlilMai 
I  of  that  planet  for  two  faoniv  and  a  ludf  aftar  tiNqr 
I  lealljr  lake  place ;  for  the  nnn  doea  not  appear  »  M 
I  or  Bet  until  the  light  moving  from  it,  at  Uie  moiaeBt 
I  it  touches  ihc  [ilaoc  of  the  boriioD,  rcnchcs  the  tje  of 
I  the  obstrvcr. 

I  The  diaincler  of  the  orbit  of  Uranus  measnrin^  it 
I  round  numbers,  3600  millions  of  miles,  its  dran- 
I  ferencc  mcaEarcs  11,300  millioos  of  miles,  over  iriiid 
I  the  pluuct  moTca  in  30,687  days.  Ita  mean  diilj 
I  moiiao  is  tbcrcfare  368,000  miles,  and  its  Iioiirij  tM- 
I  tion,  cmiscr[[iently,  about  15,300  miles. 
I  2S74.  Aji^'onn/ and  r.y<!  ,/Kini<'/,-ni.  — The  appa- 
I  rent  diiimcter  of  Uranns  in  opposition  ezooedi  4'  vj% 
I  small  fraction.  At  the  distanoe  of  the  planet  fiva 
I  the  eartb,  in  that  position,  the  Lnear  Tftlna  of  X*  is 
■  1757000000      o.„,     ., 

^06265-  =  ^21mJe.; 

The  actual  diameter  of  the  planet  is  therefore 

8421  X  41  =34,526  miles; 
being  about  half  that  of  Saturn,  and  a  little  more  than  4j  times 
tltat  of  tho  earth. 

28T5.  fiur/are  and  volume. — The  enrfaoe  of  Uranni  ia  thereftx 
10  times,  and  its  volume  82  times,  that  of  the  earth. 

2876.  Diurnal  rotation  and  jihj/neal  character  of  tmrfict  WW*- 
eerlained.  —  The  vast  distance  of  this  planet,  and  ita  jOnaaqHst 
small  apparent  magnitude  and  faint  illumiaation,  have  nndend  it 
hitherto  impracticable  to  discover  any  indications  of  ita  dinrul  rota- 
tion, the  ezistenoe  of  an  atmosphere,  or  aaj  of  the  phjrical  ehtns- 
lers  which  the  telescope  has  disclosed  in  the  case  of  the  nesfartf 
the  great  planets. 


n^  in. 


THR  HAJOH  PLAKETS. 


891 


S877.  iSUop  SfflU  and  itat. — 'Hie  app&rent  diameter  of  the  Rin, 
u  Ken  from  Unntig,  is  lesa  ttun  u 

Oseen  from  the  earth  in  the  ratio  of 
1  to  19.  The  magnitude  of  the 
smx'a  disk  at  the  earth  being  snp- 
poaed  to  be  represented  b;  x,  fy. 
791,  ita  magnitude  seen  from  Unnn* 
wonid  be  n. 
The  ilium inatiDg  and  wanning 
power  of  the  solar  rays,  under  Ae 
tame  physical  conditiont,  are  there- 
_,_  ...  fore  19*  =^361  times  less  at  Unniu 

'*"'■  than  at  the  earth. 

2878.  Suipected  ring*. —  It  was  at  one  time  sospeoted  bj  Sir 
W.  Hencbel  that  this  pUnct  was  sarronnded  bj  two  ajstema  of 
fiap  with  planes  at  right  angles  to  each  other.  Sabseqnent  obaer^ 
ntioii  has  not  realised  this  conjecture. 

2879.  JSaitOiiet.  — It  has  been  ascertained  that  Uranns,  like  the 
other  major  planets,  is  attended  bj  a  Bjetem  of  satellites,  tbe  num- 
ber of  which  is  not  jet  certainly  determined,  and  which,  from,  the 
gnat  remoteness  of  the  Uranian  system,  cannot  be  seen  at  all 
exo^^  the  aid  of  the  most  perfect  and  powerful  telesoopes. 

Sir  W.  Herschel,  soon  after  discovering  this  planet,  announced 
the  eziatenee  of  a  sjatem  of  six  satellites  atUDding  it,  haring  the 
periods  end  distances  expressed  in  the  following  Table :— 


^. 

,.^ 

"jsr"' 

0.            »            »            I 

i  1  i'  '" 

17D 

SabMqnent  ohserrations  have  confirmed  this  discovery  so  far  only 
as  relatea  to  the  four  inner  satellites.  Tbe  fifth  sod  sixth  not 
ksring  been  re^abserred,  notwithstanding  the  vast  improvement 
which  has  taken  place  in  the  constrootion  of  telescopes,  and  the 
greatlj  mnltiplied  number  snd  increased  activity  and  seal  of  ob- 
Htrer^  must  he  eonsidered,  to  say  the  least,  as  problema^cal. 

Of  the  torn  which  have  been  re-obscrred,  the  second  and  fourth 
ns  by  fiw  tbe  most  conspicuous,  and  their  distances  and  periods 
hne  been  SMertained  with  all  desirable  accnnicy  and  certainty. 
The  first  w»  re.obBerved  by  Mr.  Lassell  at  Liverpool,  and  by  H. 


892  ASTRONOMY. 

Otto  Struve  at  Dorpat,  in  1847.     The  fourth  was  observed  aVrnt 
the  same  time  by  Mr.  LasscU. 

2880.  Anomalous  inclination  of  their  orhils.  —  Contrary  to  the 
kw  which  prevails  without  any  other  exception  in  the  motions  of 
the  bodies  of  the  solar  system,  the  orbits  of  the  satellites  of  Unnu 
are  inclined  to  the  plane  of  the  orbit  of  the  planet,  and  therefbce 
to  that  of  the  ecliptic,  at  an  angle  of  78°  58',  being  little  less  thin 
a  right  angle,  and  their  motions  in  these  orbits  are  retrognde; 
that  is  to  say,  their  longitudes  as  seen  from  Uranus  continnany 
decrease. 

When  the  earth  has  such  a  position  that  the  yisual  direcdoa  is  st 
right  angles  to  the  line  of  nodes,  the  angle  under  the  plane  of  ths 
orbit  and  the  visual  line  will  be  78^  58' ;  and  in  certain  positioiis 
of  the  planet  they  will  be  seen,  as  it  were,  in  plan.  Being  nesrlj 
circular,  the  satellites  will  in  such  a  position  be  Timble  revolving 
round  the  primary  throughout  their  entire  orbits,  the  projections  not 
sensibly  differing  from  circles. 

2881.  Apparent  motiun  arid  phases  as  seen  from  Uranus. — ^The 
diurnal  rotation  and  the  direction  of  the  axis  of  the  planet  being 
unascertained,  the  inclination  of  the  orbits  to  the  planet's  equator  is 
consequently  unknown.  It  appears,  however,  that  all  the  orbits 
have  the  same  line  of  nodes,  and  arc  in  a  common  plane,  or  nearij 
so.  Twice  in  each  revolution  of  the  planet  this  plane  passes 
through  the  sun,  when  the  sat^jUites  exhibit  the  same  succession  of 
phases  to  the  planet  as  the  moon  presents  to  the  earth,  except  so  fir 
as  they  are  modified  by  the  effects  of  the  diurnal  parallax,  which 
are  considerable,  especially  in  the  case  of  the  nearer  satellites. 

Twice  in  each  revolution  of  the  planet,  at  epochs  exactly  iDte^ 
mediate  between  the  former,  the  line  of  nodes  being  at  right  anglei 
to  the  line  joining  the  sun  and  planet,  the  plane  of  the  satellites* 
orbits  is  nearly  perpendicular  to  the  same  line.  In  this  case  the 
sat<?llites,  during  their  entire  revolution,  suffer  no  other  change  of 
phase  than  what  may  be  produced  by  the  diurnal  parallax,  and  ap- 
pear continually  with  the  same  phases  as  that  which  the  moon  pre- 
senta  at  the  quarters. 

In  the  intermediate  position  of  the  planet  a  complicated  variety 
of  phases  will  be  presented,  which  may  be  traced  and  analysed  bj 
giving  due  attention  to  the  change  of  direction  of  the  line  of  nodes 
of  the  satellites'  orbits  to  the  line  joining  the  planet  with  the  sun. 

2882.  Mass  and  dcnsiti/  of  Uranus.  —  Some  uncertainty  still 
attends  the  determination  of  the  elements  of  these  more  distant  and 
recently  discovered  planets.  The  mass  and  density  of  Uranus  are 
only  provisionally  determined.  The  mass  is  assumed  to  be  the 
24,900th  part  of  that  of  the  sun,  and  the  density  the  sixth  of  that 
of  the  earth. 


THE  MAJOR  PLANETS.  898 

IV.  Neptune. 

2SS3.  Discover  If  of  Neptune.  — TTie  discovery  of  this  planet  con- 
stitutes one  of  the  most  signal  triumphs  of  mathematical  science, 
ind  marks  an  era  which  must  be  for  ever  memorable  in  the  history 
oi  physical  investigation. 

If  tho  planets  were  subject  only  to  the  attraction  of  the  sun,  they 
would  revolve  in  exact  ellipses,  of  which  the  sun  would  bo  the  com- 
mon focus ;  but  being  also  subject  to  the  attraction  of  each  other, 
vhich,  though  incomparably  more  feeble  than  that  of  the  presiding 
eentnl  mass,  produces  sensible  and  measurable  effects,  consequent 
deviations  from  these  elliptic  paths,  called  perturbations,  take 
^aee,  which  will  be  more  fully  explained  in  a  subsequent  chapter. 
The  masses  and  relative  motions  of  the  planets  being  known,  these 
disturbances  can  be  ascertained  with  such  accuracy  that  the  position 
of  any  known  planet  at  any  epoch,  past  or  future,  can  be  determined 
with  the  most  surprising  degree  of  precision. 

If,  therefore,  it  should  be  found,  that  the  motion  which  a  planet 
is  observed  to  have  is  not  in  acconlance  with  that  which  it  ought  to 
have,  subject  to  the  central  attraction  of  the  sun,  and  the  disturbing 
aotions  of  the  surrounding  planets,  it  must  be  inferred  that  some 
other  disturbing  attraction  acts  upon  it,  proceeding  from  an  undis- 
eoTcred  cause ;  and,  in  this  case,  a  problem  novel  in  its  form  and 
data,  and  beset  with  difficulties  which  might  well  appear  insuperable, 
is  presented  to  the  phjrsical  astronomer.  If  the  solution  of  the  pro- 
Uem,  to  determine  the  disturbances  produced  upon  the  orbit  of  a 
pbnet  by  another  planet,  whose  mass  and  motions  arc  known,  be 
ruprded  as  a  stupendous  achievement  in  physical  and  mathematical 
icienee,  bow  much  more  formidable  must  not  the  converse  question 
be  regarded,  in  which  the  disturbances  are  given  to  find  the  planet  I 

Such  was,  nevertheless,  the  problem  of  which  the  discovery  of 
Neptune  has  been  the  astonishing  solution. 

Although  no  exposition  of  the  actual  process  by  which  this  great 
mtellectnal  achievement  has  been  effected,  could  be  comprehended 
without  the  possession  of  an  amount  of  mathematical  knowledge  far 
exceeding  that  which  is  expected  from  the  readers  of  treatises  much 
ten  elementary  than  the  present  volume,  we  may  not  bo  altogether 
nnsnccessful  in  attempting  to  illustrate  tho  principle  on  which  an 
invesUgation,  attended  witn  so  surprising  a  result,  has  been  based, 
and  even  the  method  upon  which  it  has  been  conducted,  so  as  to 
atrip  the  proceeding  of  much  of  that  incomprehensible  character 
which,  in  the  view  of  the  great  mass  of  those  who  consider  it  without 
being  able  to  follow  the  steps  of  the  actual  investigation,  is  generally 
attached  to  it,  and  to  show  at  least  the  spirit  of  the  reasoning  by 
which  the  solution  of  the  problem  has  been  accomplished. 

For  thb  purpose,  it  will  be  necessary,  Jirst,  to  explain  the  nature 


894  ASTROKOMT. 

and  character  of  those  disturbances  which  were  obaerred  and  which 
could  not  be  ascribed  to  the  attraction  of  any  of  the  known  planets; 
and,  second f^f  to  show  iu  what  manner  an  undiscovered  planet  re- 
Tolviug  outside  the  known  limits  of  the  solar  system  could  produce 
such  effects. 

2884.  Unexplained  disturbances  observed  in  the  motion  of 
Uranvs.  —  The  planet  Uranus,  revolving  at  the  extreme  limits  of 
the  solar  system,  was  the  object  in  which  were  observed  those  dis- 
turbances which,  not  being  the  effects  of  the  action  of  any  of  the 
known  planets,  raised  the  question  of  the  possible  existence  of  another 
planet  exterior  to  it,  which  might  produce  them. 

After  the  discovery  of  the  planet  by  Sir  W.  Herschel,  in  1781, 
its  motions,  being  regularly  obser\'ed,  supplied  the  data  by  which  its 
elliptic  orbit  was  calculated,  and  the  disturbances  produced  upon  it 
by  the  masses  of  Jupiter  and  Saturn  ascertained ;  the  other  planets 
of  the  system,  by  reason  of  their  remoteness,  and  the  comparative 
minuteness  of  their  masses,  not  producing  any  sensible  effects. 
Tables  founded  on  these  results  were  computed,  and  ephemcridei 
constructed,  in  which  the  places  at  which  the  planet  ought  to  be 
found  from  day  to  day  for  the  future  were  duly  registered. 

The  same  kind  of  calculations  which  enabled  the  astronomer  thus 
to  predict  the  future  places  of  the  planet,  would,  as  is  evident, 
equally  enable  him  to  ascertain  the  places  which  had  been  occupied 
by  the  planet  in  times  past.  By  thus  examining,  retrospectively, 
the  apparent  course  of  the  planet  over  the  firmament,  and  comparing 
its  computed  placos  at  particular  epochs  with  those  of  stars  which 
had  been  o])sorvoJ,  and  which  had  subsequently  disappeared,  it  was 
ascertained  that  several  of  these  stars  had  iu  fact  been  Uranus  itself, 
whose  planetary  character  had  not  been  recognised  from  its  appear- 
ance, owing  to  the  imperfection  of  the  telescopes  then  in  use,  nor 
from  its  apparent  motion,  owing  to  the  observations  not  having  been 
sufficiently  continuous  and  multiplied. 

In  this  way  it  was  ascertained,  that  Uranus  had  been  observed, 
and  its  position  recorded  as  a  fixed  star,  six  times  by  Flamstead; 
viz.,  once  in  lOliO,  once  in  1712,  and  four  times  in  1715; — once 
by  Bradley  in  175'},  once  by  Mayer  in  175G,  and  twelve  times  by 
Lemonnier  botweon  1750  and  1771. 

Now  although  the  observed  positions  of  these  objects,  combined 
with  their  subsequent  disiippearancc,  left  no  doubt  whatever  of  their 
identity  with  the  planot,  their  observed  places  deviated  scnsiblj 
from  the  places  which  the  planet  ought  to  have  had  according  to 
the  coiiiputatiniis  foundod  upon  its  motions  after  its  discovery  in 
1781.  If  these  deviations  eould  have  been  shown  to  be  irregular 
and  governed  by  no  law,  they  would  be  ascribed  to  errors  of  obser- 
vation, if,  on  the  other  hand,  they  were  found  to  follow  a  regular 
course  of  increase  and  decrease  in  determinate  directions,  they  would 


THE  MAJOR  PLANETS.  395 

be  ascribed  to  the  agency  of  some  UDdiscovcrcd  disturbing  cause, 
irhoac  action  at  the  epochs  of  the  ancient  observations  was  different 
from  its  action  at  more  recent  periods. 

The  ancient  observations  were,  however,  too  limited  in  number 
and  too  di^^continuous  to  demonstrate  in  a  satisfactory  manner  the 
irregularity  or  the  regularity  of  the  deviation.  Nevertheless,  the 
circumstance  raised  much  doubt  and  misgiving  in  the  mind  of 
Bouvard,  by  whom  the  tables  of  Uranus,  based  upon  the  modem 
observations,  were  constructed ',  and  he  stated  that  he  would  leave 
to  futurity  the  decision  of  the  question  whether  these  deviations 
were  due  to  errors  of  observation,  or  to  an  undiscovered  disturbing 
agent.  We  shall  presently  be  enabled  to  appreciate  the  sagacity 
of  this  reserve. 

The  motions  of  the  planet  continued  to  be  assiduously  observed, 
and  were  found  to  be  in  accordance  with  the  tables  for  about  four- 
teen years  from  the  date  of  the  discovery  of  the  planet.  About  tho 
year  1795,  a  slight  discordance  between  the  tabular  and  observed 
places  began  to  be  manifested,  the  latter  being  a  little  in  advance 
of  the  former,  so  that  the  observed  longitude  L  of  the  planet  was 
greater  than  the  tabular  longitude  l'.  After  this,  from  year  to  year, 
the  advance  of  the  observed  upon  the  tabular  place  increased,  so 
that  the  excess  L  —  l'  of  the  observed  above  the  tabular  longitude 
vas  continually  augmented.  This  increase  of  L  —  i/  continued  until 
1^22,  when  it  became  stationary,  and  afterwards  began  to  decrease. 
This  decrease  continued  until  about  1830-31,  when  the  deviation 
L — l'  disappeared,  aud  the  tabular  and  observed  longitudes  again 
agreed.  This  accordance,  however,  did  not  long  prevail.  Tho 
phiuet  soon  began  to  fall  behind  its  tabular  place,  so  that  its  ob- 
served longitude  L,  which  before  1831  was  greater  than  tho  tabular 
longitude  l',  was  now  less ;  and  the  distance  l'  —  L  of  the  observed 
behind  the  tabular  place  increased  from  year  to  year,  and  still 
increases. 

It  appears,  therefore,  that  in  the  deviations  of  the  planet  from  its 
computed  place,  there  was  nothing  irregular  and  nothing  compatiblo 
with  the  suppo.sition  of  any  cause  depending  on  the  accidental 
emjrs  of  observation.  The  deviation,  on  the  contrary,  increased 
gradually  in  a  certain  direction  to  a  certain  point;  and  having 
attained  a  maximum,  then  began  to  decrease,  which  decrease  still 
continues. 

The  phenomena  must,  therefore,  be  ascribed  to  the  regular  agency 
of  some  undiscovered  di.sturbing  cause. 

125'85.  A  jjfanel  LxOirior  to  Cranus  tcouid  produce  a  like  effict. 

—  It  is  not  difficult  to  demon?jtratc  that  deviations  from  its  com- 

»     puted  place,  such  as  those  described  above,  would  be  produced  by  a 

I    phinct  revolving  in  an  orbit  having  the  same  or  nearly  the  same 

\   plane  ao  that  of  Unuiu?,  which  would  bo  in  heliocentric  conjunctiou 


896 


ASTBOSOICT. 


iritb  tbKt  planet  at  the  epoch  at  which  its  adranee  beyoDd  its  eoa- 

pated  place  attained  its  maximum. 

Let  &  B  c  D  E  F,  fig.  792,  repreaent  the  are  of  the  orUt  of  Unttm 

described  by  the  planet  doriog  the  manifestatiaa  of  the  peitcirbir 
tions.  Let  N  W  reprewnt  the 
orbit  of  the  supposed  vndiBov 
vered  planet  in  the  aaine  plin 
with  the  orhit  of  Uniniu.  Let 
a,  h,  c,  d,  t,  and/,  be  the  poei^oni 
of  the  latter  when  Uranns  is  it 
the  points  A,  B,  c,  d,  z,  and  r. 
It  is,  therefore,  sapposcd  th«t 
UraDUH  when  at  d  is  in  helio- 
centric conjunction  with  the  tnp- 
poaed  planet,  the  latter  being 
then  at  d. 

The  directions  of  the  orbital 
motions  of  the  two  planets  an 
indicated  by  the  orrowa  beside 
their  path^;  and  the  directiont 
of  the  disturbing  forces*  oier- 
plnnct  on  Uranus  arc  indicated  by  the  arrows 


Fig.  19!. 


cised  by  the  hi    _ 

bcxiitc  the  lines  joining  that  ptanet  with  Uranus. 

Now,  it  will  be  cjuiie  evident  that  the  attractifin  cserted  by  ibe 
Rupposi.>d  planet  at  u  on  Uranus  at  a  tends  to  accelL'tatc  the  IiiUer. 
lu  like  manner,  the  forces  exerted  by  the  supposed  pLinct  at  b  and 
c  upuu  Uranus  at  it  and  c  tend  to  accelerate  it.  Dut  as  Uracue 
approaches  to  D,  the  direction  of  the  disturbing  force,  being  less  Bod 
less  inclined  to  that  of  the  orbital  motion,  has  a  less  and  Icis  accele- 
rating influence,  and  on  arriving  at  D,  the  disturbing  force  being  in 
the  direction  n  il  at  right  angles  to  the  orbital  motion,  all  accelerating 
influence  censes. 

After  passing  D  the  disturbing  force  is  inclined  agninfl  the  mo- 
tion, otid  instead  of  accelerating  retards  it;  and  as  Uranus  takes 
Bueccssively  the  positions  e,  f,  &q.  it  is  more  and  more  inclined,  and 
its  retarding  influence  more  and  more  increased,  as  will  be  evidcw 
if  the  directions  of  the  retarding  force  and  the  orbital  motion,  as 
iodiealcd  by  the  arrows,  be  observed. 

It  is  then  apparent,  that  from  a  to  d  the  disturbing  force,  accele- 
rating the  orbital  motion,  will  traniifcr  Uranus  l«  a  position  in  ad- 
vance of  that  which  it  would  otherwise  have  occupied ;  and  after 
passing  D,  the  disturbing  furcc  retarding  ihe  planet's  motion  will 


the  HI 


•  To  B 


.lifv  llie  0 


.p!«n 


llie  effect  of  the 


of  rranut  on 
PerturbalioB! 
iuu  of  the  dititurbing  force  viil 


THE  MAJOR  PLANETS.  897 

oontinually  rednce  this  advance,  until  it  bring  back  tbe  planet  to  the 
place  it  would  have  oocopied  had  no  disturbing  force  acted ;  after 
which,  the  retardation  being  still  continued,  the  planet  will  fsAl  be- 
hind the  place  it  would  have  had  if  no  disturbing  force  had  acted 
npoQ  it. 

Now  it  is  evident  that  these  are  precisely  the  kind  of  disturbing 
fbrces  which  act  upon  Uranus ;  and  it  may,  therefore,  be  inferred 
that  the  deviations  of  that  planet  from  its  computed  place  are  the 
physical  indications  of  the  presence  of  a  planet  exterior  to  it,  moving 
m  an  orbit  whose  plane  either  coincides  with  that  of  its  own  orbit 
or  18  inclined  to  it  at  a  very  small  angle,  and  whose  mass  and  dis- 
tenoe  are  such  as  to  sive  to  its  attraction  tbe  degree  of  intensity  ne- 
oessaiT  to  produce  the  alternate  acceleration  and  retardation  which 
have  been  observed. 

Since,  however,  the  intensity  of  the  disturbing  force  depends 
eoDJointly  on  the  quantity  of  the  disturbing  mass  and  its  distance, 
it  is  easy  to  perceive  that  the  same  disturbance  may  ariso  from  dif- 
ferent masses,  provided  that  their  distances  are  so  varied  as  to  com- 
pensate for  their  different  weights  or  quantities  of  matter.  A  double 
mass  at  a  fourfold  distance  will  exert  precisely  the  same  attraction. 
The  question,  therefore,  under  this  point  of  view,  belongs  to  the 
class  of  indeterminate  problems,  and  admits  of  an  infinite  number 
of  solutions.  In  other  words,  an  unlimited  variety  of  different 
planets  may  be  assigned  exterior  to  the  system  which  would  cause 
disturbances  observed  in  the  motion  of  Uranus,  so  nearly  similar  to 
thoea  observed  as  to  be  distinguishable  from  them  only  by  observa- 
tions more  extended  and  elaborate  than  any  to  which  that  planet 
could  possibly  have  been  submitted  since  its  discovery. 

2886.  Raaearchcs  of  Mesxrt,  Le  Vcrricr  and  Adams. — The  idea 
of  taking  these  departures  of  the  observed  from  tbe  computed  place 
of  Uranus  as  the  data  for  the  solution  of  tbe  problem  to  ascertain 
the  position  and  motion  of  the  planet  which  could  cause  such  devi- 
ations, occurred,  nearly  at  the  same  time,  to  two  astronomers,  neither 
of  whom  at  that  time  had  attained  either  the  age  or  the  scientifio 
standing  which  would  have  raised  the  expectations  of  achieving  the 
most  astonishing  discovery  of  modern  times, 
r  M.  Le  Verrier,  in  Paris,  and  Mr.  J.  C.  Adams,  Fellow  and  As- 

[  liitant  Tutor  of  St.  John's  College,  Cambridge,  engaged  in  the  in- 
I  Testigation,  each  without  the  knowledge  of  what  the  other  was  doing, 
f  and  believing  that  he  stood  alone  in  bis  adventurous  and,  as  would 
I  then  have  appeared,  hopeless  attempt.  Nevertheless,  both  not  only 
I  lolTed  the  problem,  but  did  so  with  a  completeness  that  filled  the 
world  with  astonishment  and  admiration,  in  which  none  more  ar- 
^      dently  shared  than  those  who,  from  their  own  attainments,  were  best 

1^      qualified  to  appreciate  the  difficulties  of  the  question. 
The  question,  as  has  been  observed,  belonged  to  the  class  of  iu- 
III.  34 


898  ASTRONOMY. 

determinato  problems.  An  infinite  number  of  different  planets 
might  be  assigned  which  would  be  equally  capable  of  producing  the 
observed  disturbances.  The  solution,  therefore,  might  be  theoreti- 
callj  correct,  but  practically  unsuccc^ul.  To  strip  the  qnestion  as 
hr  as  possible  of  this  character,  certain  conditions  were  assumed, 
the  existence  of  which  might  be  regarded  as  in  the  highest  degree 
probable.  Thus,  it  was  assumed  that  the  disturbing  planet's  orbit 
was  in  or  nearly  in  the  plane  of  that  of  Uranus,  and  therefore  in 
that  of  the  ecliptic ;  that  its  motion  in  this  orbit  was  in  the  same 
direction  as  that  of  all  the  other  planets  of  the  system,  that  is,  ac- 
cording to  the  order  of  the  signs ;  that  the  orbit  was  an  ellipse  of 
very  small  eccentricity ;  and,  in  fine,  that  its  mean  distance  from 
the  sun  was,  in  accordance  with  the  general  progression  of  distances 
noticed  by  Bode,  nearly  double  the  mean  distance  of  Ur&nus.  This 
last  condition,  combined  with  the  harmonic  law,  gave  the  inquirer 
the  advantage  of  the  knowledge  of  the  period,  and  therefore  of  the 
mean  heliocentric  motion. 

Assuming  all  these  conditions  as  provisional  data,  the  problem 
was  reduced  to  the  determination,  at  least  as  a  first  approzimation, 
of  the  mass  of  the  planet  and  its  place  in  its  orbit  at  a  given  epoch, 
such  as  would  be  capable  of  producing  the  observed  alternate  acoe- 
leratiou  and  retardation  of  Uranus. 

The  determination  of  the  heliocentric  place  of  the  planet  at  a 
given  epoch  would  have  bceu  materially  facilitated  if  the  exact  time 
at  which  the  amount  of  the  advance  (l  —  l')  of  the  observed  upon 
the  tabular  place  of  the  planet  had  att;iined  its  niaximnm  were 
known ;  but  this,  unfortunately,  did  not  admit  of  being  aacertained 
with  the  necessary  precision.  When  a  varying  quantity  atttioi  hs 
maximum  i>tato,  and,  after  increasing,  begins  to  diminish,  it  ii  ita- 
tionary  for  a  hhort  interval ;  and  it  is  always  a  matter  of  difficulty, 
and  often  of  much  uncertainty,  to  determine  the  exact  moment  it 
which  the  increases  ceases  and  the  decrease  eommeuees.  Allhoqgh, 
therefore,  the  lid iocen trie  place  of  the  disturbing  planet  ooaM  be 
nearly  assigned  about  18*J'2,  it  could  not  be  determined  with  the 
desired  precision. 

Assuming,  however,  as  nearly  as  was  practicable,  the  longitode 
of  Uranus  at  the  moment  of  heliocentric  conjunction  with  the  dis- 
turbing ])lanet,  this,  combined  with  the  mean  motion  of  the  sought 
planet,  inferred  from  its  ptTiod,  would  give  a  rough  approzimation 
to  its  place  for  any  given  time. 

i!^<.S7.  hy<))i(tifs  of  flu:  iniinjlit  phi  lift  asjit't/nof  In/  tluM  fffomHtr*. 
—  Hough  aji[)r()ximatit»ns  were  not,  liowevor,  what  MM.  Le  Verrier 
and  Adams  sou-iht.  They  aimed  at  more  exact  results  j  and,  after 
invefetigations  involving  all  the  resources  and  exhausting  all  theva^t 
powers  of  analysis,  these  eminent  geometers  arrived  at  the  following 
elements  of  the  un<liseovered  planet:  — 


THB  HAJOR  PLANETS. 


VSi 


loDfllail*  ti  lb*  cpocb 


HHP  11' 


2888.  lU  actual  ijiteovery  by  Dr.  Galle  of  Berlin.  — Oa  the 
SSrd  of  September,  1846,  Dr.  Gnlle,  one  of  tbo  utronomera  of  the 
Bojel  Oberarator;  st  Berlin,  received  &  letter  from  M.  he  Verrier, 
snnoniKUDg  to  him  the  principal  results  of  bis  calcnlaCioDB,  iDforni- 
iDg  him  that  tbo  longitude  of  the  soaght  planet  must  then  be  326°, 
tad  reqnestiog  bim  t«  look  for  it.  Dr.  Galle,  assisted  bj  Professor 
Enck^,  accordiDglj  did  "look  for  it,"  nnd  found  it  that  vcrj  night 
It  appeared  aa  a  star  of  the  8tb  magnitude,  having  the  longitude 
of  326°  52',  and  coosequentlj  only  52'  from  the  place  asaigned  b; 
H.  Le  Verrier.  The  colculationa  of  Mr.  Adami;,  reduced  to  the 
ane  date,  gave  for  its  place  329°  19',  being  2°  27'  from  the  place 
■bere  it  wu  utnally  found. 

2889.  Itt  predicted  and  observed  plnret  in  near  proximify.  — 

I  To  obwrve  the  relative  proximitj  of  these  re- 
markable predictions  to  the  actual  obserred  place, 
let  the  are  of  the  ecliptic,  from  long.  323°  to 
long.  330",  he  represented  in  Jj<f.  793.  The  place 
aaaigned  bj  M.  Le  Verrier  for  ihc  sought  planet 
ia  indicated  by  the  small  circle  at  l,  that  assigned 
l^  Air.  Adams  bj  the  small  circle  at  A,  and  the 
place  at  which  it  irss  aclunl!;  found  bj  the  dot 
at  N.  The  distances  of  L  and  A  from  N  may  be 
appredated  by  the  circle  which  is  described  around 
the  dot  N,  and  which  represcnta  the  apparent  disk 
of  the  moon. 
The  distance  of  the  observed  place  of  the 
planet  from  the  place  predicted  h;  H,  Le  Verrier 
Vas  less  than  tvo  diuriiclcni,  and  from  that  pre- 
dicted bj  Mr.  Adams  kss  tbau  five  diameters,  of 
the  lunar  disk. 
2890.  Correelrd  ehmriiU  of  the  ylantt*  orlil. 
—  In  obtaining  the  clemuTits  given  above,  Mr. 
Adams  based  bis  calculalidnn  on  the  observations 
of  Uranus  made  up  to  IK  Ul,  wbilu  (he  calculations 
of  M.  JjO  Verrier  w(t«  fmindrd  im  observations 
continued  to  1845.  Uii  r^ubscijucuily  taking  into 
Tig-  TVS.  computation   the  five   years    ending  1845,   M.T. 


400 


ASTRONOMY. 


Adams  concluded  that  the  mean  distance  of  the  soaght  planet  would 
be  more  exactly  taken  at  33*33. 

After  the  planet  had  heen  actually  discovered,  and  obeervations 
of  sufficient  contiuuance  were  made  upon  ity  the  following  proved  to 
be  its  more  exact  elements  : — 


*,««. 

EiMcli  of  t)M  el(>meiitll  ~ 

1  Jan.  1847,  M.  Noon. 
<H)08n04& 

laoo  4#   90"'a. 

lM-6181  jwmn. 

Mean  lonptade  of  epochs 

Mean  diiiUnoe  from  san  ~ 

EeoMitriritr  of  orbit  - 

LoncritDdts  of  Dcrih<*lioii  ••••••  •• « •.••••••••• 

Inclin&tioii  of  ^rbit • 

Periodic  tiniA  ..« •••• 

Mfmn  Annual  notion  ••..*.>....tt.*««.-ftf«-»-«T->r«'— -«? 

2891.  Discrepancies  f/ctween  the  actual  and  predicted  elementi 
explained. — Now  it  will  not  fail  to  strike  every  one  who  devotea  the 
least  attention  to  this  interesting  question,  that  oonnderable  discrep- 
ancies exist,  not  only  between  the  elements  preaeDted  in  the  two 
proposed  solutions  of  this  problem,  but  between  the  actml  elements 
of  the  discovered  planet  and  both  of  these  solutions.  There  were 
not  wanting  some  who,  viewing  these  discordances,  did  not  hesitate 
to  declare  that  the  discovery  of  the  planet  was  the  result  of  chance, 
and  not,  as  was  claimed,  of  mathematical  reasoning,  since,  in  fact, 
the  planet  discovered  was  not  identical  with  either  of  the  two  planets 
predicted. 

To  draw  such  a  conclusion  from  such  premises,  however,  betrays 
a  total  misapprehension  of  the  nature  and  conditions  of  the  problem. 
If  the  problem  had  been  determinate,  and,  conscquentlj,  one  which 
admits  of  but  one  solution,  then  it  must  have  been  inferred,  either 
that  some  error  had  been  committed  in  the  calculations  which  caused 
the  discordance  between  the  observed  and  computed  elements,  or 
that  the  discovered  planet  was  not  that  which  was  sought,  and  which 
was  the  physical  cause  of  the  observed  disturbances  of  Uranus.  But 
the  problem,  as  has  been  already  explained,  being  more  or  less  inde- 
terminate, admits  of  more  than  one,  —  nay,  of  an  indefinite  number 
of  different  solutions^,  so  that  many  different  planets  might  be  assigned 
which  would  equally  produce  the  disturbances  which  had  been  ob- 
served; and  this  being  so,  the  discordance  between  the  two  sets  of 
predicted  elements,  and  between  both  of  them  and  the  actual  ele- 
ments, are  nothing  more  than  might  have  been  anticipated,  and 
which,  except  by  a  chance  against  which  the  probabilities  were 
millions  to  one,  were,  in  fact,  inevitable. 

So  far  as  depended  on  reasoning,  the  prediction  was  verified;  go 
far  as  depended  on  chance,  it  failed.  Two  planets  were  assigned, 
both  of  which  lay  within  the  limits  which  fulfilled  the  conditions  of 


THB  MAJOR  PLAKETS. 


401 


the  problem.  Both,  boirever,  differed  from  tlie'tme  placet  in  par- 
ticulan  which  did  not  affect  the  conditiona  of  the  problem.  All 
three  were  circuniBcribcd  within  those  licuite,  aud  subject  to  sncb 
condidona  as  would  make  them  produce  those  deTiutions  or  diatarb- 
•Koes  which  were  observed  ia  the  motiona  of  Uronoa,  and  which 
formed  the  immediate  subject  of  the  problem. 

2892.  Compariion  o/tht  rfferit  o/ tie  real  anii preciirled planelt. 
—  It  may  be  satisfactory  to  render  this  Still  more  clear,  bj  eihihiting 
ia  immediate  juxtaposition  the  motions  of  the  hypothetical  planeU 
vt  SIM.  Lc  Verrier  and  Adams  and  the  planet  actually  discovered, 
■0  as  to  make  it  apparent  that  any  one  of  the  three,  under  the  Bup- 
poaed  condidons,  would  produce  the  observed  disturbances.  Wa 
b»*e  accordingly  attempted  this  in  Jig.  794,  where  the  orbita  of 


Fig.  70*. 

Cniiii%  of  Neptune,  and  of  the  planets  assigned  b;  MM.  Le  Verrier 
ud  Aifaun*  are  laid  down,  with  the  positions  of  the  planets  reapeo- 
tirelj  in  them  for  every  fifth  year,  from  IROO  to  1845  inclusively. 
This  plan  U,  of  course,  only  roughly  made ;  but  it  is  sufficiently 
tact  for  the  purposes  of  the  present  illustration.  The  places  Ol 
Unnna  are  marked  by  O,  those  of  Neptune  by  O,  those  of  M.  La 
Tenier'a  pUnet  by  6,  and  those  of  Mr.  Adama'a  planet  by  (B- 
34* 


It  wm  be  oliMmd  that  the  diBkaoM  of  Ihft  tm  BlnUi  M^^ 
Iv  HH.  lie  Terrier  and  Aduna,  n  lakt  dova  &  fte  fii^rsBf 
mfer  leas  tnm  the  diitnioe  of  Um  planat  Neptaaa  A^  &•  ■«■ 


dialBBoeB  given  in  their  eleraeoli  difir  from  Um  maia  dWaaoB  of 
NeptatM.  This  ii  ex^ained  bj  the  egaaBtaWtiaa  at  dia  aM, 
whieh,  in  the  elements  of  both  aatneomei!^  an  wBadwiM^  bdag 
Marly  an  eighth  in  one  aad  a  mnth  la  tba  other,  and  b^  A»  jtm- 
tfcma  of  the  snpposed  planeta  in  their  leapeedTe  orbito. 

If  the  msMea  of  the  three  planeta  mre  ecpiaL  it  ia  da«  that  the 
attraetion  with  which  Le  Terner*!  planet  wenld  aet  upon  ITm^ 
would  be  len  than  that  of  the  true  phoe^  and  that  of  AdiaA 
planet  still  more  so,  each  bnng  lees  in  the  aanw  ralfe  la  Urn  mpmu 
at  ita  diatanoe  from  Ufsnna  ia  mater  thai  -that  rf  Japliaii,  Bt 
if  the  pbuMtB  are  ao  a4jnBted  that  what  i^flUHBH^^^H 
br  die  mater  mawa,  this  will  ba  titSSSB^K^^t^M 
punet  inU  exert  the  bmbc  tfstaitfag  fine  u  the  actual  idaad^as 
nr  as  lelidea  to  the  efleota  of  faiiatioa  of  diataocG.  Ii  ia  true  that, 
throngfaoot  the  arse  of  tbe  ottnta  over  vhii>h  the  Db»erv&tioiia  ei- 


are  not  eveiy  where  in  enetlj  the  mmt  ratio,  white  their  mama 
miut  neceuarilj  be  so ;  ami,  dierefbre,  (he  relative  masses,  whieh 
would  produce  perfect  oompenaatioQ  in  one  positioa,  would  not  do 
BO  in  others.  Thb  cause  of  diaorepanaj  would  operate,  howersr, 
under  the  sotoal  conditions  of  the  problem,  ia  a  degree  altogether 
incooaiderable,  if  not  iosenaible. 

But  another  cause  of  differeoce  in  the  disturbing  aclJoD  of  the 
real  and  supposed  planets  would  arise  from  the  fact  that  the  direfr' 
tioDS  of  tbe  disturbing  forces  of  all  the  tliree  pkncts  are  difiereaL 
as  will  bo  apparent  on  iospectiDg  the  figure,  in  which  the  degna  of 
divergeDce  of  these  forces  at  each  positioa  of  the  plviots  u  tndi- 
oated;  but  it  will  be  also  sppareet  that  iliis  divergence  is  ao  Tsrf 
inconsiderable,  that  its  e^ot  most  be  quite  insensiblo  in  all  pac- 
tions in  whieh  Urantu  can  be  senoosljr  affected.  Thus,  from  wW 
to  1815,  the  divergenoe  is  very  small.  It  iuLTcoses  from  1818  to 
1836  ;  bat  it  is  precisely  here,  near  the  epoch  of  hcliocentrie  eoa- 
JQOction,  which  took  place  in  1822,  that  all  the  tijrce  planets  csnb 
to  have  any  direct  effect  in  accelerating  the  molion  of  UnavL 
When  the  latter  planet  passes  this  point  sufticiontly  to  be  sensb^ 
retarded  bj  tbe  disturbing  action,  as  is  ttie  can:  after  1839,  Ihl 
divergence  again  beconies  inconsiderable. 

From  these  considerations  it  will  therefore  be  undr^rstood,  tbt 
the  distarl>ances  of  the  motions  of  Uranus,  fo  fur  aa  these  mrs 
ascertained  bj  observation,  would  be  prrduccd  witlinut  sensible 
difference,  ei^er  by  tbe  actual  planet  whicti  bas  been  discovered, or 
by  either  of  the  planets  assigned  bj  MM.  Le  Verrier  and  Adaa^ 
W  either  b;  an  indefinite  number  of  others  which  might  be 


TBB  HAJOB  PLAHITS.  408 

eilLer  within  the  path  of  Neptune,  or  between  it  and  thatof  Adame'i 
^aaet,  nr,  in  fine,  beyond  thia  —  within  certain  assignable  limiti. 

2893.  JVo  part  of  the  merit  of  thit  ditcooay  cucribahle  to  chance. 

— That  tlte  planets  tswgned  bj  MM.  La  Verrier  and  Adams  are 

not  identical  with  the  pUnet  to  the  diacorerj  of  which  thnr  re- 

■orches  hare  condnoted  pnotioal  obserrers  is,  therefore,  tmo ;  but 

it  ia  also  tnia  that,  if  they  or  either  of  them  had  been  identical 

mlh  ■^  nieh  eaaeaara  amonat  of  agreement  wonld  hare  been  pntely 

aeddentalf  and  not  at  all  the  reault  of  the  wgaoitj  of  the  mathe- 

aatioan.     All  that  human  ngaoitj  conid  do  with  the  data  pre- 

MilUiil  bj  obMivatioa  was  done.     Among  an  indefinite  number  of 

"*      '      'i  capable  of  prodocing  the  disturbing  action,  two 

,  both  of  which  were,  for  all  the  purposes  of  the  in- 

qniry,  10  nearly  coincident  with  the  real  planet  as 

^■j^^H  ilMTitabljr  and  immediately  to  lead  to  its  discovery. 

^^^^^1       2894.  Period.  —  After  a  complete  rerolntion  of 

^^^^^R  the  earth,  Neptune  is  found  to  advance  in  its  course  no 

^^^^^H  more  than  2°'187,  and  consequently  its  period  ia  — 

^^^^^H  or,  more  exactly,  164-618  years. 

^^^^^1       2895.  Dittance. — Its  mean  distance  B,  therefiire, 

^^^^^1  may  be  determined  by  the  barmonie  law : 

^^^1  B*  =  (164-6)'  =^  27093  =  (3004/. 

^^^^^H       2896.  Sdative  orbili  and  ditlanca  of  Ntptune  and 

^^^^^M  Ae  earth.  —  It  ippeare,  then,  in  fine,  that  the  system 

^^^^^1  poMeasea  another  member  still  more  remote  from  the 

^^^^^H  common  centre  of  light,  heat,  and  attraction.     In  Jiff. 

^^^^^H  795,  the  earth's  orbit  is  represented  at  ££'";  and  a 

^^^^^1  part  of  that  of  Neptune,  on  the  same  scale,  ia  repre- 

^^^^^1  lented  at  «.    The  actual  distance  of  N  from  8  is  thirty 

^^^^^H   times  that  of  K  from  B. 

^^^^^H       The  mean  distance  of  Neptune  from  the  sun  is, 

^^^^^H  therefore, 

^^^^1  2,850,000,000  miles. 

^^^^^1       2897.  Apparent  and  real  diameter.  —  The  appa- 

^^^^^1  lent  diameter  of  the  planet,  seen  when  in  opposition, 

^^^^^H  ia  about  2"'8.    Its  distance  from  the  earth  being  then, 

^^^^1  2850  —  95  =  2765  mill,  miles, 

^^^^^1  and  the  linear  ralue  of  1"  at  this  distance  being 

™^      .  2755000000  _ 


404  ASTROKOMT. 

the  actual  diameter  of  the  planet  iviU  be 

13313  X  2-8  =  37,276  miles. 

The  diameter  of  the  planet  is,  therefore,  a  little  mater  than  that 
of  Uranus,  about  half  that  of  Satam,  and  about  fonr  and  a  half 
times  that  of  the  earth. 

According  to  Mr.  Hind,  the  apparent  diameter  ia  onlj  2-6,  and 
the  real  diameter  31,000  miles;  numbers  which,  he  sajs,  are  de> 
duced  from  careful  measurements  with  some  of  the  most  powerful 
European  telescopes. 

2898.  SateUite  of  Neptune,  —  A  satellite  of  this  planet  was  dis- 
covered by  Mr.  Lassell  in  October,  1846,  and  was  afterwards  ob> 
served  by  other  astronomers  both  in  Europe  and  the  United  States. 
The  first  observations  then  made  raised  some  suspicions  as  to  the 
presence  of  another  satellite  as  well  as  of  a  ring  analogous  to  that 
of  Saturn.  Notwithstanding  the  numerous  observers,  and  the  pow- 
erful instruments  which  have  been  directed  to  the  planet  raifla  the 
date  of  these  observations,  nothing  has  been  detected  which  has  had 
any  tendency  to  confirm  these  suspicions. 

The  existence  of  the  satellite  first  seen  by  Mr.  Lassell  has^  how- 
ever, not  only  been  fully  established,  but  its  motion,  and  the 
elements  of  its  orbit,  have  been  ascertaiDcd,  first  by  the  observations 
of  M.  0.  Struve  iu  Sept.  and  Dec.  1847,  and  later  and  more  fully 
by  those  of  his  late  relative  M.  Auguste  Struve,  in  1848—9. 

From  these  observations  it  appears  that  the  distance  of  the 
satellite  from  the  planet  at  its  greatest  elongation  subtends  an  angle 
of  18"  at  the  sun ;  and  since  the  diameter  of  the  planet  subtends 
an  angle  of  2-8  at  the  same  distance,  it  follows,  therefore,  that  the 
distance  of  the  satellite  from  the  centre  of  the  planet  is  equal  to 
fourteen  semidiameters  of  the  latter. 

The  mean  daily  angular  motion  of  the  satellite  round  the  centre 
of  the  planet  i»,  according  to  the  observations  of  Struve,  61** -2625, 
and  consequently  the  period  of  the  satellite  is 

-— — rT=-  =  5-8703  days, 

or  5**  2P-  l-S"'-,  a  result  which  is  subject  to  an  error  not  exoeediog 
5  minutes. 

If  the  somidiameter  of  the  planet  be  18,750  miles,  the  actual 
distance  of  the  satellite  is 

18,750  X  12  =  225,000  miles, 

being  a  Utile  less  than  the  disUince  of  the  moon  from  the  earth's 
centre. 

2800.  Mais  and  density.  —  This  discovery  of  a  satellite  has 
supplied  the  means  of  determining  the  mass,  and   therefore  the 


THE  MAJOR  PLANETS. 


405 


denatj,  of  the  planet.  M.  Strnvey  calcalatiDg  by  the  priDdpIeir 
ahreadj  explain^,  has  found  that  the  mass  of  Neptune  is  the 
14y446tli  part  of  the  mass  of  the  sun ;  and  since  its  diameter  is 
aboat  the  20th,  and  its  Yolame  the  8000th,  part  of  that  of  the  sun, 
its  density  will  be  about  five-ninths  that  of  the  sun,  and  about  the 
seventh  part  of  the  density  of  the  earth. 

Other  estimates  make  the  mass  less.  According  to  Professor 
BoDd  it  is  the  19,400th,  and  according  to  Mr.  Hind  the  17,900thy 
of  the  mass  of  the  snn« 

2900.  Ajppartnt  magnitudt  of  the  sun  at  Neptune,  —  The  appa- 
nnt  diameter  of  the  sun,  as  seen  from  Neptune,  being  30  times  less 
than  from  the  earth,  is, 

80         ^ 

ne  rail,  therefoK,  appttn  of  the  same  magnilnde  as  Venus  seen 
iS  a  momiDg  or  evening  star. 

The  relative  apparent  magnitudes  are  exhibited  mfg.  796,  at  s 
ladH. 


It  would,  however,  be  a  great  mistake  to  infer  that  the  light  of 
the  Mil  at  Neptune  approaches  in  any  degree  to  the  faintness  of 
that  of  Yenus  at  the  earth.  If  Venus,  when  that  planet  appears 
as  a  Borning  or  evening  star,  with  the  apparent  diameter  of  60", 
m  a  loll  disk  (instead  of  one  halved  or  nearly  so,  like  the  moon 
at  the  quarters),  and  if  the  actual  intensity  of  light  on  its  surface 
were  equal  to  that  on  the  sur&ce  of  the  sun,  the  light  of  the  planet 
wooM  be  exactly  that  of  the  sun  at  Neptune.  But  the  intensity 
flf  the  light  which  falls  on  Venus  is  less  than  the  intensity  of  the 
Gght  oa  the  sun's  surfiuse  in  the  ratio  of  the  square  of  Venus'  dis- 
tance to  that  of  the  sun's  semidiametcr,  upon  the  8upf08\\iou  ^:a.V 


Ae  Hglit  ia  propagated  ataoriing  to  Ae  mm  k*  w  if  il  IhosI  ftm 
ik»  niii'a  oentre;  that  i>,  aa  the  aqoan  of  87  mUBoaa  to  th*  mpnt 
of  half  a  million  nearly,  or  aa  87*:};  that  it,  H  HT6  to  L  ^ 
therefore,  the  mrboB  of  Tenos  idbettd  (whidi  h  doM  mat)  aH  Ao 
E^t  inndoit  npon  it,  ita  appaimt  light  at  tfw  aaitt  (aattUtriag 
that  little  more  than  half  ita  iUnminated  iwAae  ii  naa)  k  IM 
lljOOO  timea  len  than  the  light  rf  the  nm  at  Meotne. 

Small,  therefore,  aa  ia  the  anpaimt  nagnltode  a  the  ■■■  at  Ni^ 
tue,  the  intenn^  of  ita  daylight  ia  piobablj  BOt  lav  iImb  Ail 
whieh  woold  be  prodnoed  hj  aboat  20,000  atan  Afaring  at  maa  k 
tho  firmament  eaeh  being  equal  ia  apleadonr  to  Veua  whim  ttri 
planet  ia  brighteat 

In  adididon  to  th«ae  eonaideration^  it  mut  not  be  tot; 
all  auch  eatimatea  of  the  oomperatiTe  efiidencj  of  the  3 
and  heating  power  of  the  ana  ia  based  npcm  the  aiqyoMtw  Art  km 
li^t  is  reoeived  nnder  like  phTrieal  eonmtiont;  ano  Aat  aaaf  4» 
eeiTable  modifications  in  the  pbjnoal  slate  of  Ae  bodj  or  ■adMl 
m  or  into  which  the  li^t  Ma,  and  in  the  atanatnre  of  Aa  iknl 
organs  which  it  affeota,  may  render  light  of  aa  extranely  ftobk  la- 
tensity  as  efficient  as  much  stronger  light  ia  fimnd  to  be  tinder  oAw 
cooditioQg. 

2901.  Sugpeeted  rinff  of  Jieptune.  —  Heaars.  I^asell  and  Challia 
b&ye  at  timea  imacincd  that  jadicstiong  of  some  anch  append^ 
as  B  ring,  seen  nea^y  edgewise,  were  percepiibk  upon  the  disk  of 
NeptuDc.  These  conjectures  have  not  yet  reouTed  any  coDfima- 
tion.  When  the  declination  of  the  plaoet  will  have  so  fiir  iaaeMsd 
as  to  present  the  riog,  if  SQcb  an  appendage  ba  really  attached  to 
the  placet,  at  a  less  oblique  angle  to  the  ntatl  ny,  Ae  qnestioo 
will  probably  be  decided. 


TBANBIT8,   AMD  OOOltLTATIOITa 


2902.  InUrpotUion  of  (xUitial  objectt.  — The  objeota  whiefa  it 
nch  oonntless  numbers  are  scattered  orer  the  firmament  hetag  it 
distances  and  in  positions  infinitely  various,  and  many  of  tbem  beng 
in  motion,  eo  that  the  directions  of  lines  drawn  from  one  to  anolhtf 
are  constantly  varying,  it  must  ocoBMonally  bappen  that  Aree  will 
come  into  the  same  tine,  or  nearly  so.  ouch  a  oonttngency  pro* 
duces  a  class  of  occBsional  sBtronomicsl  phenoioena  whidi  ate  iv' 
TCated  with  a  high  popular  aa  well  as  a  profound  acioitifie  interesL 
The  nreneia  vith  iihioti  some  of  them  are  presented,  th^  widdm 


BCLIPSK8»  TRANSITS,  AND  OCGULTATIONS.  407 

and,  to  the  Tolgar  massi  VDezpected  appearance,  and  the  singalar 
phenomena  which  often  attend  them,  strike  the  popular  mind  with 
awe  and  terror.  To  the  astronomer,  geographer,  and  navigator,  thej 
mfaserve  important  uses,  among  which  the  determination  of  terres- 
trial longitudes,  the  more  ezaot  estimation  of  the  sun's  distance 
from  the  earth  (which  is  the  standard  and  modulus  of  all  distances 
in  the  celestial  spaces),  and,  in  fine,  the  discovery  of  the  mohility 
of  light,  and  the  measure  of  its  velocity,  hold  foremost  places. 

When  one  of  the  extremes  of  the  series  of  the  three  bodies 
which  thoa  assume  a  common  direction  is  the  sun,  the  intermediate 
body  deprives  the  other  extreme  body,  either  wholly  or  partially,  of 
the  illumination  which  it  habitually  receives.  When  one  of  the 
extremes  is  the  earth,  the  interme<Uate  body  intercepts,  wholly  or 
paitiallj,  the  other  extreme  body  from  the  view  of  observers  situate 
at  places  on  the  earth  which  are  in  the  common  line  of  direction, 
and  the  intermediate  body  is  seen  to  pass  across  the  other  extreme 
body  as  it  enters  upon  and  leaves  the  common  lioe  of  direction. 
Hm  phenomena  resulting  from  such  coDtingencies  of  position  and 
direetion  are  variously  denominated  eclipses,  transits,  and  oc- 
0CLTATION8,  according  to  the  relative  apparent  magnitudes  of  the 
interposing  and  obscured  bodies,  and  according  to  the  circumstances 
which  attend  them. 

2908.  General  conditions  which  determine  the  phenomena  of  in- 
UrftmUiim  when  one  of  the  extreme  objects  is  the  earth,  —  If  the 

interposing  and  intercepted  objects  have  disks  of 
sensible  magnitude,  the  effects  attending  their  in- 
terposition will  depend  on  the  magnitude  of  the 
^^„^^       diameters  of  their  disks  and  the  apparent  distance 
^^fm]  B    between  their  centres, 
^^^s^^  Let  D  express  the  apparent  distance  between 

^ ,        the  centres  of  the  two  disks.     Let  r  be  the  semi- 

^^  •]€    diameter  of  the  nearer,  and  r^  that  of  the  more 
^W*^^      distant  disk. 

2904.  Condition  of  no  interposition,  —  If  D 
be  greater  than  r  -f  ^y  as  represented  at  A,  fig. 
797,  the  disks  must  be  entirely  outside  each  other, 
and  oonsequentiy  no  interposition  can  take  place. 
The  nearest  points  of  the  edges  of  the  disks  are, 
in  this  case,  at  a  distance  equal  to  the  difference 
between  d  and  r  -f  f',  that  is,  d  —  ^r  -f  f'). 

External  contact, — If  D  =  r  -f  r ,  as  at  B,  the 
disks  will  touch  without  interposition.  This  is 
called  the  position  of  external  contact. 

2905.  Partial  interpotifion, — If  d  be  less  than 
r+f',  the  nearer  disk  will  be  partially  interposed, 

9^  797.         as  at  0.     In  this  case,  the  greatest  breadth  of 


o 


Oa  oliMsrad  put  of  tlie  awn  nmoto  dkk  ii  (r  +  O— 0.    It  b 
vtUmt  that  the  Imb  (be  dutanea  V  Ii^  ths  ptain  «fll  !>•  flk  ' 
Imkdth,  and  the  greater  the  part  obmiTad. 

-  iSW.  Internal  coiUaa  0/ inttipa&H^  dut. — K  «ha  faitwpoM^  ■ 
diak  be  len  than  the  mora  diatan^  h  will  radoaa  tht  httar  to  s 
flrcMent,  the  pcnnta  of  tlie  honM  at  which  nwet,  u  umiiaitail  at 
S,  when  0  =  / — r,  that  ia,  when  the  dirtanoa  betwaan  the  oantoai 
ia  eqnal  to  the  difleranoe  of  the  apparent  aami-diamelera. 

2907.  Oenfrical  inlerpotitiom  of  hntr  diit. — If  is  tha  mm 
ease  the  oentrea  coincide,  ae  at  s,  the  neafer  diak,  DOTaring  all  dw 
oentnl  portion  ot  the  more  distant,  will  leava  niwoTOad  arawad  it  a 
i^olar  ring  or  annalna  of  riaible  anrftee^Hha  bnadth  ti  lAieh  ^H 
be  the  difference  r  —  r'  of  the  aeni-diaineten. 

2908.  Complete  i»terp<mti(m.—I[  the  nearer  diak  ba  paatar  ^ 
the  more  remote,  and  the  diatanoe  i>  between  tha  eeatoaa  ba  aot 
greater  than  r — i',  the  difference  of  the  iMimi  iliai»al<iia,  tha  Bon 
remote  diik  will  be  oompleteljr  oorered,  and  will  oontinoe  aajntil 
the  eentrei  separate  to  a  greater  diatanoe  than  r — f',  aa  rapmaalil 
at  rand  o, 

L    SoLUt  ECUPSEB. 

2909.  The  case  of  the  sun  and  moon  presents  all  these  miov 
appeanincea.     The  disks,  though  nearly  equal,  are  each  sobject  to 

a  variation  of  magnitude  coofined  within  certain  narrow  limits,  as  ' 
hsa  been  already  cxpUined ;  and,  in  ooii«equance,  the  disk  of  tbe 
moon  is  eometimea  a  little  greater,  and  sometimes  a  little  lesa^  than 
that  of  the  BUD.  Their  centres  move,  as  has  been  explained,  in  two 
apparent  circles  on  the  firmament;  that  of  the  snn  in  the  ecliptis, 
and  that  of  the  moon  in  a  circle  inclined  to  the  eeliptio  at  a  small 
angle  of  about  5°.  These  circles  intersect  at  two  opposite  pnnti  of 
tbe  finnament,  called  the  moan's  nodes  (2473).  In  consequenee  of 
the  very  small  obliquity  of  the  moon's  orbit  to  the  ecliptia,  the  diS' 
tance  between  these  paths,  even  at  a  considerable  distance  at  eitber 
side  of  tbe  node,  is  necessarily  Small.  Now,  since  the  centres  of 
the  disks  of  the  sun  and  moon  must  each  of  them  pass  once  in  eKh 
revolutioD  through  each  node,  it  will  ncoeasarilj  happen  &Din  tisH 
to  time  that  they  will  be  both  at  the  same  moment  either  at  the 
node  itself,  or  at  some  points  of  their  respeetiTe  paths  tm  nrar  i^ 
that  their  apparent  distance  asunder  will  be  less  than  lite  Hom  if 
their  apparent  semi-diameters,  and  either  total  or  parti.!!  interps- 
ntion  must  take  place,  according  to  the  relative  magnitudes  of  ihor 
disks,  and  to  tbe  distance  between  the  points  of  their  respcetiTa 
paths  at  which  their  centres  are  simultaneously  fonud. 

2910.  Partial  m/iir  fclipse.  —  If  the  apparent  distanea  d  betwtea 
their  centres  be  less  than  the  sum  (r  +  r*;,  but  greater  thaa  tb 
difference  (r  —  r')  of  their  apparent  eemi-diameters,  a  partkl  iiila> 


SCLIPSEEf,  TBAN8IT8,  AND  0CCULTATI0K8.  409 

position  will  take  place  (2905).  The  greatest  breadth  of  the  ob- 
aeured  parts  of  the  solar  disk  will  in  this  case  be  equal  to  the  dif- 
feieooe  between  the  sum  of  the  apparent  semi-diametera  and  the 
distance  between  the  centres  of  the  two  disks^  that  is,  (r  -f  O  —  ^- 

2911.  Magnitude  of  eclipses  expressed  by  digits.  —  If  the  ap- 
parent diameter  of  the  obscured  object  be  supposed  to  be  divided  into 
twelve  equal  parts,  each  of  these  parts  in  reference  to  eclipses  is 
called  a  Diorr,  and  the  magnitude  of  an  eclipse  is  expressed  by  the 
number  of  digits  contained  in  the  greatest  breadth  of  the  obscured 
part  of  the  di£.  Thus  the  magnitude  of  the  eclipse  will  be  found  by 

dividing  r  +  /  —  d  by  j^  or  by  -g-. 

2912.  Total  solar  eclipse. —  To  produce  a  total  solar  eclipse,  it  is 
neoessaij,  1st,  that  the  apparent  diameter  of  the  moon  should  be 
equal  to  or  greater  than  that  of  the  sun,  and  2dly,  that  the  apparent 
plaoes  of  their  centres  should  approach  each  other  within  a  distance 
not  greater  than  /  —  r,  the  difference  of  their  apparent  semi- 
diameters.  When  these  conditions  are  fulfilled,  and  so  long  as 
they  continue  to  be  fulfilled,  the  eclipse  will  be  total  (2908). 

The  greatest  value  of  the  apparent  semi-diameter  of  the  moon 
being  1006",  and  the  least  value  of  that  of  the  sun  being  945'',  we 
shall  hftve 

t^  —  r=  61". 

The  greatest  possible  duration,  therefore,  of  a  total  solar  eclipse  will 
be  the  time  necessary  for  the  centre  of  the  moon  to  gain  upon  that 
of  the  son  61"  x  2  =  122".  But  since  the  mean  synodic  motion 
of  the  moon  is  at  the  rate  of  30"  per  minute,  it  follows  that  the 
dontioa  of  a  total  solar  eclipse  can  never  exceed  four  minutes. 

2918.  Annular  eclipses.  —  When  the  apparent  diameter  of  the 
DOOD  is  less  than  that  of  the  sun,  its  disk  will  not  cover  that  of  the 
HID,  even  when  concentrical  with  it.  In  this  case,  a  ring  of  light  would 
be  apparent  round  the  dark  disk  of  the  moon,  the  breadth  of  which 
woald  be  equal  to  the  difference  of  the  apparent  semi-diameters,  as 
represented  at  e,  Jig.  792.  When  the  disks  are  not  absolutely  con- 
eentrical,  the  distance  between  their  centres  being,  however,  less 
than  the  difference  of  their  apparent  semi-diameters,  the  dark  disk 
of  the  moon  will  still  be  within  that  of  the  sun,  and  will  appear  sur- 
roonded  by  a  luminous  annulus,  but  in  this  case  the  ring  will  vary 
IB  breadth,  the  thinnest  part  being  at  the  point  nearest  to  the  moon's 
centre ;  and  when  the  distance  between  the  centres  is  reduced  to 
exact  equality  with  the  difference  of  the  apparent  semi-diameters, 
the  ring  becomes  a  very  thin  crescent,  the  points  of  the  horns  of 
wkieh  noitei  as  represented  at  Dfjig.  792. 

m.  35 


410  ABTBONOMT. 

The  greatest  breadth  of  the  crefloent  will  be  ia  thii  ease  equal  to 
the  difference  of  the  apparent  diameters  of  the  sun  and  mooo. 

The  greatest  apparent  semi-diameter  of  the  sun  being  16'  IS'', 
and  the  least  apparent  semi-diameter  of  the  moon  being  14'  44",  the 
greatest  possible  breadth  of  the  annoluswhen  the  eclipse  is  eentzical 
will  be 

r  —  /  =  16'  18"  — 14'  44"  =  1'  34'  =  94", 

which  is  about  the  20th  part  of  the  mean  apparent  diameter  of  the 
sun. 

The  greatest  interval  during  which  the  eclipse  can  continue  an- 
nular is  the  time  necessary  for  the  centre  of  the  moon  to  more 
synodically  over  94"  x  2  =  188",  and,  since  the  mean  synodic 
motion  is  at  the  rate  of  30''  per  minute,  this  interval  will  be  about 

'^^  =  6*26  minutes 

or  about  six  minutes  and  a  quarter. 

2914.  Solar  eclipses  can  only  occur  at  or  near  the  epoch  of  new 
moons.  —  This  is  evident,  because  the  condition  whicn  limits  the 
apparent  distance  between  the  centres  of  the  disks  to  the  sum  of 
the  apparent  semi-diameters,  iDvolves  the  consequence  that  this  dis- 
tance cannot  much  exceed  30',  and  as  the  difference  of  longitudes 
must  be  still  less  than  this,  it  follows  that  the  eclipse  can  only  take 
place  within  less  than  half  a  degree  in  apparent  distance,  and  within 
less  than  two  hours  of  the  epoch  of  couj unction. 

2915.  Effects  of  parallax.  —  Since  the  visual  directions  of  the 
centres  of  the  disks  of  the  sun  and  moon  vary  more  or  leas  with  the 
position  of  the  observer  upon  the  earth's  surface,  the  conditions 
which  determine  the  occurrence  of  an  eclipse,  and  if  it  occur,  those 
which  determino  its  character  and  magnitude,  are  necessarily  differ- 
ent in  different  parts  of  the  earth.  While  in  some  places  none  of 
the  conditions  are  fulfilled,  and  no  eclipse  occurs,  in  others  an  eclipse 
is  witnessed  which  varies  from  one  place  to  another  in  its  magnitude, 
and  in  some  may  be  total,  while  it  is  partial  in  others. 

If  the  change  of  position  of  the  observer  upon  the  earth's  sur- 
face affected  the  visual  directions  of  the  centres  of  the  two  disks 
equally,  which  would  be  the  case  if  they  were  equally  distant,  or 
nearly  so,  no  change  in  the  apparent  distance  between  them  would 
be  produced,  and  in  that  case,  the  eclipse  would  have  the  same 
appearance  exactly  to  all  observers  in  every  part  of  the  earth.  But 
the  sun  being  about  400  times  more  distant  than  the  moon,  the 
visual  direction  of  the  centre  of  its  disk  is  affected  by  any  difference 
of  position  of  the  observers,  to  an  extent  400  times  less  than  thai 
)f  the  moon's  centre. 


■CLIFBBS,  TRANflnS,  AHD  OCCULTAIIOKa. 
Let  i,  S,  lod  H, 


411 


>.  79S,  represeot  acctionf  of  the  niD,  earth, 
MM  moon,  made  hy  the  plane  vhich  passes 
through  their  centres.  Let  a  line  P  m  <  be 
dnwn,  touchiDg  the  sun  and  moon,  bat  bo  that 
the;  ^all  lie  on  opposite  sidca  of  it>  It  is  evi- 
dent that  to  an  observer  at  p,  the  dark  disk  of 
the  mooD  would  touch  that  of  the  snu  exter- 
naU;;  for  the  apparent  distance  between  the 
eentrea  would  bo  measured  bj  the  angle  b  p  m, 
which  is  equal  to  the  sum  s  P  «,  tbe  apparent 
■emi-diameter  of  tbe  sun,  and  M  p  m  that  of  the 
moon. 

From  the  point  i  let  lines  be  supposed  to  be 
drawn,  touching  tbe  cartb  at  p  and  j/.  It  is 
evident  that,  to  an  observer  situate  between  p 
and  p',  the  apparent  distanoe  of  the  centres  of 
the  moon  and  sun  would  be  greater  than  the  sum 
of  their  apparent  semi-diameters,  and  thej  would 
therefore  be  separated  at  the  nearest  points  of 
their  disks  by  a  apace  equal  to  the  ezoeia  of  this 
distanoe  above  tbe  sum  of  the  apparent  semi- 
diameters. 

Adopting  the  signs  already  used,  let  r  express 
the  apparent  semi-diameter  of  the  san,  r'  that 
of  the  moon,  and  D  the  apparent  distanoe  be- 
tween their  centres,  we  shall  have  D  greater 
than  r  -{-  /  for  every  point  from  p  to  p,  and 
the  ezoesa  will  ioeresso  coatinosUy  from  v 
to/. 

On  the  other  baud,  for  every  point  between 
P  and^,  D  will  be  less  than  r  4.  /,  and  the  bub 
will  be  eclipsed,  the  magnitude  of  tbe  eclipse 
augmenting  gradually  from  p  to  ^. 
Hifl  phenomena  varying  therefore  indcGoitcly  with  the  position 
rf  tbe  ODeerrer  npon  the  earth,  it  is  necessary,  in  order  (o  render 
thdr  prediction  practicable,  to  select  a  fixed  position  for  which  they 
■•J  be  caJcnlated,  fbrmulie  being  established,  and  tables  prepared, 
ij  which  the  difference  between  the  appearances  there  and  at  any 
Itopoaed  place  may  bo  computed.  The  fixed  point  selected  for  this 
pnpow  is  the  centre  e  of  the  earth. 

Tiu  angular  distance  between  tbe  centres  of  the  disks  of  tbe  sun 
tad  moon,  as  seen  from  any  plaoe,  such  as  p  fur  example,  is  called 
their  ofparetit  distaoce  at  that  place,  aud  their  angular  distance,  as 
■wo  from  the  centre  k  of  tbe  earth,  is  called  tbeir  trat  distance. 
Tbn^  srH  ia  the  apparent  distance  between  the  centres  at  p,  and 


Hc-TM. 


412  A8TB0K0MT. 

SIM  US  their  tnie  distaDoe.  It  will  be  easy  to  show  the  reUtioii 
which  exists  between  these  two  distances. 

By  the  principles  of  elementary  geometry  we  have 

8EM  =  80M  —  PSE,  S0M  =  P0E  =  MP8  +  PMX, 

and  consequently 

SEM=MPS  +  PME  —  P8K. 

But  the  angle  p  M  e  is  the  diurnal  parallax  of  the  mooDy  and  p  s  E 
that  of  the  sun,  estimated  in  the  plane  of  the  figure.  If  these  be 
expressed  by  <J  and  m  respectively,  and  the  apparent  and  true  dis- 
tances between  the  centres  by  D  and  d'  respectively,  the  above  rela- 
tion will  be 

d'=  D  -f  »' — «, 
and  consequently 

d'  —  D  =  »' — «; 

that  is  to  say,  the  true  distance  exceeds  the  apparent  by  as  much  as 
the  parallax  of  the  moon  exceeds  that  of  the  sun. 

At  the  place  p,  from  which  the  disks  appear  in  external  contact, 

D  =  r  +  /, 
and  therefore 

d'  — (r  +  r')  =  w'  — «; 

consequently,  when  external  contact  takes  place,  we  have 

d'=  r  +  /  4-  «' — «; 

that  is,  the  true  djstancc  between  the  centres  is  equal  to  the  sum  of 
the  apparent  diameters  added  to  the  difference  of  the  parallaxes. 

To  simplify  the  explanation,  we  have  here  supposed  the  place  of 
observation  to  be  in  the  plane  which  passes  through  the  centres  of 
the  sun,  moon  and  earth,  or,  what  is  the  same,  the  centres  of  the 
disks  of  the  sun  and  moon,  to  be  in  the  same  vertical  at  the  time 
of  the  observation.  In  the  actual  calculations  necessary  to  supply 
an  exact  prediction  of  the  beginning,  middle,  the  end,  and  the  mag- 
nitude of  a  solar  eclipse,  many  particulars  must  be  taken  into  ac- 
count, which  are  not  adapted  to  a  work  such  as  the  present,  hut 
which  present  no  other  difficulty  than  such  as  attends  elahorata 
arithmetical  computation. 

2916.  Shadoio  })roduccd  hi/  an  opaque  (jlohe.  —  Connected  with 
the  phenomena  of  eclipses  and  transits  are  certain  properties  of 
shadows. 

When  a  luminous  body,  radiating  light  in  all  directions  around 
it,  throws  these  rays  upon  an  opaque  body,  that  body  prevents  a 
portion  of  the  rajs  from  penetrating  into  the  space  behind  it.  That 
part  of  the  space  from  which  the  light  is  thus  excluded  by  the  in- 
terposition of  the  opaque  body,  is  called  in  astronomy  the  shadow 
of  that  body. 

The  shape,  magnitude,  and  extent,  of  the  shadow  of  an  opaque 


HUKBITS,  AKD  OCCULTATIOHS. 


faodj  win  depend  partly  on  tli«  ili&pe  and  nugDitnde  of  the  op«{i]e 
bod;  itaelf,  and  putij  on  that  of  the  body  firom  which  the  tigtit 


2917.  Method  of  dettrmxning  the  form  and  dimeHnotu  of  the 
Aadav.  —  la  the  ouea  wbiob  are  actually  presented  in  utronomy, 
tbe  lamiDoiiB  body  being  the  ron,  and  the  opaqae  body  »  planet  or 
Mtellite,  both  are  globee,  and  the  former  of  mach  greater  dimen- 
■ana  than  the  latter.  It  ia  easy  to  show  that  in  BUob  caae  tbe 
Aadow  will  be  a  eone,  projected  to  a  certain  distance  behind  the 
(fiM{iie  body,  lie  length  of  this  cone,  and  the  angle  formed  at  its 
mtez,  nay  be  conpnted,  when  the  real  diameters  of  the  inn  and 
Ac  body  which  forma  the  shadow,  and  the  distance  of  the  one  from 
Ae  other,  are  known. 
liOt  b  U  and  a  a',  fig.  799,  represent  a  section  of  the  ran  and  the 
opaque  body.  Suppose  the  lines  h  a  and  V  al  drawn 
toDching  these.  Iiet  them  be  aontiaued  nntil  they 
^  meet  st/.  If  similar  lines  be  supposed  to  be  drawn 
thrODgh  all  points  surrounding  both  globes,  they  will 
include  a  cone  the  diameter  of  whose  base  is  h  V, 
wbose  sides  are  i/and  V  f,  and  whose  vertex  is  f. 
It  will  be  erident  that  tbe  sun's  rays  will  be  excluded 
from  all  that  part  of  the  cone  which  is  between  a  </ 
and  tbe  vertex  /.  This  part  of  the  cone,  theref<»e, 
having  the  section  of  tbe  opaque  body  at  a  a'  for  its 
base,  and  the  point/for  its  vertex,  is  the  shadow. 

To  aeoertain  the  length  I  of  the  shadow,  let  r  and 
¥  express  tbe  semi-diameters  of  tbe  sun,  and  the  body 
a  <i  respectively,  and  let  d  express  the  diatanoe  h  a 
between  them.  We  shall  then  have,  by  the  prio- 
dplea  of  elementary  geometry, 

r:t'::I+d:I, 
and  oonieqnently, 

rxl  =  r'xl+i'xd, 


/xrf 


;  X  (r  —  tO  =  r*  X  d, 


tbat  ia,  the  length  of  tbe  shadow  is  foui.d  by  multi- 
plying  the  distance  from  the  sun  by  the  semi-diameter 
of  the  body  which  forms  tbo  shadow,  and  dividing  the 
product  by  the  difference  betveen  the  scmi-diametera. 
To  determine  the  semi-angle  a/e  of  the  cone,  we 
have 

a/e  =  2062C5"  X  j. 

85* 


414  ASTRONOMT. 

2918.  Method  of  determining  the  limits  of  the  penumhra,  —  If 
tangents  be  drawn  transversely,  snch  as  h  a'  and  U  a,  and  be  con- 
tinued beyond  the  points  a  and  a',  the  snn's  rays  will  be  partially 
ezcluded  from  the  space  included  between  p  a  and /a.  Any  point 
on  the  line  ap  will  receive  light  from  all  points  of  the  sun's  disk. 
If  the  point  thus  illuminated  be  moved  sradoally  from  p  towards 
Oj  it  will  receive  less  and  less  of  the  sun's  Bght^  nnce  the  globe  a  a' 
will  be  more  and  more  interposed  between  it  and  the  snn.  Thus,  a 
point  placed  at  d  receives  light  only  from  those  points  of  the  sun 
which  lie  between  c  and  h,  the  rays  proceeding  frt)m  all  points  be- 
tween V  and  c  being  intercepted  by  a  a'.  As  the  point  o'  is  moved 
towards  o,  the  corresponding  point  e  moves  towards  hj  so  that  the 
portion  of  the  sun  from  which  it  receives  light  constantly  decreases 
until  it  arrives  at  the  boundary  a /of  the  shadow,  where  all  the 
rays  are  intercepted. 

The  light  being  thus  partially  intercepted  from  the  ^pace  bounded 
by  the  lines  a  p  and  a  f  this  space  is  called  the  penumbra. 

The  angle  j>  a  f,  which  measures  the  penumbra,  is  equal  to  the 
visual  angle  bah,  subtended  by  the  sun  at  the  object  which  forms 
the  shadow. 

2019.  Tftfn/  and  jxirfial  huhir  eclipses  explained  ht/  the  lunar 
shuhnc.  —  The   moon    prcgccts   behind   in   a  conical  shadow,  the 
dimensions  of  which  can  be  ascertained  by  the  methods  explained 
above.      If    the   moon   comes   between   the   sun    and    the   earth, 
which  it  rauht  do  near  conjunction,  if  it  be  not  far  removed  from 
the  node  of  its  orbit,  this  shadow  will  be  projected  on  a  part  of  the 
hemisphere  of  the  earth  which  is  turned  to  the  sun,  provided  its 
length  be  greater  than  the  moon's  distance,  as  represented  in  fiy. 
800.     In  this  case,  the  shadow  will  move  over  certain  points  of  the 
surface  of  the  earth  lying  around  the  point  to  which  its  axis  is 
directed.     The  light  of  the  sun  being  altogcfthcr  intercepted  within 
the  limits  of  the  f^liadow,  a  total  eclipse  will  take  place,  the  dui* 
tion  of  which  will  be  determined  by  the  limits  and  movement  of  the 
shadow  thus  projected,  which  is  in  effect  the  intersection  of  the 
conical  shadow  of  the  moon  and  the  earth's  surface. 

To  those  parts  of  the  earth  which  are  outside  the  limits  a  a'  of 
the  shadow,  but  within  those  pp  of  the  penumbra,  a  partial  eclipse 
will  be  exhibited,  the  magnitude  of  which  will  be  so  much  the 
greater  the  nearer  the  place  is  to  the  axis  of  the  shadow.  All  sucb 
parts  will  be  more  faintly  illuminated  in  proportion  to  the  extent  of 
the  sun's  disk  which  is  obscured. 

2020.  Annular  eclipses  explained  hi/  sJufdow.  —  If  the  length 
of  the  shadow  be  less  than  the  moon's  distance  from  the  earth,  the 
vertex  not  reaching  to  the  earth,  no  part  of  the  earth's  surface  can 
be  immersed  in  the  shadow.  In  that  case,  a  centrical  annular 
^cVjpBe  will  be  exhibited  at  those  points  of  the  earth's  surftce  to 


BCUPBBg,  TRANSITS,  AND  OCCITLTATIONS. 


415 


which  the  axis  of  the  shadow  is  directed.    This  case  is  represented 
in  fig^  801,  where /represents  the  vertex  of  the  moon's  shadow. 


Fig.  800. 


Fig.  801. 


At  all  places  within  the  circle  npon  the  earth,  of  which  a  a'  is  the 
diameteri  there  will  he  a  annular  eclipse,  and  at  the  centre  of  the 
cwele  the  eclipse  will  be  centrical,  the  annulns  being  of  uniform 
bnadth.  Outside  this  circle,  so  far  as  the  penumbra  extends,  the 
cdipae  will  be  partial,  its  magnitude  decreasing  as  the  distance  of 
te  plaoe  from  the  centre  of  Uie  circle  increases,  until  at  the  limit 
ef  the  pennmbra  the  phenomena  ceases  to  be  exhibited. 

2921.  JPouibiltty  of  annular  eclipses  proved,  —  To  establish  the 
posailnlity  of  an  annular  eclipse,  and  to  show  the  relative  positions 
of  the  earth  and  moon,  in  their  respective  orbits,  when  such  a  phe- 
■omenon  takes  place,  it  must  be  considered  that  it  is  necessary  that 
the  length  of  the  moon's  shadow  be  less  than  the  moon's  distanco 
Cram  the  earth.  Bj  substituting  for  r  and  r',  in  the  general  for- 
malk  for  the  value  of  /  (2917),  the  actual  values  of  the  semi-diame- 
toi  of  the  sun  and  moon,  we  find 

/     _   1076   _    1 
7=7  ""  441000  "■"  440' 


416  ASTRONOMT. 

Tho  extreme  limite  of  the  flon'e  distuee  d  being 

cr= 96,600000, 
(f  =  93,400000, 

the  greatest  and  least  values  of  ^  the  length  of  the  moon's  shadot 
wiUbe 


r  =  96,600000  X  ^  =219546, 

440 

r  =  98,400000  X  :4a  =  212272- 

440 

But  the  extreme  distances  of  the  moon  from  the  oentre  of  the  wA 
are, 

lOka 

greatest  distance 251760, 

least  distance 221290, 

and,  therefore,  the  extreme  distances  from  the  surface  are 

MUeft.  Milen.  ICIlea. 

greatest  distance  =  251760  —  3963  =  247797, 
least  distance       =  221290—3963  =  217327. 

Since,  therefore,  the  length  of  the  moon's  shadow  when  greatest, 
exceeds  the  moon's  distance  from  the  surface  of  the  earth  whea 
least,  the  surface  may  intersect  the  shadow  at  a  point  within  iti 
Tcxtex  ;  and  since  the  length  of  the  shadow  when  least,  is  less  than 
the  moon's  distance  from  the  surface  of  the  earth  when  greatest, 
the  vertex  of  the  shadow  may  pass  between  the  moon  and  the  earth 
without  touching  the  surface.  In  the  former  case,  there  will  be  a 
total  solar  eclipse  at  all  places  within  the  section  of  the  shadow 
made  by  the  earth's  surface,  and  in  the  latter,  there  will  be  an  an- 
nular eclipse  at  all  places  within  the  section  of  the  cone  a/c^^fg. 
801,  formed  by  the  continuation  of  the  cone  of  the  shadow  beyond 
its  vertex  /. 

The  extreme  distance  of  the  vertex  of  the  cone  /,  fig,  800,  within 
the  surface  of  the  earth,  in  the  case  of  a  total  eclipse,  will  evidently 
be 

210545  —  217327=2218. 

and  the  extreme  distance  of  the  yetiej^fyfig.  799,  of  the  cone  from 
the  surface,  in  case  of  an  annular  eclipse,  is 

Milec 

247797  —  212272  =  35525. 

Thus,  the  vertex  of  the  shadow,  when  directed  to  the  earth's  centre, 

ranges  from  2218  miles  below  the  surface  to  35,525  miles  above  it. 

Since  the  surface  of  the  earth  cuts  off  about  the  100th  part  of 


BCUPSBBk  TBAN8R9,  AND  OCCUI.TAIION& 


417 


t-J 


the  length  of  the  ehadoWy  the  diemeter  of  the  dronlar  shadow  pro- 
jected upon  the  earth,  which  is  the  section  of  the  conical  shadow, 
is  about  the.  100th  part  of  the  moon's  diameter,  or  about  20  miles, 
which,  however,  is  increased  by  the  effect  of  the  curvature  of  the 
earth,  and  considerably  so  by  the  obliquity  of  its  surface  to  the  axis 
of  the  shadow. 

In  the  same  manner  it  may  be  shown,  that  the  diameter  of  the 
circle  over  which  the  eclipse  may  be  annular,  measured  at  right 
angles  to  the  axis  of  the  shadow,  is  about  the  sixth  part  of  the  diam- 
eter of  the  moon,  which  in  like  manner  is  augmented  by  curvature 
and  obliquity. 

2922.  S^r  ecliptic  limits,  —  The  moon's  orbit  being  inclined  to 
the  eeliptie,  at  an  angle  of  5®,  and,  consequently,  the  distance  of  the 
bood's  centre  from  the  ecliptic  varying  in  each  month  from  0^  to 
5%  while  the  interpoution  of  the  moon  between  any  place  on  the 
earth  and  the  sun  requires  that  the  apparent  distance  of  their  centres 
dioald  not  exceed  the  sum  of  their  apparent  semi-diameters,  which 
aever  much  exceed  half  a  degree,  it  is  clear  that  an  eclipse  can 
aever  happen  except  when,  at  the  time  of  codj unction,  the  apparent 
istanoe  of  the  moon's  centre  from  the  ecliptic  is  within  that  Umit;  a 
floodition  which  can  only  be  frifilled  within  certain  small  distances 
rftbe  moon's  nodes. 

There  is  a  certain  distance  from  the  moon's  node,  beyond  which 
i  solar  eelipae  is  impoisible,  and  a  certain  lesser  distance,  within 
that  phenomena  is  inevitable.    These  distances  are  called  the 

iw  SCLIPTIO  LIMITS. 

The  mere  inspection  of  Jig,  799,  will  show  that  no  solar  eclipse 

take  place  unless  some  part  of  the  globe  of  the  moon  pass  within 

fiaea  o  a  and  U  a',  which  touch  externally  the  globes  of  the  sun 

earth.    It  follows,  therefore,  that  the  major  limit  of  the  dbtance 

Iks  moon's  centre  from  the  ecliptic,  or  its  latitude  at  the  time  of 

which  is  compatible  with  the  occurrence  of  an  eelipae, 

w/fffOr  what  is  the  same,  the  angle  m'  dd.    Let  this  angle  be 

by  L,  and  we  have 

L  =  m'a'n' -f  nV«  +  »(/(/ 
bj  the  principle  of  geometry, 

sa'  d  ^=a!  d  e  —  a!  se^ 
therefore, 

jj=zm'a^n'  -i-n'a'i  +  of  d  e  —  a'ie. 

w^afn^  and  n' a^  $  are  the  apparent  semi-diameters  of  the  sun 
Boon,  and  a'd  e  and  a'  se  Kre  their  horizontal  parallaxes,  respeo' 
If  the  former  be  expressed  by  i  and  s^,  and  the  latter  by  h 
ff  we  shall  have 

h  =  i  +  t^  +  h'  —  h. 


»w 


AaTROSOMT. 


It  fiitlowi,  Iberefore,  that  a  solar  eclipse  o&naot  take  place,  xaiiat 
tbe  latiliide  of  tbc  mooD  at  conjunctioii  be  leas  tliao  the  sum  eT  tba 
Appitrcat  scmi-dinnietera  of  the  sun  and  moon,  added  to  the  diffenooi 
of  their  horizontal  parallaxes. 

But  sinca  all  these  quanUtica  vary  betireeD  a  certain  mnjor  aM  x 
oertain  mioor  limit,  an  eclipse  will  be  posaible  or  oertdo,  according 
ea  the  moon's  latitude  at  coDJuactioa  is  withiD  the  one  limit  or  Sm 
Other.  If  tbe  latitnde  be  witbia  tbe  mujor  limit,  a  solar  eclipsa  «tt 
take  plane ;  and  if  the  several  quantities  have  such  values  as  ftiH 
the  above  conditioD,  it  Kill  take  place.  If  the  latitode  be  iridiil 
the  minor  limit,  an  eclipse  nniiC  take  place;  because,  vrhat«ncbl 
their  values,  the;  must  fulfil  tho  conditioD. 

2923.  Extreme  and  mran  va!ua  of  grmi-Jiamften  and  &araM< 
tal  paraUaxfx  of  mn  and  moon.  —  The  extreme  and  mean  nloM 
of  these  qnantities,  which  are  very  importsat  in  tbe  tlteor^  tt 
eclipses,  and  other  parta  of  practical  ajjiranomj,  are  ^ven  in  thi  M 
lowing  table : — 


Appatvat  HmMluii 


The  major  Huitt  of  i.  mil  therefore  ba 
l'=  1=34' 14", 
md  the  minor  limit 

l"=  1=  24'  19". 

To  detenniuo  the  distances  from  the  node,  which  correspond  li 
these  liniiis  of  the  moon's  lititod 
at  coBJunrtion,  let  N  M  yt',Jig.WS. 
represent  a  part  of  the  moon' 
path,  N  B  s'  a  part  of  the  ecliptic 
>i  s  the  major,  and  ti'  ^  tbe  mine 
limit  of  the  value  of  L.  The  tri 
angle  M  N  s  and  m'  N  s'  are  Bpheri 
and  N  s',  if  rigorously  computed 
id  formula  of  epberies 


rfJL. 


cat  triangles, 
would  requin 
trigonometry. 


»ill.  hm 
plane  tri 
(2294). 


ind  the  distances  n 
the  application  of  the  rules  a 

No  error  of  importance,  for  the  present  illustradoo 
be  entailed  upon  tho  results,  by  treating  them  m 
s,  and  applying  to  them  the  principles  explAined  il 
shall  then  have 


SCLIP8X8»  TRANSITS,  AND  OCCULTATIONS.  419 

II N  8  =  5^  8'  48"    M  8  =  1^  34'  14"    m'  s'  =  1^  24'  19", 
N  8  =  1*^  34'  14"  X  ^^  =  17^  27'  48", 

N  8'  =  1*>  24'  19"  X  ^^  =  15°  37'  36". 

Thus  it  appean,  that  when  the  distance  from  the  node  at  opposition 
ii  greater  than  17^  27'  48",  an  eclipse  cannot,  and  when  less  than 
16^  G'  16",  mutt  take  place.  Between  these  limits  it  may  or  may 
Dot  oocor,  according  to  the  magnitude  of  the  parallaxes  and  apparent 
diimetere. 

Since  the  sun  takes  more  than  a  month  to  move  through  32°  of 
the  ecliptic,  it  follows  that  at  least  one  conjunction  must  take  place 
within  16^  of  each  node,  and  that  one  solar  eclipse,  at  least,  must 
oeeor  near  each  node,  and  therefore  two,  at  least,  annually.  But  it 
may  happen  that  two  solar  eclipses  shall  occur  at  the  same  node, 
udthis  wiU  take  place  if  the  moon  be  in  conjunction  at  more  than 
U|^,  and  leas  than  15°  37'  36",  from  the  node ;  for  in  that  case,  it 
will  be  again  in  conjunction  in  29}  days,  in  which  time  the  sun  will 
more  through  29°,  and  will  therefore  be  at  14^°  on  the  other  side 
of  the  node,  and  therefore  within  the  ecliptic  limit. 

Thus,  it  is  possible  that  two  solar  eclipses  may  take  place  at  each 
aode,  and,  therefore,  four  within  the  year.  But  even  more  is  pos- 
nUe ;  for,  as  will  hereafter  appear,  the  nodes  of  the  moon's  orbit 
hxe  a  retrograde  motion  on  the  ecliptic,  the  consequence  of  which 
ii,  that  the  sun  arriyes  at  each  node  in  less  than  a  year  after  it  has 
lut  passed  through  it,  and  consequently  another  solar  eclipse  mai/ 
happen,  before  the  lapse  of  a  solar  year,  at  the  same  node  at  which 
tke  first  occnrred. 

2924.  Limits /or  total  and  annular  eclipses,  —  It  is  evident  that 
BO  total  or  annular  eclipse  can  be  witnessed,  unless  the  globe  of  the 
Mxm  be  fully  within  the  tangents  ba  and  6' a',  Jig,  799.  That 
tUf  Day  take  place,  the  apparent  distance  of  the  moon's  centre  m' 
from  </  most  be  less  than  n'  o'  by  the  moon's  semi-diameter  m'  n\ 
n  that  we  shall  have 

l^^  n' a' i/  —  n' a' m'  =i  sa* U  +  sa' o —n' a' m' ] 

lod,  from  what  has  been  explained  above,  this  becomes 

L=  «  — /  + A'  — /i. 

By  assagning  to  these  quantities  the  values  which  render  L 
greatest  and  least,  we  shall  find  that  when  greatest, 

L  =  62'  44"  =  1°  2'  44", 

tod  when  least, 

L  =  62'49"; 


Vn  ASTRONOMY.  ^^ 

Bad  according  t«  the  method  previously  applied,  we  i 

■pOodiDg  dielaDce  from  the  Dodea 

s'6'  =  9=47'19". 

A  tola]  or  atinukr  eclipse  is  therefore  pomilfe,  il 
tultea  place  wilbin  IPST'ilG",  and  certain,  if  it  take; 
9' 47' 19"  of  the  node.  It  will  be  total  or  nnnalar, 
the  apparent  diameter  of  the  moon  is  greater  or  lese 

the    BUD. 

iQ2h.  Appfaraveet  olUnding  total  tolar  erfipies. 
consequence  of  the  diffusion  of  knowledge  b,  th&t  wl 
the  vagne  aeDse  of  wonder,  with  which  nngnkr  phei 
ture  are  beheld,  it  locreaBes  the  feeling  of  admirtibon  . 
nious  lawH,  the  development  of  whieh  renders  easi! 
effecta  apparentlj  atrange  and  uaaccoun table.  It  nia.j 
what  a  een^e  of  astonishment,  and  even  terror,  the  ton: 
pearsnce  of  an  object  like  the  sun  or  moon  luUBt  bav 
HD  age  when  the  cauaea  of  eclipsee  were  known  only  t 
Bueh  phenomena  were  regarded  oa  precnrson  of  dM 
History  inforins  ub  that  in  ancient  times  armies  have  b 
by  the  effects  of  the  consternalion  spread  among  tbem ) 
occurreoce  of  an  eclipsa  of  the  sun.  Commanders  » 
to  poaeeaa  Bome  Bcientific  knowledge,  have  taken  adn 
work  upon  the  credulity  of  those  around  them  by  m 
with  prodigies,  tho  near  approach  of  which  they  wei 
of,  illuatrstiDg  thus,  in  a  siogalar  and  perverted  manot 
tiial  knowledge  is  power.* 

The  spectacle  presented  during  a  total  eclipse  is  ah 
posing.  The  darkness  is  somctioies  so  intend  as  I 
Drightcr  sUrs  and  plancta  visible.  A  gndden  fall  of  t 
aeuBJble  in  the  air.  Vegetables  and  animals  compo 
as  they  are  woot  to  do  after  sunset.  Flowers  close,  ai 
roost  Nevertheless,  the  darkoess  is  difierent  from 
nocturnal  darkness,  and  is  attended  with  a  certain  indi 
earthly  light,  which  throws  upon  surrounding  objecb 
Eometimes  reddish,  and  eometimea  cadaverously  green. 

Many  interesting  narratives  have  been  published 
observers,  who  have  been  bo  fortunate  as  to  witneaa 

2926.  Bail^»  beads.  —  When  the  disk  of  the  mo 
over  that  of  tho  snn,  has  reduced  the  ktter  to  &  thi 

■  Columbus  is  Buid  to  have  avuled  himaelf  of  hJa  acq 
practical  aatraaomj  to  predict  ■  solar  eclipse,  and  uaed  th* 
neaDB  of  eatablishiog  bis  authorit;  over  the  orawi  of  I 
■Aowed  indicalioni  of  mutiaoiu  disobedieDoe. 


ECLIPSES,  TRANSITS,  AKD  OCCDLTATIONa.  421 

IS  observed  by  Mr.  Francis  Baily,  that  immcdiBtely  before  the 
ginning,  or  af^er  the  end  of  complete  obacuratioo,  tbo  crescent 
peued  u  ■  band  of  briUiant  poinia  scparahMl  by  dark  spaces,  so 


Mto^fetoittlieapp«araDceof  ftatriagof  bnlSHi^lNik"  fit 
phBlMWMOon,  which  has  giuce  been  frequeutlj  n-olM^««d,  tt«M 
■gquied  the  name  of  "Bailj'a  beads." 

VnrtbOT  obBeiration  Bhowed,  that  before  the  fijnnalioD  o(  Ae 
"beads"  the  homs  of  the  cTeeceiit  were  Eomelimee  inlem^tidMi 
linken  faj  Uiok  eti^aks  thrown  terou  iboai. 

Theae  phenomena  an  ronghlj  Bketobed  in  J!ff».  803,  SIX. 
He.  set. 


ii»aM. 


Fig.  80r.  Tt.  H8. 

Figg.  805  to  SOS  are  taken  from  the  originil  aketohea  of  Mr. 
Baity,  represeoling  the  progreaaive  disappearanoe  of  the  beada  iflet 
the  termination  of  the  complete  obaonratioD. 

2927.  Protfuced  by  lunar  ntountaittM,  projected  on  ihe  tnn't 
diik.  ~~  These  phenomena  arise  &om  the  projection  of  the  edge  of 
the  moon's  diek,  serrated  bj  nnmerons  inequalities  of  the  anrfact, 
approaching  so  close  to  the  ezlernBl  edge  of  the  son's  disk,  that 
the  point?  of  the  projections  eiUnd  to  the  latter,  while  the  inter- 
mediate spaces  rcTnain  uncovered.  This  maj  be  very  appropriately 
illustmted  by  laying  the  blade  of  a  oironlar  saw,  having  finelj-«iit 
teeth,  orcr  a  white  circle  of  nearly  eqnal  diameter  npnn  a  black 


ECLIPSES,  TRANSITS,  AND  OCCULTATIONS.  428 

floand.     The  white  parta  between  the  teeth  will  appear  like  a  neck- 
koe  of  white  pearls. 

The  fact,  that  in  some  cases  the  beads  have  not  been  seen,  or  if 
Ken,  appeared  in  a  less  conspicnous  manner,  may  be  explained  by 
the  greater  or  less  preyalence  of  mountainous  masses,  on  that  part 
of  the  moon's  surfiice  which  forms  the  edge  of  its  disk  at  different 
times. 

The  beads,  in  general,  disappear  suddenly,  at  the  moment  of  the 
oommenoement  of  total  obscuration,  and  reappear  on  the  other  side 
of  the  lunar  disk,  with  a  somewhat  startling,  instantaneous  effect,  at 
the  moment  the  total  obscuration  ceases. 

2928.  Flame4ike  protuberances,  —  Immediately  after  the  com- 
menoement  of  the  total  obscuration,  red  protuberances,  resembling 
lamely  i^ipear  to  issue  from  the  edge  of  the  moon's  disk.  These 
•ppeftniMe0|  which  were  first  noticed  by  Yassenius,  on  the  occasion 
of  tlie  total  solar  eclipse  which  was  visible  at  Gottenberg  on  3rd 
Maji  1788,  have  been  re-observed  on  the  occurrence  of  every  total 
lolar  e^pse  which  has  taken  place  since  that  time,  and  constitute 
one  of  the  most  curious  and  interesting  effects  attending  this  class 
of  phenomena. 

2929.  Soiar  eclipse  of  1851.  —  A  total  eclipse  of  the  sun  took 
place  on  the  28th  tiuly,  1851,  which  became  a  subject  of  systematic 
observation  by  the  most  eminent  astronomers  of  the  present  day. 
A  conflidenble  number  of  English  observers,  aided  by  several 
forngnen,  distributed  themselves  in  parties  at  different  points  along 
the  path  of  the  shadow,  so  that  the  chances  of  the  impediments 
that  might  arise  from  unfavourable  conditions  of  the  atmosphere 
mi^t  be  diminished.  The  reports  and  drawings  of  these  various 
obeenren  have  been  collected  by  the  Hoyal  Astronomical  Society, 
and  pnUiahed  in  their  transactions. 

The  Astronomer  Eoyal,  with  two  assistantit,  Messrs.  Dunkin  and 
Humphreys,  authorised  by  the  Board  of  Admiralty,  selected  certain 
parta  of  Sweden  and  Denmark  as  the  most  eligible  station.  Pro- 
fesBor  Airy  observed  at  Gottenberg)  Mr.  Dunkin  at  Christiana,  and 
Mr.  Humphreys,  assisted  by  Mr.  Miland,  at  Christianstad. 

2930.  Observations  of  the  Astronomer  Roi/al.  —  The  weather  on 
the  whole  proved  favourable  at  Gottenberg.  We  take  from  tho 
report  of  the  Astronomer  Koyal  the  following  highly  interesting 
particulara  of  the  progress  of  tho  phenomenon. 

"  The  approAch  of  the  totality  was  accompanied  with  that  indescribably 
nysterious  and  gloomy  appearance  of  the  whulc  surrounding  prospect 
vhich  1  have  seen  on  a  former  occasion.  A  patch  of  clear  blue  sky  in  the 
icnith  became  purple-black  while  I  was  gazing  at  it.  1  tonk  oft'  the  higher 
power,  with  which  I  hud  scrutinized  the  sun,  and  jtut  on  the  lowest  powei 
(magnifying  about  84  times).  With  this  I  saw  the  mountains  of  the  moon 
parfactly  welL     I  watched  carefully  the  approach  of  the  moon's  limb  to  the 

i*t  limb,  which  my  graduated  dark  glass  enabled  mo  to  se^  Vn  ^^oX  '^ct* 


424  ASTRONOBfY. 

faction ;  I  saw  botb  lirobs  perfectly  well  defined  to  the  lart,  And  saw  the 
line  becoming  narrower  and  tbe  cusps  becoming  sbarper  withont  any  dis- 
tortion or  prolungation  of  the  limbs.  I  saw  the  moon's  serrated  limb  ad- 
vance up  to  the  sun's,  and  the  light  of  the  sun  glimmering  thronjdi  the 
hollows  between  the  mountain  peaks,  and  aaw  these  glimmering  spots  ex- 
tinguished one  aft«r  another  in  extremely  rapid  succesaioD,  but  without 
any  of  the  appearances  which  Mr.  Daily  has  described.  I  saw  the  sna 
coyered,  and  immediately  slipping  off  the  dark  glass,  inttantly  saw  the  ap- 
pearances represented  &i  a  b  c  d^fig.  1,  PI.  XIII. 

«  Before  alluding  more  minutely  to  these.  I  must  advert  to  tbe  darkness. 
I  have  no  means  of  ascertaining  whether  the  darkness  really  was  greater 
in  the  eclipse  of  1842 ;  I  am  inclined  to  think  that  in  the  wonderful,  and  I 
may  say  appalling,  obscurity,  I  saw  the  grey  granite  hills  within  sigbt  of 
Hyal'as  more  distinctly  than  the  darker  country  surrounding  the  Soperga. 
But  whether  because  in  1851  the  sky  was  much  less  clouded  than  in  1842 
(so  that  the  transition  was  from  a  more  luminous  state  of  sky  to  a  dark- 
ness nearly  equal  in  both  cases),  or  from  whatever  cause,  the  BaddenaesB 
of  the  darkness  in  1851  appeared  to  me  much  more  striking  than  in  1842. 
My  friends  who  were  on  the  upper  rock,  to  which  the  path  waa  very  good, 
had  great  difficulty  in  descending.  A  candle  had  been  lighted  in  a  lantera 
about  a  quarter  of  an  hour  before  the  totality ;  Mr.  Haselgren  was  nnable 
to  read  the  minutes  of  the  chronometer-face  without  having  the  lantern 
held  close  to  the  chronometer. 

**  The  corona  was  far  broader  than  that  which  I  saw  in  1842:  roughly 
speaking,  its  breadth  was  little  less  than  tlie  moon's  diameter ;  but  its  oat- 
line  was  very  irregular.  I  did  not  remark  any  beams  projecting  from  it 
which  deserved  notice  as  much  more  couspicuous  than  the  others ;  but  the 
whole  was  beamy,  radiated  in  structure,  and  terminated  (though  very  io- 
definitely)  in  a  way  which  reminded  me  of  the  ornament  frequently  placed 
round  a  mariner's  compass.  Its  colour  was  white,  or  resembling  that  of 
Vinui.  I  saw  no  flickering  or  unstcadinef's  of  light.  It  was  not  separated 
from  the  moon  by  any  dark  ring,  nor  had  it  any  annular  structure ;  it  looked 
like  a  radiating  luminous  cloud  behind  the  moon. 

"  The  form  of  the  prominences  was  most  remarkable.  That  which  I 
have  marked  (o)  reminded  me  of  a  bomerang.  Its  colour  for  at  least  two- 
thirds  of  its  breadth,  from  the  convexity  tuwards  the  concavity,  was  full 
Ittkc-red,  the  renminder  was  nearly  white.  The  most  brilliant  part  of  it 
was  the  swell  farthest  from  the  moon's  limb  ;  this  was  distinctly  seen  by  ny 
friends  and  myjfolf  with  the  naked  eye.  I  did  not  measure  its  height;  hut 
judging  generally  by  its  proj^ortion  to  the  moon's  diameter,  it  must  hate 
been  3^.  This  estimation  perhaps  belonjrs  to  a  later  period  of  the  eclipse. 
The  prominence  {h)  was  a  pale  white  semi-circle  based  on  the  moon^s  limb. 
That  marked  (c)  was  a  red  detached  cloud,  or  balloon,  of  nearly  circular 
form,  separated  from  the  moon's  limb  by  a  space  (differing  in  no  way  from 
the  rest  of  the  corona)  of  nearly  its  own  breadth.  That  marked  (<f)  was  a 
small  triangular  or  conical  red  mountain,  perhaps  a  little  white  in  the 
interior.  These  were  the  appearances  seen  instantly  after  the  formatioa 
of  the  totality. 

•*  I  employed  myself  in  an  attempt  to  ilelineate  roughly  the  appearances 
on  the  western  limb,  and  1  took  a  hasty  view  of  the  country ;  and  I  then 
examined  the  moon  a  secoml  time.  I  believe  (but  I  did  not  carefully  re- 
mark) that  the  prominences  ah  c  had  iucrea.sed  in  height;  but  (</)  had  now 
disappeared,  and  a  new  one  (f)  had  risen  up.  It  was  impossible  to  see  this 
change  without  feeling  the  conviction  that  the  prominences  belonged  to  the 
sun  and  not  to  the  moon. 


ECLIPSKS,  TRANSITS,  AND  OCCLLTATIONS.  4*25 

**  I  Qgfiin  looked  round,  when  I  saw  a  scene  of  unexpected  beauty.  The 
Mothem  part  of  the  sky,  as  I  have  said,  was  covered  with  uniform  white 
cloud ;  but  in  the  northern  part  were  detached  clouds  upon  a  ground  of 
dear  sky.  This  clear  sky  was  now  strongly  illuminated  to  the  height  of 
80®  or  35®,  and  through  almost  90®  of  azimuth,  with  rosy-red  light  shining 
through  the  intervals  between  the  clouds.  I  went  to  the  telescope,  with 
tho  hope  that  I  might  be  able  to  make  the  polarisation-observation,  (which, 
MM  mj  apparatus  was  ready  to  my  grasp,  might  have  been  done  in  three  or 
four  seconds,)  when  I  saw  that  the  nerra,  or  rugged  line  of  projections, 
shown  at  (/},  had  arisen.  This  tierra  was  more  brilliant  than  the  other 
promineoces,  and  its  colour  was  nearly  scarlet.  The  other  prominences 
had  perhaps  increased  in  height,  but  no  additional  new  ones  had  arisen. 
The  appearance  of  this  nerra,  nearly  in  the  place  where  I  expected  the  ap- 
pearance of  the  sun,  warned  me  that  I  ought  not  now  to  attempt  any  other 
physical  observation.  In  a  short  time  the  white  sun  burst  forth,  and  the 
eorona  and  every  prominence  vanished. 

'<  I  withdrew  from  the  telescope  and  looked  round.  The  country  seemed, 
though  rapidly,  yet  half  unwillingly,  to  be  recovering  its  usual  cheerftil- 
ness.  My  eye,  however,  was  caught  by  a  duskiness  in  the  south-east,  and 
I  immediately  perceived  that  it  was  the  eclipse-shadow  in  the  air  tra- 
vailing away  in  the  direction  of  the  shadow's  path.  For  at  least  six  seconds 
tlus  shadow  remained  in  sight,  far  more  conspicuous  to  the  eye  than  I  had 
anticipated." 

2931.  Ohtervations  of  Mestrs,  Dunkin  and  Humphrey$. —^ 
Owing  to  the  nnfavourablo  state  of  the  atmosphere,  the  observa- 
tkms  of  the  other  members  of  the  Admiralty  party  were  not  80 
Mtu&ctory  as  those  of  its  chief.  Nevertheless,  both  observers  saw 
the  red  promioeDces,  though  imperfectly,  as  compared  with  the 
nsults  of  the  observations  of  the  Astronomer  Koyal.  Baily's  beads 
were  seen  by  Mr.  Dunkin,  as  well  before  as  after  the  total  obscu- 
ntioo.  Their  appearance  was  of  intense  brilliancy,  compared  by 
the  observer  to  a  diamond  necklace.  Their  effect  on  the  observer 
was  "quite  overpowering,''  being  unprepared  for  a  sight  so  mag- 
nificent 

At  Christianstad,  the  planets  Venus,  Mercury,  and  Jupiter, 
tad  the  stars  Arcturus  and  Vega,  were  visible  during  the  totality 
of  the  eclipse. 

2932.  Obiervalioni  of  W,  Gray^  at  Tune,  near  Sarpshorg,  — 
Thif  gentleman  also  saw  Baily's  beads,  both  before  and  after  the 
total  obficuration.  He  saw  four  of  the  red  projections,  three  of 
which  are  represented  in  Jig.  2,  pi.  xiii.,  the  fourth  resembling  c  and 
d  in  form,  and  diametrically  opposite  to  a  in  position  on  the  moon's 
limb.  The  apparent  height  of  a  was  estimated  at  IJ',  and  its 
bieadth  62^,  but  the  altitude  of  this  afterwards  increased  to  1}'. 
There  was  a  dark  shade  in  the  curved  portion,  which  gave  it  a  re- 
semblance to  a  gas  flame.  The  remainder,  however,  was  rose-red, 
not  uniform,  and  very  pale,  like  the  innermost  parts  of  the  petals 
of  a  rose.  The  red  prominence  opposite  to  a  had  an  apparent  alti- 
tude of  Vj  and  a  deeper  red  colour.  The  prominences  c  and  <2  wet% 
Citiiiiated  at  abont  bO^  in  size. 

36* 


426  A8TR0N0MT. 

During  the  totality,  the  light  seemed  like  thit  of  an  erening  in 
August  at  au  hour  and  a  half  after  sunset-. 

2933.  Observatians  of  Messrs.  Stephenson  and  Andre%o$  at 
Fredrichsvaam. — Baily's  beads  were  seen  both  before  and  after  the 
total  obscuration.  The  crescent^  before  disappearing,  was  seen  is  a 
fine  thread  of  light,  which  broke  up  into  fragments,  and  whan  it  re- 
appeared, it  gave  the  idea  of  globules  of  mercury  rnahing  amoDgrt 
each  other  along  the  edge  of  the  moon.  In  a  second  or  two  after 
the  disappearance  of  the  crescent,  a  rose-coloured  flame  shot  oat 
from  the  limb  of  the  moon,  which  in  form  resembled  a  sickle ;  see 
Jtg.  8.  It  increased  rapidly,  and  then  two  other  rose-ooloored  pro- 
minences, above  and  below  it,  started  out,  differing  in  shape,  bat 
evidently  of  tho  same  character.  Besides  these,  there  were,  as  well 
between  them  as  elsewhere,  around  the  moon's  edge  other  lurid 
points  and  other  indistinct  Unes.  The  height  of  the  principal  pro- 
minence was  estimated  at  about  the  twentieth  of  the  moon's  diune- 
ter;  that  is,  about  1}'.  The  chief  prominences  looked  like  boninff 
volcanoes,  and  the  lurid  points  and  lines  reminded  the  observen  d 
dull  streams  of  cooling  lava. 

2934.  Observations  of  Mr,  LasseU  at  Trollhattan  Falls. — Having 
heard  the  red  promiDences  seen  in  the  former  total  eclipses  described 
as  faint  appearances,  the  astonishment  of  the  observer  may  be  ima- 
gined when  he  saw  around  the  dark  disk  of  the  moon,  after  the 
commencement  of  total  obscuratioD,  prominences  of  the  most  bril- 
liant lake  colour,  —  a  splendid  pink,  quite  defined  and  hard,^^.  4. 
They  appeared  not  to  be  absolutely  quiescent.  The  observer  judged 
from  their  appearance  that  they  belonged  to  the  sun,  and  not  to  the 
moon. 

2935.  Observations  nf  Mr,  Ilimi  at  Ravehborgy  near  Engclhohn, 
—  Baily's  beads  were  seen,  both  before  and  after  the  total  obscura- 
tion, in  such  a  manner  as  to  leave  no  doubt  of  their  cause  being 
that  already  explained.  In  five  seconds  after  the  commencement 
of  the  total  obscuration,  the  corona  or  glory  around  the  moon's  disk 
was  seen.  Its  colour  seemed  to  be  that  of  tarnished  silver,  brightest 
next  the  moon's  limb,  and  gradually  fading  to  a  distance  equal  to 
one-third  of  her  diameter,  where  it  became  confounded  with  the 
general  tint  of  the  heavens.  Appearances  of  radiation  are  men- 
tioned, similar  to  those  described  by  Professor  Airy. 

**  On  first  yicwing  the  Bun,"  suys  Mr.  Hind,  *<  without  the  dark  glass^after 
the  commcDcemeut  of  totality,  three  rcse-coloured  prominenceB  immedi- 
ately caught  my  eye,  and  others  were  seen  a  few  seconds  later  Qfy.  6). 
The  largest  and  most  remarkable  of  them  was  situate  about  5®  noxlh  of 
the  parallel  of  declination,  on  the  western  limit  of  the  moon ;  it  wu 
Straight  through  two-tliirds  of  its  length,  but  curved  like  a  sabre  near  the 
extremity,  the  concave  edge  being  towards  the  horizon.  The  edge*  vere 
of  a  full  rose-pink,  the  central  parts  plainer,  though  still  pink. 

'  Twenty  seconds,  or  thereabouts,  after  the  disappesrance  of  the  son,  I 


ECLIPSES,  TRANSITS,  AND  OCCULTATIONS.  427 

ittiiDatad  its  length  at  45^^  of  arc,  and  on  attentivelj  watehing  it  towards 
tbe  and  of  totality,  I  saw  it  matarialljr  lengthened  ^probably  to  2^),  the 
aoon  having  apparently  left  more  and  more  of  it  Tiable  as  she  travelled 
■eroaa  the  sun.  It  was  always  corved,  and  I  did  not  remark  any  change 
if  fSoaiBy  Bor  the  slic^test  motion  daring  the  time  the  son  was  hidden.  I 
mw  this  extraordinary  prominence /our  teamdt  a/Ur  the  md  qf  iaUUHiff  bnt 
at  this  time  it  appeared  detached  from  the  snn's  limb,  the  strong  wlute 
Bdit  of  the  oorona  interrening  between  the  limb  and  the  base  of  ue  pro- 
wneneeL 

**  Aboat  10^  sontli  of  the  above  object,  I  saw,  during  the  totality,  a  de- 
tached triangnlar  spot  of  the  same  colour,  snspended,  as  it  were,  in  the 
H^t  of  the  eorona,  which  gradually  receded  from  the  moon's  dark  limb, 
as  die  moired  onwards,  and  was,  therefore,  clearly  connected  with  the  son. 
lis  fotm  and  poution,  with  respect  to  the  large  prominence,  continued 
txaetly  ^e  same  so  long  as  I  obserred  it  On  the  south  limb  of  the  moon 
appesred  a  long  range  of  rose-coloured  flames,  which  seemed  to  be  affected 
a  tremulous  motion,  though  not  to  any  groat  extent 

**  Tha  bright  rose-red  of  the  tops  of  these  pnjections  gradually  faded 
their  bases,  and  along  the  moon*s  limb  appeared  a  bright  narrow 
of  a  deep  violet  tint:  not  far  from  the  western  extremity  of  this  long 
9i  red  flamea  was  an  isolated  prominence,  about  4(K^  in  altitude,  and 
of  similar  sise  and  form,  at  an  angle  of  146^  from  the  north 
tewarda  the  east:  the  moon  was  deddedly  reddish-purple  at  the  beginning 
sf  totality,  bat  the  reddish  tinge  disappeared  before  its  termination,  and 
Iha  diak  asaomed  a  dull  purple  colour.  A  bright  glow,  like  that  of  twi- 
fig^t,  iodieated  the  position  where  the  sun  was  about  to  emerge,  and  three 
m  iimr  aaeonds  lat«r  the  beads  again  formed,  this  time  instantaneously, 
tat  leas  anmerous,  and  even  mom  uregular,  than  before.  In  five  seconds 
Mva  the  son  reappeared  as  a  very  fine  orescent  on  the  sudden  extinction 
ef  the  beada." 

2086.  OhiervaHoru  of  Mr,  Dawes  near  Engelholm,  —Mr.  Dawes 
obwrfed  the  beads,  and  foand  all  the  circumstances  attending  their 
appeuaooe  inch  as  to  leave  no  doubt  as  to  the  truth  of  the  cause 
gemnllj  assigned  to  them.  He  obserred  the  corona  a  few  seconds 
ifter  the  oommencement  of  the  totality,  and  estimated  its  extreme 
breadth  at  half  the  moon's  diameter,  the  brightness  being  greatest 
•ear  the  moon's  limb,  and  gradually  decreasing  outwards.  The 
phenomena  of  the  red  protuberances,  witnessed  by  Mr.  Dawes,  are 
ao  elearlj  and  satisfiu^torily  described  by  him,  that  we  think  it  best 
km  to  give  the  aooount  of  them  in  his  own  words, — 

«*  Throaf^ovt  the  whole  of  the  quadrant,  from  north  to  east,  there  was 
ae  visible  ptotaberanoe,  the  corona  being  uniform  and  uninterrupted. 
Betaeen  the  east  and  south  points,  and  at  an  angle  of  about  176^  fh>m 
the  aortli  point,  appeared  a  large  red  prominence  of  a  very  regular  conical 
knUf/g.  o.  When  first  seen,  it  might  be  about  1^  in  altitude  from  the 
•ige  of  the  noon,  bnt  its  length  diminished  as  the  moon  advanced. 

**  The  position  of  this  protuberance  may  be  inaccurate  to  a  few  degrees, 
Wag  aiore  haatily  noticed  than  the  others.  It  was  of  a  deep  rose  colour, 
•ad  lather  paler  near  the  middle  than  at  the  edges. 

"  Pjroeeeding  southward,  at  about  145<>  from  the  north  point,  commenced 
ft  low  ridge  of  red  prominencea,  resembling  in  outline  the  tops  of  a  very 
iiregalar  vaage  of  hills.    The  highest  of  these  probably  did  not  ftx<QM4 


W*.  nUitdnntiBd*!  AMwhHHwH".! 
•bo«tl97<>  fMa  tka  north  |Kdiit,&itaM hita(  ttM^artt  fkml  to* 
AarplT-deAnod  edp  of  th«  uww.  Th*  ImgalMWw  «l  Oa  )tif  «r  ttii 
■tdg*  aMitiwl  u  b«  pwoMaeB^  Int  Oay  MrMdjr  myiawa  ta  ^lidrii 
fron  thawwttawmrdBlhsMit;  pfobaMy  m  ■tinoaphria  ph— — w,  m 
Oa  triad  waa  la  th«  wmt 

••At  abont  220'eonnuwMl  aaatte low  ildfa  of  Aa  MMa  aiuMtab 
lad  axtanffiafc  to  about  2S0°,  leai  alontad  than  Oa  oOar,  aafl  aha  Iw 
bngolai  in  aatlinB,  azoapt  that  at  afaoot  SSS'  a  tvj  HHaikaUa  >Nt» 
baraoM  naa  from  It  to  aa  aldtodo  of  \y,  or  mora.  Tha  tint  aC  laalav 
ridgamaanlharpala^Bk;  Oa  oohnr  of  tka  aun  danlad  nadaMfi 
waa  daddedly  darter,  and  lis  briglitnow  mnoh  mora  iMi  b  fkv  M 
naaablad  a  A^*  tuA,  tha  eooTax  dde  Mng  Bortbvard^  aad  4a  « 
-  ■■^   -nth,    na^~ ^ '^     "■ ^' 


lew  itAja  aonnoMad  with  It,  w 
Iha  «Bd  of  tht  tataU^. 

"A  BmaQ  donUa-pdntad  pioinlM 
nothar  tow  ana  wlUi  a  Imad  baae,  ai 
»oa«  eolonrad  tin^  hot  xathar  palar  than  tha  laqa  aM  at  22t*. 

«Alino«tdiTaatl7|irw>Bd]nK,ar  at  S70<>,  appawad  a  hlmajfalMjpte 


fink  bodj,  fM9MH<i4  aalt  ware,fBlk»««  _    . 

tha  aooo'i  adga  whoi  Int  aaaa,  aad  tha  aaparaltaB  fa 
adnnoed.  It  had  Iha  appaariaoo  of  a  laiga  aaolod  pwtwIiwMaat  ^M 
bsM  waa  hidden  by  aoma  lotartenlog  aoft  and  lU-dannad  aiilwlaaaa.  Itt 
the  npper  p&rt  or  a  conical  mountain,  the  lower  portion  of  whidi  Wit 
obscarfrd  by  doucU  or  thick  milt.  I  think  tbe  apex  of  tfali  objcflt  Bail 
have  been  at  least  1'  in  atlitnde  from  the  moon'a  limb  when  flnt  ae^  aad 
more  than  \Y  towards  the  end  of  total  obaanratian.  Ita  oolonr  waa  fia^ 
and  I  thought  it  paler  in  the  middle. 

"  To  the  north  of  thi«,  at  aboDt  280°  or  286°,  appeared  tha  most  woadw- 
fol  phenomeaon  of  the  whole.  A  red  protuberance,  of  Tirid  hrinhtw 
and  very  deep  tint,  arose  to  a  height  of,  perhaps,  1}'  when  firet  aaen,  aad 
increwied  in  length  to  2',  or  more,  ae  the  moon's  progresa  rerealad  It  man 
eomplelely.  In  shape  it  somewhat  reaembled  a  TWiiiA  eiRutcr,  tha  MMlhaa 
edge  being  conTai.  nnd  the  eouthero  ooocaTe.  Towarda  tha  apex  It  baii 
anddenly  to  the  eouth,  or  upwards,  aa  seen  in  the  teleaeope.  Ita  northan 
edge  was  well  defined,  and  of  a  deeper  colour  than  the  reit,  anadaSy 
towardg  its  baae.  I  should  call  it  a  neK  earmint.  The  aosthem  edn  vai 
laae  distinctly  defined,  and  decidedly  paler.  It  gave  ma  tha  In  nil  lilMiai  of 
a  Bomewbat  conical  proluberanee,  partly  hidden  on  ita  aonthera  rfdt  to 
Bome  interrening  subatanee  of  a  soft  or  floeculaut  eharaotar.  Tha  apai  ef 
this  protuberance  wnt  paler  than  the  base,  and  of  a  purplish  tinga,  and  B 
certainly  had  a  fiickering  motion.  Its  baae  was,  from  first  to  laat,  ahaiplj 
boonded  by  the  edge  of  the  moon.  To  tny  great  astonishment,  thia  nar- 
velloua  object  amlinatd  vitibte  for  ahovl  five  tteendt,  aa  nearly  aa  I  aoald 
jndge,  tffler  tie  mn  brgim  lo  rcapptar,  which  took  place  tnany  dograea  ta 
the  soutb  of  the  situation  it  occupied  co  the  moon's  oiTcamfaraiiaa>  It 
then  rapidly  faded  away,  bat  it  did  not  roniiA  butunfmawa^.  Frua  its 
extraordinary  eiic,  curious  farm,  deep  colour,  and  riTid  brightaoaa,  tUa 
protuberance  absorbed  much  of  my  attention  ;  and  I  am,  tharofocw,  nitabla 
to  slate  prcqi:je1y  nhat  chntiges  occurred  in  the  other  phenomena  towuda 
the  end  of  the  total  obscaralion. 

■'  The  are,  from  about  283<>  to  the  north  point,  waa  antiRl-  tiwa  trtm 
promiDeaoes,  and  also  f^m  any  roseate  tint." 


BOUPSEQi  TRAKSITS^  AND  OCCULTATIONS.  429 

29S7.  EffacU  of  (oial  cbtcuration  on  turrounding  objects  and 
Kenery.  — Although  the  different  parties  of  obserrers  scattered  over 
the  path  of  the  idood's  shadow  were  not  equally  fortunate  in  having 
a  clear  unclouded  sky,  thev  were  all  enabled  to  observe  and  record 
the  effects  of  the  total  obscuration  upon  the  surrounding  objects 
and  oountiy.  Dr.  Eobertson  of  Edinburgh,  Dr.  Robinson  of  Ar- 
magh, and  some  others,  witnessed  the  eclipse  from  an  island  off  the 
coast  of  Norway,  in  lat  61^  21',  at  a  point  in  the  path  of  the  axis 
of  the  shadow.  The  precursory  phenomena  corresponded  with  those 
docribcd  by  oiher  observers.  The  atmosphere  was,  however,  ob- 
■eured  by  doadsi  which  appeared  to  rush  down  in  streams  from 
tke  place  of  the  son.  The  aea-fowl  flocked  to  their  customary 
places  of  rest  and  shelter  in  the  rocks.  The  darkness  at  the  moment 
of  total  obflooration  was  sudden,  but  not  absolute ;  for  the  clouds 
had  left  an  open  strip  of  the  sky,  which  assumed  a  dark  lurid 
enDg^,  which  changed  to  a  greenish  colour  in  another  direction, 
and  ahed  upon  persons  and  objects  a  faint  and  unearthly  light 
Lamps  and  candies,  seen  at  fifty  or  sixty  yards  distance,  were  as 
linUe  as  in  a  dark  night,  and  the  redness  of  their  light  presented  a 
staDge  contrast  with  the  general  green  hue  of  every  thing  around 
thtm.  ''The  appearance  of  the  country,"  says  Dr.  Eobertsoni 
■'seen  through  the  lurid  opening  under  Uio  clouds,  was  most  q^ 
palliiig.  The  distant  peaks  of  the  Tostedals  and  Dorieffeld  moun- 
tnns  were  seen  still  illuminated  by  the  sun,  while  we  were  in  utter 
daikaess.  Never  before  have  we  observed  all  the  lights  of  heaven 
and  asrth  so  entirely  confined  to  one  narrow  strip  along  the  horizon, 
^  never  that  peculiar  sreenish  hue,  and  never  that  appearance  of 
outer  darkness  in  the  pboe  of  observation,  and  of  excessive  distance 
in  the  veige  of  the  horizon,  caused  in  this  case  by  the  hills  there 
bdag  mora  highly  illuminated  as  they  receded  by  a  less  and  less 
fl^psedsnn.'' 

Jur.  Hind  says,  that  during  the  obscuration  "  the  entire  landscape 
was  overspread  with  an  unnatural  gloom;  persons  around  him  assumed 
n  nneartUy  cadaverousaspect ;  the  distant  sea  appeared  of  a  lurid  red ; 
the  sonthem  heavens  had  a  sombre  purple  hue,  the  place  of  the  sun 
being  indicated  only  bv  the  corona  ;  the  northern  heavens  had  an 
intense  Tiolet  hue,  and  appeared  very  near.  On  the  east  and  west 
of  llie  northern  meridian,  bands  of  light  of  a  yellowish  crimson 
odloar  were  seen,  which  gradually  faded  away  into  the  unnatural 
pinple  of  the  sky  at  greater  altitudes,  producing  an  effect  that  can 
sever  be  efGused  from  the  memoiy,  though  no  description  could 
pve  A  just  idea  of  its  awfiil  grandeur.'' 

At  several  places  in  Prussia,  where  the  heavens  were  unclouded 
luu^  the  total  obscuration,  a  great  number  of  the  more  conspicuous 
stUB^  ss  well  as  the  planets  Jupiter,  Venus,  and  Mercury,  were 
visible.    Several  flowering  plants  were  observed  to  close  thftix  VAn^ 


AETttOBCatt. 


ttf.a 


MM,  Uids  lAaxih  bad  been  pnnoiuly  ijing  kbont  £a^(Mn^ 
ud  domestio  fowls  went  to  roost. 

2988.  Evidence  of  a  lolar  atmotphere.  — Man;  of  the 

■MU  atteDdiiig  total    soUr  eclipses  afford    stroDg    oortol 

erideiiM  (rf  tbe  existence  of  a  flolar  atmosplieie,  ezteadinr  to  %  IM 
bMgbt  liian  the  luininouB  coating  of  ue  snn,  tbe  pn&U^rf 
whieh  hu  been  alreadv  shown  (2550). 

Ufl  oorma,  or  brignt  raj  or  glory,  sarronnding  tbe  dark  Ak  n( 
the  mooB  whore  it  covers  die  ean,  b  obeerred  to  be  conoentriB  witk 
the  moon  ooljr  at  tbe  moment  when  the  latter  is  coDcentrio  witt  ftl 
■nn.  Is  other  positions  of  tbe  moon's  disk,  it  appe&ra  to  bs  OOK- 
oentrio  with  the  eun.  This  would  be  tbe  effect  prodneed  hf  a  mIK 
■on-lnminons  atmosphere  faintly  reflecting  the  snn'e  Bcht 

The  flORUM  npplics  no  exact  data  by  which  ths  Sd^t  of  & 
adar  atmoepfaere  thus  faintly  reflcctiog  light  can  be  aaMriaioed;  bit 
Sr  J,  HerBchel'  tbinks,  that  iroro  tbe  manner  in  which  the  £i^ 
Bntion  of  light  is  ntanifesled  on  the  Eun's  dish,  being  by  no  meau 
ndden  on  approacbiug  the  bordets,  but  extending  to  some  diatanM 
within  the  disk,  tbe  height  must  not  only  he  great  in  an  abaohitt 
■snae,  but  mutt  even  be  a  very  conuderable  fraction  of  the  nui't 
KiAi-diemeter ;  and  this  inference  is  strongly  confirmoii  hy  the  inmt- 
nous  corona  surronnding  the  eclipsed  disk. 

2939.  J'roballe  eauta  of  the  red  emanatioiu  in  total  wbr 
tdip$et.  —  It  appears  to  be  agreed  generally  among  astronomot 
that  the  red  emaoatiooa  above  described  are  solar,  and  not  Imui. 
If  they  be  adniitt«d  then  to  be  solar,  it  is  scvoely  possible  to 
imagine  tbem  to  be  solid  matter,  notwithstanding  the  apparent  eoo- 
itancy  of  their  form  in  the  brief  interval  daring  which  at  any  ow 
tame  tbcy  are  vbible ;  for  the  entire  dnration  of  their  visibili^  hsi 
never  yet  been  so  much  as  four  minntes.  To  admit  the  poaauMli^ 
of  their  being  solar  mountains  projectiog  above  the  Inminons  atWK 
sphere  sun-ouodiDg  the  sun,  and  rising  to  tbe  height  in  the  extokr 
and  non-luniinouB  atmosphere  forming  the  corona  iimi  iissij  to 
explain  their  appearance,  we  most  suppose  their  height  to  ainooBt  to 
nearly  a  twentieth  part  of  tbe  son's  diameter,  that  is,  to  44,000 
miles. 

The  feet  that  they  are  gaseous  and  not  solid  matter  appeai% 
therefore,  to  be  conclusively  established  by  their  enormous  ms^ 
nitnde,  tbe  great  height  above  the  surface  of  the  sns  at  which  th^ 
are  placed,  their  faint  degree  of  illumination,  and  the  oireniuluMM 
of  their  being  sometimes  detached  at  their  base  from  the  visihU 
limb  of  tbe  bud.  These  circumstances  render  it  probable  that  these 
renarkablo  appearances  are  produced  by  cloudy  masses  of  exbems 
tenuity,  snpportciJ,  and  probably  produced  in  an  extenrave  spherical 
shell  of  noD-lnminous  gaseous  matter,  surrounding  and  riring  sbofS 
the  iDminoDs  surface  of  the  sun  to  a  great  altitude. 


ECLIPSES,  TRANSITS,  AND  OCCl'LTATIONS.  431 

n.  LuNAB  Eclipses. 

2940.  Oauie  of  lunar  ed^ms, — ^When  the  moon  is  in  opposition, 
iti  apparent  disUuoe  from  the  plane  of  the  ecliptic  or  its  latitude, 
vafjing  from  0°  to  apwards  of  5^,  is  at  times  less  than  the  apparent 
semi-diameter,  om,  fig.  798,  of  the  section  of  the  earth's  conical 
shadow ;  in  which  case,  falling  more  or  less  within  the  shadow,  it 
will  be  deprived  of  the  sun's  light,  and  will  therefore  he  eclipsed. 

The  circumstances  and  conditions  attending  such  a  phenomenon 
depend  evideutlj  on  the  dimensions  of  the  earth's  shadow,  the  mag- 
utiide  of  its  section  at  the  moon's  distance,  and  the  position  of  the 
nooo  in  relation  to  it. 

2941.  DinxeMuyiis  of  the  earth's  ahadow,  —  Let  s,  A,  /,  and  hi 
expiess,  as  before,  the  apparent  semi-diameters  and  horizontal  paral- 
laxes of  the  sun  and  moon,  and  let  s  express  the  semi-angle  efa! 
of  the  conical  shadow,  and  s'  the  apparent  semi-diameter  oa'n  of 
tike  eectioQ  of  the  shadow  at  the  moon's  distance.  Bj  the  common 
principles  of  geometry  we  shall  then  have 

8=s  —  A        8'  =  A'  —  8  =  A-fA  —  «. 

Let  L  express  the  length  a'f  of  the  shadow,  in  semi-diameters  of 
the  euth.     We  shall  then  have  (2297) 

206265      206265 
L  = = T-, 

8  8 A 

f  and  A  being  expressed  in  seconds. 
The  mean  value  of  s — A  being  952'',  we  shall  have 

L  =  206. 

2942.  QmJitionM  which  determine  lunar  eclipses,  —  As  the  earth 
■ores  in  its  orbit  round  the  sun,  this  conical  shadow  is  therefore 
eonstantly  projected  in  a  direction  contrary  to  that  of  the  sun.  The 
axis  itffjig.  794,  of  the  cone  is  always  in  the  plane  of  the  ecliptic, 
ad  its  vertex  /  describes  an  orbit  which  lies  in  the  plane  of  the 
•rfiptir-,  outside  that  of  the  earth,  at  a  distance  somewhat  above  206 
leiu-diameters  of  the  earth.  Any  body,  therefore,  which  may 
happen  to  be  in  the  plane  of  the  ecliptic,  or  sufficiently  near  to  it, 
and  within  this  dbtance  of  the  path  of  the  earth,  will  be  deprived 
of  the  snn's  light  while  it  is  within  the  limits  of  the  cone.  The 
moon  bang  the  only  body  in  the  universe  which  passes  within  such 
a  distanoe  of  the  earth,  is  therefore  the  only  one  which  can  be  thus 
obseuied. 

At  the  distance  of  the  moon,  which  is  less  than  one-third  of  tho 
length  of  the  shadow,  the  section  of  the  dark  cone  is  a  circular  disk, 
the  apparent  semi-diameter  of  which,  according  to  what  has  just 
been  proved,  subtends  an  angle,  the  mean  and  extreme  values  oC 


4M  JBTBMOHXi 

which  will  be  found  bj  ipTing  to  tha  qmntitiei  whioh  eotar  dM  f» 
oeding  formula  for  s',  their  mean  and  extreme  TaioBi. 

The  greatest  talae  of  flf  will  be  ftmid  bj  aabtneliDg  At  kH* 
TaloB  of  the  sum  of  the  horiiontal  pazmllaxieay  and  it  ia  Uieiali 

Its  least  value  is  found  bj  sabtracting  the  greatest  vahM  of  the  m/i 
semi-diameter  from  the  least  values  df  the  horiiontal  paTallaysip  al 
it  is  therefore 

s' =  54^  7"— Iff  18"  =  87' 49^. 

The  mean  value  of  sf  is,  in  like  manner, 

8'  =  6r47''  — ie'2"  =  4r46". 

The  section  of  the  shadow  may  therefore  be  regarded  as  a  dsdE 
disk,  whose  apparent  semi-diameter  varies  between  ST' 49''  ani 
46^  42^^,  and  the  true  place  of  whose  centre  is  on  m  pmnt  on  tk 
ediptie  180°  behind  the  centre  of  ihe  sun.  A  lunar  eelipaa  is  jk^ 
dnced  by  the  superposition,  partial  or  total,  of  this  disk  on  that  of  tk 
moon,  and  the  circumstances  and  conditions  whidi  detenaine  woA 
an  eclipse  are  investigated  upon  the  principles  Ursady  ez]dained. 

By  the  solar  tables,  the  apparent  position  of  the  centre  of  the  si% 
from  hour  to  hour,  may  be  ascertained,  and  the  position  of  the  centra 
of  the  section  of  the  shadow  may  thence  be  inferred.  From  tba 
lunar  tables,  the  position  of  the  moon's  centre  being  in  like  manner 
determined,  the  distance  between  the  centres  of  the  section  of  tbs 
shadow  and  the  moon's  disk  can  be  ascertained.  When  this  distanee 
is  equal  to  the  sum  of  the  apparent  semi-diameters  of  the  mooo's 
disk  and  the  section  of  the  shadow,  the  eclipse  will  begin ;  the  dmv 
ment  when  the  distance  is  least  will  be  the  middle  of  tho  edipse, 
and  the  line  of  greatest  obscuration ;  and  when  the  distance  between 
the  centres  increasing  becomes  again  equal  to  the  sum  of  the  apparent 
semi-diameters,  the  eclipse  will  terminate.  The  computation  of  sD 
these  conditions,  and  the  time  of  their  occurrence,  presents  no  othtf 
difficulty  than  those  of  ordinary  arithmetical  calculation. 

The  magnitude  of  the  eclipses  is  measured,  like  that  of  the  sia, 
by  the  difference  between  the  sum  of  the  semi-diameters  and  the 
distance  between  the  centres. 

The  occurrence  of  a  total  eclipse,  and  the  moment  of  its  com- 
mencemeDt,  if  it  take  place,  are  determined  by  the  distance  between 
the  centre  of  the  shadow  and  that  of  the  moon  becoming  equal  to 
the  difference  between  the  semi-diameter  of  the  shadow  and  that  of 
the  moon.  Thus,  a  total  eclipse  will  take  place  if  the  moon's  lantads 
in  L  in  opposition  be  less  than 

h  =  8'  —  ^  =  (h  +  hT)  —  (s  +  ^); 

that  is,  less  than  the  difference  between  the  sum  of  the  boriionisl 
iliajies  and  the  sum  of  the  semi- diameters. 


ECLIPSES,  TRANSITS,  AND  OL'Cl'LTATloXS.  433 

Since  the  sum  of  the  horizontal  parallaxes,  even  when  least,  is 
much  greater  than  the  sum  of  the  apparent  semi-diameters,  even 
vhen  greatest,  a  total  eclipse  of  the  moon  is  always  possible,  pro- 
Tided  the  centre  of  the  moon  approaches  near  enoagh  to  the  centre 
of  the  shadow^  and  for  the  same  reason  an  annual  lunar  eclipse  is 
impossible. 

2948.  Lunar  ecHptic  limits.  —  That  a  lunar  eclipse  may  take 
place,  it  is  necessary  that  the  moon,  when  in  opposition,  should 
approach  the  ecliptic  within  a  distance  less  than  the  sum  of  the 
apparent  semi-diameters  of  the  moon  and  the  section  of  the  shadow. 
Let  its  latitude  in  opposition  be  L,  the  limiting  value  of  this  will  be 

l'  =  A  +  A'  -I-  •  —  «. 

If  the  latitude  of  the  moon  be  less  than  this  ^which  is  the  sum 
of  the  semi-diameters  of  the  moon  and  shadow;  an  eclipse  must 
lake  place. 

Bot,  as  in  the  case  of  solar  eclipses,  the  quantities  composing  this 
being  yariable,  the  limit  itself  is  variable.  If  such  values  be 
assigned  to  the  component  quantities  as  to  render  l'  the  greatest 
possible,  we  shall  obtain  the  latitude  within  which  an  eclipse  is  pos- 
nble.  If  such  values  be  assigned,  as  will  render  l'  the  least  pos- 
■ble,  we  shall  obtain  the  latitude  within  which  an  eclipse  is 
iMTitsble. 

To  obtain  the  major  limit,  we  must  take  the  greatest  value  of  h, 
Vf  sod  /,  and  the  least  value  of  «.     This  will  give 

l'  =-  61'  27"  +  16'  46"  —  15'  46"  =  1^  2'  28" ; 

ad  to  obtain  the  minor  limit,  we  must  assign  the  least  values  to 
kf  Vj  sod  /|  and  the  greatest  to  <,  which  will  give 

L'  =  54'  7"  +  14'  44"  —  16'  18"  =  52'  33". 

The  corresponding  distances  from  the  node^  determined  in  the  same 
aanner  as  in  the  oaae  of  the  solar  ecliptic  limits,  will  be,  for  the 
Major  limit, 

N8  =  11°  34' 38", 

lad  for  the  minor  limit, 

n'  8  =  9^  24'  22". 

If  the  moon  in  opposition  be  within  11^  34'  38"  of  its  node, 
therefore,  a  lunar  eclipse  may  take  place,  and  will  do  so,  if  the  ap- 
parent diameters  and  parallaxes  have  the  necessary  values ;  but  if 
it  take  place  within  9^  24'  22"  of  the  node,  an  eclipse  must  take 
place,  becanse  the  same  quantities  must  be  within  the  requisite 
limits. 

Since  the  snn  moves  through  these  limits  on  each  side  of  the 
■ode,  in  from  18 1  to  22}  days,  it  may  happen  ihat  wilhm  IYlq  Wm.^ 

HI.  57 


ASTaONOMT. 

tioD  may  take  place  at  either  node,  aud  cousequentlj  that 
t»  eclipae  may  Uike  place  nkhiu  the  jear. 
4.   Limit*  for  a  total  eclipse.  —  It  has  becu  explaiaed  tLat  ■ 
eclipse  can  onl^  take  place  wheD  the  moon's  latitude  in  oppo- 
^u  ia  less  than 

L  =  (A  4-  A-}  ~  (I  +  *")• 
'"  Hetermiiie  the  limit  within  wbich  ft  total  eclipse  is  potnble,  «i 
iBiign  to  A  +  A'  its  greatest,  and  to  *')-■'  ita  least,  riJiM> 

L'  =  (61'  27")  -  I")  =  ZV  SB". 

._^  distance  from  the  node  Gor.^poiii    ig  to  thb  is  theiefon 

N  s  =  CSC  58'0  X  ^^"*"  =  5°  M'  21". 

To  del«rinine  the  limit  nit  a  total  eclipse  is  incTitiblc, 

ast  assign  to  A  +  A'  its  to  a  +  «'  its  greatest,  nine. 

<  give 

l"  =  (54'  7")  —         4")  =  21'  3", 
v>d  the  ODTTCBponding  distance  from  lae  node  is 

N'  B'  =  (-21'  3")  X  ^^^  =  3°  65'  5". 

'When  the  distAUce  from  the  nodo  at  opposition,  therefore,  ii 
greater  than  5°  44'  21",  a  total  cnlipse  cannot,  and  when  less  tlita 
3°  54'  5",  it  most,  take  place.  Between  these  Jimils  it  may  or  nwy 
not  occur,  according  to  the  magnitude  of  the  parallnxes  and  apponol 
diameters. 

2945.  Greatat  duration  of  total  ecUpsi: — The  duration  ofatokl 
eolipae  depends  on  the  distance  over  which  the  centre  of  the  raoon'l 
disk  moves  relatiTcl;  to  the  shadow  while  passing  from  the  first  to 
tbe  last  internal  contact.  This  maj  vary  from  0  to  twice  the  greatest 
possible  distaocc  of  tbe  moon's  centre  froin  tbe  centre  of  the  sbsdow 
at  the  moment  of  iolernal  contact,  that  is,  to 

2l'  =  2(A+A')  — 2(<  +  «'), 
aod  this  at  its  greatest  value  is,  as  has  been  already  nhown, 

2l'  =  2  X  {30'58")  =  61'56"; 
and  since  tbe  moon's  centre  moves  synodically  through  half  a  minntf 
of  »p!ice  in  each  minute  of  time,  the  interval  necessary  ta  moie  over  j 
61'  66"  will  bo  two  hours  aud  four  mioote?,  which  ia  therefore  th. 
greatest  possible  duration  of  a  total  lunar  eclipse. 

2946.  Relative  number  of  lolaT  and  lunar  edipM*. —  li  mSi' 
evident,  from  what  has  been  ezplainod,  that  the  freqaenc^  of  e 
it  much  grefttei  than  that  of  lunar  eolipaes,  sinoe  two  at  le^(  of 


XCUPSES,  TRANSITS,  AND  OCCULTATIONS. 


435 


\ 


former  musfj  and  five  may,  take  place  within  the  year,  wbile  Dot 
one  of  the  latter  may  occur.  Nevertheless,  the  number  of  lunar 
which  are  exhibited  at  any  given  place  on  the  earth  is  greater  than 
that  of  solar  eclipses,  because,  although  the  latter  occur  with  so  njuch 
greater  frequency,  they  are  seen  only  within  particular  limits  on  the 
earth's  surface. 

2947.  Effects  of  (he  earth's  penumbra.  —  Long  before  the  moon 
enters  within  the  sides  of  the  cone  of  the  shadow,  it  enters  the  pe- 
nnmbra,  and  is  partially  deprived  of  the  sun's  light,  so  as  to  render 
the  illumination  of  its  surface  sensibly  more  faint.  When  once  it 
passes  within  the  line  a'j/,  fig.  799,  forming  the  external  limit  of 
the  penumbra,  it  ceases  to  receive  light  from  that  part  of  the  sun 
which  is  near  the  limb  h.  As  it  advances  closer  to  a'/,  the  edge 
of  the  true  shadow,  more  and  more  of  the  solar  rays  are  intercepted 
bj  the  earth ;  and  when  it  approaches  the  edge,  it  is  only  illumi- 
nated by  a  thin  crescent  of  the  sun,  visible  from  the  moon  over  the 
edge  of  the  earth  at  al.  It  might  be  thus  inferred,  that  the  obscu- 
ration of  the  moon  is  so  extremely  gradual,  that  it 
would  be  impossible  to  perceive  the  limitation  of  the 
shadow  and  penumbra.  Nevertheless,  such  is  the 
splendour  of  the  solar  light,  that  the  thinnest  crescent 
of  the  sun,  to  which  the  part  of  the  moon's  surface 
near  the  edge  of  the  earth's  shadow  is  exposed,  pro- 
duces a  degree  of  illumination  which  contrasts  so 
\(i  strongly  with  the  shadow  as  to  render  the  boundary 
of  the  latter  so  distinct,  that  the  phenomenon  pre- 
sents one  of  the  most  striking  evidences  of  the  ro- 
tundity of  the  earth,  the  form  of  the  shadow  ibeing 
accurately  that  which  one  globe  would  project  upon 
another. 

2948.  Effects  of  refraction  (f  the  eartKs  atmo- 
tphere  in  total  ccUpse.  —  If  the  earth  were  not  sur- 
rounded with  an  atmosphere  capable  of  refracting  the 
sun's  light,  the  djsk  of  the  moon  would  be  absolutely 
invisible  after  entering  within  the  edge  of  the 
shadow.  For  the  same  reason,  however,  that  wo 
continue  to  see  the  sun's  disk,  and  receive  its  rays 
after  it  has  really  descended  below  the  horizon,  an 
observer  placed  upon  the  moon,  and  therefore  the  sur- 
face of  the  moon  itself,  must  continue  to  receive  tho 
sun's  rays  after  the  interposition  of  tho  edge  of  the 
earth's  disk  as  seen  from  the  moon.  This  refracted 
light  falling  upon  the  moon  after  it  has  entered  within 
J%.  S09.  the  limits  of  the  shadow,  produces  upon  it  a  peculiar 
illumination,  corresponding  in  faintness  and  colour  to 
Ike  imjs  thus  transmitted  through  the  earth's  atmosphere. 


4M  ASiaOSOKT. 

To  render  thia  more  dear,  let  e/,_/E7.  809, 
of  the  e&rth  at  right  angles  to  the  axia  /  ot  tbe  shadow,  and  )«t 
acf  repreBent  the  limits  of  ihe  almoaphere.  Let  **/  be  tbe  ray 
Vrooeeding  from  the  edge  of  the  son,  and  forming  therefore  Uu 
tNnandaij  of  the  shndow,  considered  without  reference  to  ^e  atnio- 
rohere.  But  the  solar  rays  in  pawing  throagh  the  convex  ahdl  of 
ur,  between  a  aad  e,  are  tweeted  as  tbey  would  be  by  a  convex  len 
eoinpoaed  of  a  tniuparent  refracting  medium  (1028),  and  an 
tlieiefbre  lendeied  oonvergent,  so  that  tbe  ny  ( e,  instead  of  fMnng 
direotlf  to  m,  will  be  bent  inwards  lowarda  m',  while  the  ray  whia 
'  really  peases  from  e  to/ia  one  which  comes  in  the  dinectian /e,aBd 
tlieiefore  from  a  point  within  the  son's  disk.  The  mooa'e  dU^ 
therefore,  or  any  poiot  of  it  which  is  within  the  angle  ikcm',  wiD 
reoeire  this  refracted  light,  and  will  be  illaminated  b;  it  in  aiooA 
aaoe  with  its  colour  and  inteoaity. 

The  deflection  which  a  solar  ray  suffers  in  pas^ng  tlireugh  tha 
atmosphere  towards  e  on  tbe  side  of  the  sun,  is  equal  to  the  hori- 
■onttl  refraodoD,  and  as,  according  to  tbe  prioeiples  of  optiosf  10S4), 
it  Buffers  an  equal  refraction  in  passing  out  on  tbe  crtltec  nlt^  tli< 
total  deflection,  which  is  measured  by  the  angle  m  e  m',  it  tinto  |b 
horizontal  refractloa.  But  ihe  mean  value  of  the  horizontal  nfhc- 
tion  being  33',  the  mean  Tslne  of  the  angle  »i  e  m'  will  be  Qff.  Sat 
aincQ  the  greatest  value  of  m  e  o  is  45'  42"  (2942),  it  rallows  Hut 
the  refracted  ray  em' will  fall  upon  the  seetioo  of  the  shadow  at* 
point  beyond  its  centre  ;  and  since  tbe  same  will  take  pkee  at  lU 
points  around  the  shadow,  it  follows  that  tlie  entire  aeotuu  nil]  be 
more  or  less  illaminated  by  the  light  thus  refracted  :  the  inlBliliiy 
of  ancb  illumination  Increases  from  the  centre  towards  the  borden. 

2949.  The  lunar  du&  viiihle  during  lofal  ohsniratitxn.  —  Whca 
the  moon's  limb  first  enters  the  shadow  at  m,  tbe  contrast  md  citre 
of  the  part  of  the  disk  still  enlighl«ned  bj  the  dircot  rays  of  tiw 
sun  render  the  eye  insensible  to  the  more  feeble  illuminatiw  pn> 
duced  upon  the  eclipsed  part  of  the  disk  by  the  retracted  rtjft  Ai, 
however,  tbe  eclipse  proceeds,  and  the  magnitude  of  the  pari  <f  the 
disk  directly  entighteDed  decreases,  the  eye,  partly  reliend  fivn 
the  excessive  glare,  begins  to  pcrosive  very  faintly  the  eelipsol 
limb,  which  Is  nevertheless  visible  from  the  beginning  in  a  telescope, 
in  which  it  appears  with  s  dark  grey  hue.  When  the  entire  disk 
has  passed  into  the  shadow,  it  becomes  distinctly  visible,  diowing  a 
gradation  of  tints  from  a  bluish  or  greeoish  on  the  ontnde  to  a 
gradually  increasing  red,  which,  further  in,  changes  to  a  etdoar 
resembling  that  of  incandescent  iron  when  at  a  dull  red  heat.  At 
the  lunar  disk  approschcs  the  centre  of  tlje  shadow,  this  red  liiia 
is  spread  all  over  it.  Its  illumination  in  this  position  is  eometiiuK 
■0  strong  as  to  throw  a  sensible  shadow,  and  to  modor  dittiiMtl/ 


■CUPflES,  TRAHBITEI,  AHD  OCCULTAIIOH?L 


487 


ni1>l«  in  the  telescope  the  liDetments  of  light  and  ihadow  apon  its 

These  effects  are  altogether  similar  to  the  eucoeuion  of  tints 
developed  in  our  atmoapUere  at  aanset,  and  arise,  in  fact,  from  the 
aame  canse,  operating,  however,  vitb  a  two-fuld  intensity.  The 
■olar  raj'B  traversing  twice  the  thickness  of  air,  the  blue  and  green 
lights  are  more  effectually  absorbed,  and  a  still  more  inteuse  red  is 
imparted  to  the  tints  transmitted.  Without  pursuing  these  conse- 
onences  further  here,  the  student  will  find  no  difficulty  in  tracing 
uem  in  the  effects  of  sunset  and  of  sunrise,  and  of  evening  and 
noraing  tirilight. 

m.   EcLiFBXS,  Transits,  and  Ocgultations  of  toe  Jovian 

SrSTEH. 

2950,  The  motions  of  Jupiter  and  his  satellites,  as  seen  from  the 
earth,  exhibit,  from  time  to  time,  all  the 
effects  of  interposition. 

Let  J  J*,  fiif.  810,  represent  the  planet, 
j/j'  its  conical  shadow,  n  J  the  sun,  x 
and  if  the  po.-iitions  of  the  earth  when 
the  planet  is  in  quadrature,  in  which 
position  the  shadow  1/3'  is  presented 
with  least  obliquity  to  the  vieosl  line, 
and  therefore  least  foreshortened,  and 
most  distinctly  seen.  Let  bU  1^  d  repre- 
sent the  orbit  of  ono  of  the  satellites, 
the  plane  of  which  coincides  nearly  with 
that  of  the  planet's  orbit,  and,  for  the 
purposes  of  the  pmspnt  illustration,  the 
ktter  may  bo  considered  as  coinciding 
with  the  ecliptic  without  producing  sen- 
sible error. 

From  E  suppose  the  risnal  lines  E  3 
and  £  y  to  be  drawn,  meeting  the  path 
of  the  satellite  at  d  and  g,  and  at  i/and 
V,  and,  in  like  manner,  let  the  corres- 
ponding viauul  lines  from  E*  meet  it  at 
(?  and  cf,  and  at  a'  and  V.  I^t  c  and 
if  be  the  poiiii!i  whuru  the  path  of  the 
satellite  crosses  iho  limits  of  the  shadow, 
and  h  and  h'  tlie  points  where  it  crosses 
the  extreme  solar  rajs  whith  pass  along 
those  limits. 

If  I  express   the   length  j/  of  the 

shadow,  J  the  distince  nf  the  planet 

rif.  n*.  ^m  the  sun  in  semi -diameters  of  the 


phsrt.MKlraDdt'tlM  KDii-diaiiwIm  of  dM  m  wl  «•  ]Imi 
ntptalmlj,  we  ihall  hava  O^OIT) 


I  =  rf  X  - 


:^ 


Bat 

d  =  11227  r  »  441000  /  =  4400; 

Mtdlhoebn 

I  =  11227  X  ^^^^  =  1247; 

Uttt  ii  to  lay,  the  length  of  the  diulow  is  1247  aami-dBBielan  cf 
the  plweL  Now,  nnce  the  diilBDoa  of  the  moit  i^u>t»  nIdlitBii 
not  so  maoh  u  27  Bemi-diunetefg  of  the  phoet  (2760),  aad  daei 
the  orUta  of  the  ntellHea  are  almoet  enotly  in  tlw  ^n*  of  :thi 
orbit  of  the  pUnet,  it  is  oTident  that  thej  will  ateemin^  am 
through  the  ehadow,  and  almost  thnogh  iti  axil,  emj  iwmiin, 
and  the  lengths  of  their  pathe  in  the  shadow  will  bs  tc>j  Uttlllaa 
than  the  diameter  of  the  plaoet. 

The  fourth  eatellite,  in  ezlremel;  lan  oaaa 
tion  to  this,  pasaiDg  through  oppoeition  witbont 
In  general,  however,  it  may  be  ooasidered  that  all  thfl 
opposiucm  pass  through  the  shadoir. 

2951.  Jiffpctg  of  inlerjKHition. — The  planet  and 
lihit,  from  time  to  time,  fou  " 

2952.  iBt.  £'7.;mm  n/ t) 
the  satcUiles  pasa  behind  the  planet.  Their  entnaea  into  the 
shadow,  culled  the  immersion,  ia  marked  bj  their  sodden  oztuMtiaB. 
Their  passage  out  of  the  shadow,  called  their  mi«nioM,  is  mamfasted 
by  their  being  Euddenly  relighted. 

2953.  2Dd.  Eclipses  of  the  planet  by  the  tateOita.  —  What  tht 
satellites,  at  the  periods  of  their  oonjanetiooi,  pass  botweM  tba 
lines  «J  and  /f,  their  shadowe  are  projceted  on  the  mataet  of  Ibe 
planet  in  the  same  manner  aa  the  afandow  of  the  moon  is  pnjsiteJ 
on  the  earth  in  a  solar  eclipse,  and  in  this  ease  tha  ahaAnr  naj  be 
seen  moring  across  the  disk  of  the  planet,  in  a  direotion  puilU  to 
its  belts,  as  a  small  round  and  intensely  hlaok  spot. 

2954.  3rd.  Oa-ultniiont  of  the  latdlile*  by  Aa  pianet.  — When 
a  satellite,  passing  behind  the  planet,  is  between  the  taagODte  SJe' 
sad  Eo'b',  drawn  from  the  earth,  it  ia  concealed  from  the  obaener 
on  tbe  earth  by  the  interposition  of  the  body  of  the  pUoet.  It 
suddenly  disappears  on  one  side  of  the  plants  disk,  and  aa  sod- 
denly  reappears  on  tbe  other  side,  haying  passed  over  that  part  of 
ita  orhitwhich  is  included  between  the  tangents.  Thia  ' 
is  called  an  occultation  of  the  satellite. 

2935.  4th.   Trannl*  of  ihr  taldlil'*  ovfr  lAe  planet. 


lOLIPSSS,  TRAH8ITS,  AND  OCCULTATIONS.  489 

aatellite,  being  between  the  earth  and  planet,  passes  between  the 
tangents  e  j  and  E  j',  drawn  from  the  earth  to  the  planet,  its  disk  is 
projected  on  that  of  the  planet,  and  it  may  be  seen  passing  across, 
as  a  small  brown  spot,  brighter  or  darker  than  the  ground  on  which 
it  is  projected,  according  as  it  is  projected  on  a  dark  or  bright  belt. 
The  entrance  of  the  satellite  upon  the  disk,  and  its  departure  from 
it,  are  denominated  its  ingren  and  egress, 

2956.  All  iJiese  phenomena  manifested  at  quadrature.  —  When 
the  planet  is  in  quadrature,  and  the  shadow  therefore  presented  to 
the  visual  raj  with  least  effect  of  foreshortening,  all  these  several 
phenomena  may  be  witnessed  in  the  revolution  of  each  satellite. 

The  earth  being  at  e  or  e',  the  visual  lino  E  J  or  e'  /  crosses  the 
boundary  a/  or  a;  of  the  shadow  at  a  distance  2/  /  or  x  J  from  the 
pknet^  which  bears  the  same  ratio  to  its  diameter  as  the  distance  of 
Jupiter  from  the  sun  bears  to  the  distance  of  the  earth  from  the 
SOD,  as  18  evident  from  the  figure.  But  Jupiter's  distance  from  the 
son  being  five  times  that  of  the  earth,  it  follows  that  the  distance 
z  J  is  five  diameters,  or  ten  semi-diameters,  of  the  planet.  But 
nnoe  the  distance  of  the  first  satellite  is  only  six,  and  that  of  the 
weond  somewhat  less  than  ten,  semi-diameters  of  the  planet,  it  fol- 
kiws  that  the  paths  of  these  two  will  lie  within  the  distance  x  J 
or  iff. 

The  planet  being  in  quadrature  90^  behind  the  sun,  the  earth 
will  be  at  E,  and  the  entire  section  ccf  of  the  shadow,  at  the  dis- 
taneet  of  the  third  and  fourth  satellites  (which  are  15  and  27  semi- 
diametera  of  the  planet  respectively),  will  be  visible  to  the  west  of 
the  planet,  so  that  when  these  satellites,  moving  from  b,  as  indi- 
eated  by  the  arrow,  pass  through  the  shadow,  their  immersion  and 
emersion  will  be  both  manifested  on  the  west  of  the  planet,  by  their 
sodden  disappearance  and  reappearance  on  entering  and  emerging 
from  the  shadow  at  c  and  d.  But  the  section  of  the  shadow,  at  the 
distanoes  of  the  first  and  second  satellites,  being  nearer  to  the  planet 
than  X  a/,  will  be  visible  only  at  its  western  edge,  the  planet  inter- 
eeptioff  the  visual  ray  directed  to  the  eastern  edge.  The  immer- 
sioD|  therefore,  of  these  will  be  manifested  by  their  sudden  disap- 
pearance on  the  west  of  the  planet,  at  the  moment  of  their 
immeFsioD ;  but  the  view  of  their  immersion  will  be  intercepted  by 
che  body  of  the  planet,  and  they  will  only  reappear  after  having 
pasiicd  behind  the  planet. 

The  third  and  fourth  satellites,  after  emerging  from  the  shadow 
at  c ,  and  appearing  to  be  relighted,  will  again  be  extinguished  when 
they  eome  to  the  visual  ray  e  j  a',  which  touches  the  planet.  Tbo 
momeot  of  passing  this  ray  is  that  of  the  commencement  of  their 
oocnltation  by  the  planet  They  will  continue  invisible  until  they 
arrive  at  the  other  tangential  visual  ray  £  j'  h',  when  they  will  sud- 
denly reappear  to  the  east  of  the  plane^  the  occultation  ceasing. 


440  ASTRONOMY. 

In  the  cases  of  the  first  and  second  satellites,  the  commencemeDt 
of  the  occultatioD  preceding  the  termination  of  the  eclipse,  it  is  not 
perceived,  the  satellite  at  the  moment  of  the  interposition  of  the 
edge  of  the  planet  not  having  yet  emerged  from  the  shadow.  In 
these  cases,  therefore,  the  disappearance  of  the  satellite  at  the  com- 
mencement of  the  eclipse,  and  its  reappearance  at  the  termination 
of  the  occultation,  alone  are  perceived,  the  emersion  of  the  shadow 
being  concealed  by  the  occultation,  which  has  already  commenced, 
and  the  disappearance  at  the  commencement  of  the  occultation  being 
prevented  by  the  eclipse  not  yet  terminated. 

When  the  satellite,  proceeding  in  its  orbit,  arrives  at  h'j  its 
shadow  falls  upon  the  planet,  and  is  seen  from  the  earth,  at  E,  to 
move  across  its  disk  as  a  small  black  spot,  while  the  planet  moved 
from  h'  to  h. 

When  the  planet  arrives  at  g,  it  passes  the  visual  ray  E  j',  and 
while  it  moves  from  g  to  r/,  its  disk  is  projected  on  that  of  the 
planet,  and  a  transit  takes  place,  as  already  described. 

Thus,  at  quadrature,  the  third  and  fourth  satellites  present  sae- 
cessively  all  the  phenomena  of  interposition  :  1st,  an  eclipse  of  the 
satellite  to  the  west  of  the  planet  shows  both  immersion  and  emer- 
sion ;  2nd,  an  occultatii)n  of  the  satellite  by  the  planet,  the  disap- 
pearance aud  reappearance  being  both  manifested;  3rd,  the  eclipse 
of  the  planet  by  the  satellite ;  and  4th,  the  transit  of  the  satellite 
over  the  planet. 

2057.  Kffrcts  moilifnd  at  otJirr  elongations.  —  There  is  a  certain 
limit,  such  as  e,  at  which  the  emersion  of  the  third  and  fourth 
satellites  is  intercepted,  like  that  of  the  first,  by  the  ])ody  of  tho 
planet.  This  is  dcterininocl  by  the  place  of  the  earth  frora  which 
the  visual  ray  c  J  r'  is  directed  to  the  eastern  edge  of  the  section  oi 
the  shadow  at  the  planet's  distance.  Witiiin  this  limit  the  phe- 
nomena for  the  third  and  fourth  satellites  are  altogether  similar  to 
those  already  explained  in  the  case  of  the  first  and  second  satellites 
seen  from  E. 

When  the  earth  is  between  t  and  f  no  eclipses  can  be  witnes>p«l 
Tliose  of  the  satellites  are  rendered  invisible  by  the  interposition  of 
the  planet,  and  those  of  the  planet  by  the  interposition  of  the 
satellites. 

When  the  earth  is  at  e'  and  e',  tlie  phenomena  are  similar  t<^ 
those  manifested  at  e  and  E,  but  they  are  exhibited  in  a  difftTcut 
order  aud  direction.  The  occultation  of  the  satellite  precedes  its 
eclipse,  and  the  latter  takes  place  to  the  east  of  the  planet.  In 
like  manner,  the  transit  of  the  satellite  precedes  the  eclipse  of  the 
planet. 

The  student,  aided  by  the  diagram,  and  what  has  been  explaiueii^ 
will  find  no  difficulty  in  tracing  those  and  other  consequences. 


ECLIPSES,  TRANSITS,  AND  OCCULTATIONS.  441 

2958.  Fhenomena  predicted  in  Nautical  Almanack.  —  The 
times  of  the  occurrence  of  all  these  several  phenomena  are  calcu- 
lated and  predicted  with  the  greatest  precision,  and  may  be  found 
registered  in  the  Nautical  Almanack,  with  the  diagrams  for  each 
month,  to  aid  the  observer.  The  mean  time  of  their  occurrence  at 
Greenwich  is  there  given,  so  that  if  the  time  at  which  any  of  them 
are  observed  to  occur  in  any  other  place  be  observed,  the  difference 
of  such  local  time  and  that  registered  in  the  Almanack  will  give 
the  longitude  of  the  place  east  or  west  of  the  meridian  of  Greenwich. 

2959.  Motion  of  light  discovered^  and  its  velocit^measured  hy 
means  of  these  eclipses,  —  Soon  after  the  invention  of  the  telescope, 
Roemer,  an  eminent  Danish  astronomer,  engaged  in  a  series  of  ob- 
servations, the  object  of  wbich  was  the  discovery  of  the  exact  time 
of  the  revolution  of  one  of  these  bodies  around  Jupiter.  The  mode 
in  which  he  proposed  to  investigate  this  was,  by  observing  the  suc- 
cessive eclipses  of  the  satellite,  and  noticing  the  time  between  them. 

Now  if  it  were  possible  to  observe  accurately  the  moment  at  which 
the  satellite  would,  after  each  revolution,  either  enter  the  shadow, 
or  emerge  from  it,  the  interval  of  time  between  these  events  would 
enable  us  to  calculate  exactly  the  velocity  and  motion  of  the  satellite. 
It  was,  then,  in  this  manner  that  Koemer  proposed  to  ascertain  the 
motion  of  the  satellite.  But,  in  order  to  obtain  this  estimate  with 
the  greatest  possible  precision,  he  proposed  to  continue  his  observa- 
tions for  several  months. 

Let  us,  then,  suppose  that  we  have  observed  the  time  which  has 
elapsed  between  two  successive  eclipses,  and  that  this  time  is,  for 
example,  forty-three  hours.  We  ought  to  expect  that  the  eclipse 
would  recur  after  the  lapse  of  every  successive  period  of  forty-three 
hoars. 

Imagine,  then,  a  table  to  be  computed  in  which  wo  shall  calculate 
and  register  before-hand  the  moment  at  which  every  successive 
eclipse  of  the  satellite  for  twelve  months  to  come  shall  occur,  and 
let  QB  conceive  that  the  earth  is  at  a,  at  the  commencement  of  our 
obeenrations ;  we  shall  then,  as  Koemer  did,  observe  the  moments 
at  which  the  eclipses  occur,  and  compare  them  with  the  moments 
remtered  in  the  table. 

Let  the  earth,  at  the  commencement  of  these  observations,  be 
supposed  at  E,  fg,  756,  where  it  is  nearest  to  Jupiter.  When  the 
carUi  has  moved  to  e",  it  will  be  found  that  the  occurrence  of  the 
eclipse  is  a  little  later  than  the  time  registered  in  the  table. 

Aa  the  earth  moves  from  if'  towards  e"',  the  actual  occurrence  of 
the  eclipse  is  more  and  more  retarded  beyond  the  time  of  its  com- 
puted occurrence,  until  at  e"',  in  conjunction,  it  is  found  to  occur 
about  sixteen  minutes  later  than  the  calculated  time. 

By  observations  such  as  these,  Koemer  was  struck  with  the  fact 
that  his  predictions  of  the  eclipses  proved  in  every  case  to  be 


«niie  It  wtrald  at  first  occar  to  bim  tint  Ah  jhiwpmjy  aUl 
naa  from  wme  crrora  of  his  obserTatJoDs ;  bat,  if  neb  wenrn 
ewe,  it  might  be  expected  that  the  result  would  betnj  that  kind  «t 
inesolarity  which  is  always  the  chanoTer  of  sach  errort.  Thoail 
womd  be  expected  tli»t  the  prodidtied  liuM  wooU  ami  ill  J—  U 
later,  and  aometimes  earlier,  tfaan  the  ohesmd  tiae,  tad  tiial  H 
vould  be  later  aod  earlier  to  an  irregnlar  extent  On  tbe  flOBbiiT, 
it  vaa  obaervied,  that  while  the  eutii  mored  flcm  ■  to  ^»ll* 
obMrred  time  waa  ooDtiimaUj  later  than  the  pndioted  tiae,  mt. 


noreorer,  that  the  iDterral  by  whieh  it  was  latsr  taaHaaaSh  ui 
ngnlarly  incretaed.  This  wu  ao  eSeot,  then,  loo  renlar  ad  b» 
mtent  to  be  npposed  In  ■liiinfiiini  rim  laiiiiil  nnnii  iiTiiliiwiiiiii, 


it  tnnat  haTe  ita  widn  in  eome  phjaioal  eanae  vt  a  ng^lu  Und. 
Hm  attention  of  Hoemer  b^g  tiina  attraeted  to  tlw  ^mmdat,ht 

determined  to  pnmie  the  inTeatigation  by  eonlinning  to  uheww  tti 
aelipaea.  IKme  aoootdingly  rolled  on,  ud  the  eaiu,  tmHi|porA| 
the  aatronomer  with  it,  nwred  from  ^  to  ^. 

b  ma  now  fixind,  diat  though  the  time  obeemd  wu  ktor  tkn 
ttw  oompnted  time,  it  waa  not  ao  moch  so  as  at  i^ ;  md  m  H» 
earth  again  approaohed  oppoaition,  the  difference  beouw  kM  ui 
leas,  HDtil,  on  arriTing  at  e,  the  powtion  of  oppoaition,  the  obaemd 
eclipse  af^reed  in  time  exactly  with  the  computation. 

From  this  course  of  observation  it  became  apparent  that  the  late- 
ness of  the  eclipse  depended  altogether  on  the  increased  distasM 
of  the  Garth  from  Jupiter.  The  greater  that  distance,  the  later  w>i 
the  occurrcDce  of  the  eclipse  as  apparent  to  the  obaervere,  and  en 
calculating  the  change  of  distance,  it  was  found  that  the  delay  rf 
the  eclipse  w.is  exactly  proportional  to  the  increaae  of  the  earA'l 
distance  fri'in  the  place  where  the  eclipse  occurred.  Thoi,  wfata 
the  dirtli  WHS  it  e"',  the  eclipse  was  observed  sixteen  minntei,  ct 
ab<iui  1000  seconds,  later  than  when  the  earth  was  at  e.  Tbt 
diameter  of  the  orbit  of  the  earth,  Ee",  measuring  about  tVB 
hundred  milliona  of  miles,  it  appeared  that  that  distance  pradond 
a  delay  of  a  thousand  seconds,  which  was  at  the  rate  of  two  hnmbtd 
tbouaand  miles  per  second.  It  appeared,  then,  that  for  every  two 
hundred  thousand  miles  that  the  earth's  distance  from  Jupiter  vtf 
ioertiased,  the  observation  of  the  eclipse  was  delayed  one  aecond. 

Such  wcro  the  facts  which  presented  themselves  to  Roemer.  Hem 
were  they  to  be  explained  ?  It  would  be  absurd  to  suppoee  thai 
the  actual  occurrence  of  the  eclipse  was  delayed  by  the  inereaied 
distaocc  of  the  earth  from  Jupiter.  These  phenomena  depend  oolj 
on  the  motion  of  tbc  satellite  and  the  position  of  Jupiter*!  shadow, 
and  have  nothing  to  do  with,  and  can  have  no  dependence  on,  tha 
position  or  motion  of  the  earth,  yet  unquestionably  the  time  thej 
apptar  to  occur  to  an  observer  upon  the  earth,  I 
le  distance  of  the  earth  from  Jnpitcr. 


Z 


BCLIP8B8,  TRANSITS,  AND  OCCULTATIONS.  4^3 

To  solve  ihu  difficulty,  the  happy  idea  occurred  to  Roemer  that 
16  momeDt  at  which  we  see  the  extinction  of  the  satcjlite  by  its 
itrance  into  the  shadow  is  not,  in  any  case,  the  very  moment  at 
hich  that  event  takes  place,  bnt  sometime  afterward,  vis.,  such  an 
iterval  as  is  sofficient  for  the  light  which  left  the  satellite  just  before 
s  eztinetioii  to  reach  the  eye.  Viewing  the  matter  thus,  it  will 
B  apparent  that  the  more  distant  the  earth  is  from  the  satellite, 
16  loDser  will  be  the  interval  between  the  extinction  of  the  satel- 
t6  ftnd  the  arrival  of  the  last  portion  of  light  which  left  it  at  the 
irtli ;  bat  the  moment  of  the  extinction  of  the  satellite  is  that  of 
be  commencement  of  the  eclipse,  and  the  moment  of  the  arrival  of 
lie  light  ftt  the  earth  is  the  moment  the  commencement  of  the 
^M6  is  observed. 

Thus  Roemer,  with  the  greatest  felicity  and  success,  explained 
he  discrepancy  between  the  calculated  and  the  observed  times  of 
he  eclipses ;  but  he  saw  that  these  circumstances  placed  a  great  dis- 
»very  at  his  hand.  In  short,  it  was  apparent  that  light  is  propa- 
Eited  through  space  with  a  certain  definite  speed,  and  that  the 
aroamstances  we  have  just  explained  supply  the  means  of  measuring 
that  velocity. 

We  have  shown  that  the  eclipse  of  the  satellite  is  delayed  one 
Kcond  more  for  every  two  hundred  thousand  miles  that  the  earth's 
iistance  from  Jupiter  is  increased,  the  reason  of  which  obviously  is, 
that  light  takes  one  second  to  move  over  that  space;  hence  it  is 
ippaient  that  the  velocity  of  light  is  at  the  rate,  in  round  numbers, 
of  two  hundred  thousand  miles  per  second. 

By  more  exact  observation  and  calculation  the  velocity  is  found 
to  be  192,000  miles  per  second,  the  time  taken  in  crossing  the 
earth's  orbit  being  16m.  26*63. 

2960.  Eclipses  of  Saturn's  satelHtes  noi  observable.  —  Owing  to 
the  obliquity  of  the  orbits  of  the  Satumian  satellites  to  that  of  the 
primary,  eclipses  only  take  place  at  or  near  the  equinoxes  of  the 
plnet,  the  satellites  revolving  nearly  in  the  common  plane  of  the 
squalor  and  the  ring.  When  they  do  take  place,  these  eclipses  are 
n  difficult  of  observation  as  to  be  practically  useless  for  the  dete> 
Bination  of  longitudes^  and  have^  consequently,  received  but  little 
atentioD. 

IV.  Transits  of  the  inferior  planets. 

2961.  Conditions  which  determine  a  transit.  —  When  an  inferior 
[Janet,  being  in  inferior  conjunction,  has  a  less  latitude  or  distance 
from  the  ecliptic  than  the  sun's  semi-diameter,  it  will  be  less  distant 
from  the  sun's  centre  than  such  semi-diameter,  and  will  therefore 
be  within  the  sun's  disk.  In  this  case,  the  planet  being  between 
ihe  earth  and  the  sun,  its  dark  hemisphere  being  turned  towards 
the  earth,  it  will  appear  projected  upon  the  sun  s  disk  as  an  lii- 


444  Asnovoitr. 

teofldy  black  round  spot  The  appirantmoCiflii  of  thephBeiWag 
theo  retrograde,  it  will  appear  to  oiove  aenM  the  diak  ef  the  an 
from  east  to  west  in  a  line  sennblj  paralld  to  the  eeljpliai 

Sneh  a  phenomenon  ia  oalled  a  TBAvarTi  and  aa  it  em  otij  take 
plaoe  with  planets  whioh  pass  between  tiie_  earth  and  mB^  it  ii 
limited  to  YeDos  and  Meroniy. 

NotwithstandiDg  the  Yery  small  obliqnilj  of  the  otbita  of  dust 
planets,  it  is  evident  that  transits  ean  only  take  place  wkn  the 

planet  is  within  an  extremely  aaaU 
distanoe  of  ita  node.  Let  v  he  the 
node.  Jiff.  Sllj  #  the  eentve  of  the 
sun's  diu  on  the  eeBpde^  «t  the  dis- 
Fig.  811.  tanoe  Nf  from  the  node  at  vUeh  the 


edge  jp  of  the  diak  jmft  tooehea  Iht 
is  ement  f 


orbit  MO  of  the  planet  It  is  ement  that  a  transit  eaa  only  tahs 
place  when  the  sun's  centre  is  at  a  less  distance  tlum  ns  fiooi  At 
node. 

Let  0  express  the  obliquity  p  N  s  of  the  planet's  orbit  The  mesa 
▼alue  of  the  semi^diameter  s  p  of  the  sun  being  19  or  O^rSGflL  «f 
shaU  have  (2294) 

o  o 

The  obliquity  of  Mercury's  orbit  being  7",  we  shall  have 

N«  =  l^!i5  =  2<^18  =  2*>  IC, 

and  that  of  Venus'  orbit  being  3^*39^  we  shall  have 

.51® -24 

Thus  the  distances  from  the  node  within  which  the  transits  tike 
place,  the  planet  being  in  conjunction,  are  2®  11'  for  Merourj|tod 
4®  B(y  for  Venus. 

2962.  Intervah  of  the  occurrence  of  transits.  —  The  transits  of 
Mercury  and  Venus  are  phenomena  of  rare  occurrence,  especially 
those  of  Venus,  and  they  arc  separated  by  very  unequal  interrals- 
The  following  are  the  dates  of  the  successive  transits  of  Mercury 
during  the  latter  half  of  the  present  century  : — 

1845 May  8. 

1848 Nov.  9. 

1861 Nov.ll. 

1868 Nov.  4. 

1878 May  6. 

Those  of  Venus  occur  only  at  intervals  of  8,  122,  8,  106,  8, 122, 
fto.,  years.  Two  only  will  take  place  in  the  present  centnrv — in 
1874  and  1882.  r  r  j 


SCUPBK8,  TBAHSIT8,  AND  OCOULTATIONS. 


445 


2968.  7%e  tim'f  distance  determined  hy  the  transit  of  Vcmu,  — 
The  transits  of  Veniis  have  aoqaired  immense  interest  and  import- 
■noei  from  the  eirciimatance  of  their  supplying  data  by  which  the 
son's  distance  from  the  earth  can  be  determined  with  far  greater 
precision  than  by  any  other  known  method.  The  transits  of  Mer- 
C017  would  supply  like  data,  but  owing  to  the  greater  distance  of 
that  planet  from  the  earth  when  in  inferior  conjunction,  the  con- 
ditions affecting  the  data  are  not  nearly  so  favourable  as  those  sup- 
plied by  Venus. 

The  details  of  this  celebrated  problem  arc  much  too  complicated, 
■nd  involYe  calculations  too  long  and  intricate,  to  admit  of  being 
folly  explained  here,  but  there  is  no  difficulty  in  rendering  the  prin- 
eipb  and  spirit  of  the  solution  intelligible. 

It  will  oe  observed  that  although  the  exact  determination  of  the 
abeolate  distances  of  the  planets  from  the  sun  be  attended  with  some 
difficolty,  there  is  none  in  the  determination  of  their  relative  dis- 
tances. The  observation  of  their  synodic  motions,  which  may  be 
made  with  great  precision,  supplies  the  data  necessary  for  the  solu- 
tion of  this  problem  (2593),  and  it  is  thus  ascertained  that  the  dis- 
tances of  the  earth  and  Venus  from  the  sun  are  in  the  ratio  of  1000 
to  723. 

It  follows,  therefore,  that  when  Venus  is  directly  interposed  be- 
tween the  earth  and  sun,  as  she  always  must  be  when  a  transit  takes 
place,  the  ratio  of  her  distances  from  the  earth  and  sun  is  that  of 
277  to  723. 

I^*"  V,  Jig.  812,  represent  the  place  of  the 
planet  at  conjunction,  and  let  ee  and  s  s'  be  two 
lines  taken  at  right  angles  to  the  plane  of  the 
ecliptic,  and,  therefore,  to  the  direction  of  the 
planet's  motion.  The  planet  v,  viewed  from  any 
points,  such  as  p  and  jp',  upon  the  line  e  ^,  will  be 
seen  as  pnvjectcd  on  corresponding  points  p  and  p' 
of  the  line  s  b'.  Now  it  is  evident  that  the  dis- 
tance between  the  points  p  and  l*'  will  bear  to  the 
distance  between  the  points  p  and  p'  the  same 
ratio  as  VP  bears  to  v/?,  that  is,  728  to  277,  or 
261  to  1. 

If,  therefore,  the  distance  between  the  points 
p  and  ;/  upon  the  earth  be  known,  or  can  be  as- 
certained (which  it  always  may  be),  the  distance 
between  the  corresponding  points  p  and  p^  on  the 
sun  will  be 


Tic.  812. 


III. 


vv^=pp'  X  2  61. 

If  the  points  p  and  p^  were  visibly  marked  upon 
the  sun,  so  that  the  apparent  distance  betweeii  \)^^m 

38 


446 


AnCROVOMT. 


mlwmtk&r,  th«  Kbmt  wha  rf 


oould  be  ezaotly  metsnied  with  tlw  HuwvHvva 
I''  at  the  sun  would  be  aaeertiined ;  for  if  • 
the  apparent  distance  between  p  and  v^  thw  at 
have  for  the  linear  Taloe  id  V 

_  p  j/  _  pjf  X  8'61 


Supplied  with  this  datom,  the  diatanoe  d  of  the 
earth  would  be  (2294) 

r?=^-i- X  206265. 


rail  fipoa  Aa 


If  the  places  of  obeervadon  p  and  j/  be  not  plaeed  npoo  a  be 
at  right  angles  to  the  coliptiey  its  prmection  on  sneh  a  fim  can  be 
ascertained  by  computation,  and  may  oe  substttoted  fbr  It.' 

It  IS  evident,  therefore,  that  the  problem  is  redooed  to  Uia  del«^ 
mination  of  the  apparent  ancle  subtended  at  the  earth  by  the  two 
points  of  the  sun's  disk  p  and  p^,  upon  which  the  planet  la  prqjceled 
when  yiewed  from  the  two  places  j>  and  t/  upon  the  earth. 

But  since  the  blsck  spot  formed  by  tne  projection  of  the  phnst 
is  in  continual  motion  on  the  disk  of  the  sun,  it  would  be  innaefi- 
cable  to  determine  its  position  at  any  given  moment  with  the  oegree 
of  precision  necessary  to  compare  observatioDS  of  this  delicate  kind 
made  at  distant  places  on  the  earth.  Besides  which,  to  render  the 
observations  made  at  precisely  the  same  moment  of  absolute  time 
comparable,  it  would  be  necessary  that  the  difference  of  the  longi- 
tudes of  the  stations  be  known  with  a  degree  of  precision  not  attiin- 
able  under  the  circumstances. 

A  happy  expedient,  however,  has  been  imagined  by  which  thii 
difficulty  has  been  effectually  surmounted.  It  will  be  remembered 
that  the  motion  of  the  planet  v  is  at  right  angles  to  the  plane  of 
the  diagram,  and  therefore  to  the  line  ss'  supposed  to  be  dnwn 
upon  the  disk  of  the  sun.  The  apparent  paths  of  the  projectioDS 
p  and  P^  of  the  planet  on  the  sun's  disk  will  therefore  be  also  at 
right  angles  to  this  line  8  s',  and  parallel  to  each  other,  being,  in 

fact,  both  parallel  to  the  ecliptic. 

Let  s  f^yjig^  813,  represent  the  disk  of  the  snn 
which  is  at  right  angles  to  the  line  joining  the 
earth  and  planet  with  the  sun's  centre,  and  there- 
fore  to  the  plane  of  Jit/.  812.  Let  p  and  p',  foj. 
813,  represent  two  points,  upon  which  the  pUnet 
is  simultaneously  projected,  as  viewed  from  p 
and  p'fjjff.  812.  Let  s^,fg,  813,  be  thatdia- 
amctcr  of  the  sun's  disk  which  is  in  the  plane  of 
the  ecliptic.  The  apparent  paths  of  the  pro- 
jections of  the  planet  on  the  sun's  disk  will  be  parallel  to  8  s',  and 
will  therefore  be  m  n  and  m'  n'.     Now,  if  the  planet,  as  it  moves, 


Fig.  813. 


SCUPBB^  TRANSITS,  AND  OCCULTATIONS.  447 

were  to  lea^e  a  penDanent  mark  npon  the  disk  of  the  son,  lodioatiDg 
the  line  its  projection  followed,  seen  from  each  place,  it  would  be  an 
msj  matter  to  measure  the  apparent  distance  pf^  between  these 
lines,  and  thna  solve  the  problem.  No  such  permanent  mark,  nor 
any  other  Tiaible  indication,  however,  exists. 

The  synodic  motion  of  the  planet,  that  is  to  say,  its  motion  rela- 
tively to  the  sun,  however,  being  computed  and  known  with  the  ut- 
most precision,  this  motion  has,  with  the  greatest  felicity  and  suo- 
cesB,  been  used  as  a  means  of  estimating  the  distances  between  the 
dhords  m  n  and  m'  n'  of  the  sun's  disk,  along  which  the  planet  ap- 
pears to  move.  The  time  taken  at  each  place  by  the  planet  to  move 
over  the  chords  fit  n  and  m'  n'  being  exactly  observed,  and  the  rate 
of  the  apparent  motion  of  the  planet  being  exactly  known,  the 
number  of  seconds  in  each  of  the  chords  can  be  ascertained.  From 
these  data  the  length  of  pp^  may  be  computed.     We  shall  have 

cP*  =  cm*  —  wip* 

The  distances  rp  and  cp^  being  thus  determined,  their  difference 
vill  be  PP^,  which  will  therefore  be  known. 

To  determine  with  the  necessary  precision  the  duration  of  the 
taisit  at  each  place  of  observation,  it  is  necessary  to  ascertain  the 
txtct  moment  at  which  the  centre  of  the  planet's  disk  crosses  the 
Emb  of  the  sun  at  the  beginning  and  end  of  the  transit ;  but  as  the 
eeDtre  of  the  planet's  disk  is  not  marked  by  any  visible  or  distin- 
nishable  point,  this  cannot  be  directly  observed.  It  is  ascertained 
oj  noting,  as  precisely  as  possible,  the  times  of  external  and  internal 
eontact  of  the  planet's  disk  with  the  limb  of  the  sun,  both  at  the 
bepnning  and  end  of  the  transit  The  middle  of  the  interval  be- 
tween external  and  internal  contact  in  each  case,  is  the  moment  of 
the  passage  of  tho  centre  of  the  planet's  disk  over  the  limb. 

It  is  evident  that  the  solution  of  this  problem  includes  the  deter- 
ttination  of  the  horizontal  parallax  of  the  sun ;  for  the  linear  value 
of  1^  at  the  sun  as  seen  from  the  earth  is  the  same  as  the  linear 
Tdoe  of  I''  at  the  earth  as  seen  from  the  sun.  By  the  method  just 
cij^uned,  this  is  found  to  be  at  the  mean  distance,  466  miles,  and 
•inoe  the  horizontal  parallax  rt  of  the  sun  is  the  angle  which  the 
lemi-diameter  of  the  earth  subtends  at  the  sun,  it  is 

8963       ^„  . 

''  =  -466-  =  ^-^ 

and  the  distance  itself  of  the  sun  is 

d  =  206265  X  466  =  96,119,490  miles. 

In  the  practical  application  of  this  method,  various  circumstances 
aie  taken  into  account,  such  as  the  effects  of  the  diurnal  rotation  of 


44B  ASKBOaOMT.  .      ■ 

y.  OocuLtATioirft.  '*• 

2964.  OccvUaiion  defined.  —  When  tny  odMiidL  oljefl^  Ae  wot 
excepted,  is  concealed  by  the  interpodtion  of  another,  it  k  and  to  be 
OCCULTED,  and  the  phenomenon  ia  called  ooonxffATEOir. 

Strictly  speaking,  a  solar  eclipse  ia  an  oeeoHation  of  the  ami  hy 
the  moon,  but  usage  has  pvmk  to  i^  h]^  exoeptMn,  the  mudbo  of  an 
edipse. 

2966.  Oecult€Uum$hythemoon. — The  phenomena  of  this  chm, 
which  possess  greateat  astronomical  inteieat,  are  thoae  of  atars  and 
planets  by  the  moon.  That  bodr,  meaaoring  about  half  a  dsgne 
u  diameter,  moves  in  her  monthly  course  so  as  to  ooonlt  eveiy 
olject  on  the  firmament  wbich  is  included  in  a  lone  extending  to  a 
quarter  of  a  desree  at  each  side  of  the  apparent  path  of  her  eentra. 
All  the  stars  whose  places  lie  in  this  aone  are  snoeeasiYely  oeonlted^ 
and  disappearances  and  resppearances  of  the  more  oonspienous  onei^ 
as  well  as  those  of  the  planets  which  may  be  found  within  the 
limite  of  the  same  lone,  present  some  of  the  most  striking  effiseto 
which  are  witnessed  by  observers. 

The  astronomical  amateur  will  find  in  the  Nautical  AhnanaA  S 
table  in  which  all  the  principal  occultations,  both  of  stars  and 
plaDctSy  are  predicted. 

The  disappearance  takes  place  always  at  the  limb  of  the  moon, 
which  is  presented  in  the  direction  of  its  motion. 

From  the  epoch  of  full  moon  to  that  of  new  moon  the  mooQ 
moves  with  the  enlightened  edge  foremost,  and  from  new  moon  to 
fall  moon  with  the  dark  edge  foremost.  During  the  former  intervil, 
therefore,  the  objects  occulted  disappear  at  the  enlightened  edge, 
and  reappear  at  the  dark  edge,  and  during  the  latter  period  tbej 
disappear  at  the  dark,  and  reappear  at  the  enlightened  eage. 

The  disappearances  and  reappearances  when  the  moon  is  a  ores' 
cent  are  especially  remarkable.  If  the  disappearance  take  phM 
at  the  convex  edge,  notice  of  its  approach  is  given  by  the  vuQds 
proximity  of  the  star,  which,  at  the  moment  of  contact,  is  suddsnlj 
extinguished.  Its  reappearance  is  more  startling,  for  it  seems  to  b 
suddenly  lighted  up  at  a  point  of  the  firmament  nearly  htlf  s 
degree  from  the  concave  edge  of  the  crescent.  K  the  dtsappeu^ 
ance  take  place  at  the  dark  edge,  it  is  much  more  striking ;  the 
star  appearing  to  '*  go  out''  of  itself  at  a  point  of  the  sky  where 
nothing  iuterferes  with  it. 

The  moon's  horizontal  parallax  amounting  to  nearly  twice  iti 
diameter,  the  part  of  the  firmament  on  which  it  is  projected  tnd 
which  is  its  apparent  place,  differs  at  different  parts  of  the  earth. 
In  different  latitudes  the  moon,  therefore,  in  the  course  of  the 
month,  appears  to  traverse  different  zones  of  the  firmament,  and 
consequently  to  occult  different  stars.    Stars  which  are  occulted  is 


BCLIPSE8,  TRANSITS,  AND  OCCULTATIONS. 


449 


certain  latitudes  are  not  occalted  at  all  at  others,  and  of  those  which 
are  occulted,  the  durations  of  the  occultations  and  the  moments 
and  places  of  disappearance  and  reappearance  are  different. 

To  lender  this  more  intelligible,  let  n  s,  fig,  814,  represent  the 

earth,  n  being  its  north,  and  s  its  south 
pole.  Let  m  w!  represent  the  moon,  and 
m*  and  m'*  the  direction  of  a  star  which 
is  occulted  by  it  It  must  be  observed, 
that  the  distance  of  the  star  being  practi- 
cally infinite  compared  with  the  diameter 
of  the  moon,  the  lines  m^  and  m'*  are 
parallel.  Let  these  lines  be  supposed  to 
be  continued  to  meet  the  earth  at  /  and  X. 
Let  similar  lines,  parallel  to  these,  be 
imagined  to  be  drawn  through  all  points 
of  a  section  of  the  moon  made  by  a  piano 
at  right  angles  to  the  direction  of  the  star 
passing  through  the  moon's  centre.  Such 
lines  would  form  a  cylindrical  surface,  the 
base  of  which  would  be  the  section  of  the 
moon,  and  it  would  be  intersected  by  the 
surface  of  the  earth,  a  portion  of  which 
would  be  included  within  it,  one  half  of 
which  is  represented  by  the  darkly  shaded 
part  of  the  earth  between  I  and  V,  It  is 
clear  that  the  star  will  be  occulted  by  the 
moon  to  all  observers  situated  within  this 


Fig.  S14. 


space. 


While  this  cylindrical  space  is  carried  by  the  moon's  orbital  mo- 
tion from  west  to  east,  the  surface  of  the  earth  included  between  the 
parallels  of  latitude  /  n  and  V  n\  is  also  carried  from  west  to  east, 
Imt  much  more  rapidly,  by  the  diurnal  rotation,  so  that  the  places 
between  these  parallels  are  continually  overtaking  the  cylindrical 
fpaoa  which  limits  the  occultation. 

It  is  evident  that  beyond  /n  and  V  n',  which  are  called  the  ''  limit- 
ag  parallels^''  no  occultation  can  take  place.  At  I  and  V  the  star 
is  seen  just  to  touch  the  moon's  limb  without  being  occulted,  but 
within  those  limits  it  will  be  occulted.  The  middle  parallel  o  o\ 
between  the  limiting  parallels,  is  that  at  which  a  central  occultation 
ii  aeeni  and  where  therefore  the  duration  is  greatest. 

The  occultation  may  be  seen  from  any  place  upon  the  earth  which 
Hcf  within  the  shaded  zone,  and  will  be  seen  provided  the  pheno- 
menon  occur  during  the  night,  and  that  the  star  at  the  time  be  above 
the  horizon  at  such  an  altitude  as  to  render  the  event  observable. 

In  the  Nautical  Almanack  these  '^  limiting  parallels "  for  every 
aoBRMcnous  occultation  are  tabulated,  as  well  as  the  data  necessary 

88* 


to  «uiUe  ta  olscmr  it  uty  pnpowl  iBliMe  te  ■ 
whether  eiiy  pBrticnler  ooenltition  wiB  be  obHmbu. 

206S.  DflermmatiiM  of  hmgitKia  hg  tmar  oeemHatbn—li 
aammoo  with  ell  pbenomeiu  whieh  ma  be  aiaotlj  imdlflted^  uA 
whose  niBDifestatioii  u  inetuiteiMonit  Deoaltatkni  oc  atm  hj  the 
noon  ue  eminently  tiaefiil  for  the  ezaot  deteiminitiM  of  lon^tadei. 
The  freqnenoy  of  their  OGourrence  grntlT  ineteaaee  Uuir  atilttf 
in  thie  reepeot,  end  elthoo^,  for  niutioil  parpaeae,  the  iiliiiiii 
euDot  alwejB  choose  bis  time  of  obaemtion,  and  tberefcra  eamMl 
be  left  dependent  on  them,  the^  oome  in  aid  of  the  hmar  nwlhod  m 
TerifioalacHu;  u>d  for  geognphioal  purposes  on  Lmd,  an  viMnK  Urn 
best  means  wbidi  aeienoe  has  supplied.  The  timei  of  the  £m^ 
naranee  u>d  resppearanoe,  as  obserred,  being  emparad  with  tha 
Oreenvidi  limes  tabnlaled  is  the  Nantioal  Alntanaw,  tba  diflmaaa 
of  lbs  londtodes  is  inferred  after  a^ljing  the  nnnmnaij  oonseiioM. 

2967.  OeaMaliont  indicate  Ae  pranee  or  aiMNoa  ^  «*  oIbM' 
token  around  Ae  oexmUmg  hodg.  ^  When  a  star  is  oooaltal  fav  tbi 
mtk  of  Uie  moon  or  planet,  its  bri|htaesi^  prenoaalj  to  ito  Asap- 
peanuoe,  would  bs  more  or  less  dimmed  by  the  atmombem  wa- 
founding  niah  object,  if  it  ezisted.  Snoh  a  gradnal  ifiiuuMi  of 
brightneM  previoaBly  to  disappcanmce,  aa  well  as  a  like  inonase  of 
brightness  after  reappearance,  is  obBervsble  in  occultatiDns  bj  the 
disks  of  planets,  but  never  b;  the  disk  of  the  moon. 

It  is  hence  inferred  that  tLe  planets  have,  and  the  moon  baa  no^ 
an  atmosphere. 

It  might  be  objected  that  the  laaar  atmosphere  nay  not  ban 
snfficient  density  to  prodnoe  any  seosible  diminution  of  brightoeu. 
Aootber  test  Las,  however,  been  found  in  the  effect  which  the  re- 
fraction of  an  atmosphere  would  have  in  decreasing  the  duration  i£ 
an  occultation  (2483).  No  such  decrease  being  observed,  it  i> 
inferred  that  no  atmosphere  exists  around  the  moon. 

2968.  Singular  vitibiliijf  of  a  ttar  after  the  commencemmt  i^ 
oeeultation.  —  Some  observers,  of  sufBcient  weight  and  authority  to 
command  general  confidence,  have  occaidonslly  witnessed  a  pheno- 
menon in  occultutions  which  has  been  hitherto  uuexplained.  At 
cording  to  them,  it  Bometimes  happens  that  after  the  occulted  M 
has  passed  behiod  the  limb  of  the  moon  it  continues  to  be  seen,  ui 
even  for  a  considerable  time,  notwithstanding  the  actual  interpv- 
sition  of  the  body  of  the  moon.  If  this  be  not  an  optical  iUnwa, 
and  if  the  visual  rays  actually  come  straight  to  the  observer,  thej 
must  pass  through  a  deep  Qssure  in  the  moon.  Such  a  soppodtioa 
is  compatible  with  the  rare,  and  apparently  fortuitous,  occurreow 
of  the  phenomenon. 

2969.  Svggntfd  appfiratum  of  lunar  occullalwnt  to  moht 
double  ttart.  —  Sir  J.  Herschel  thinks  that  these  oocnltatioM 
voold  supply  means  of  ascertaintog  the  double  character  of  hbm 


TABULAB  S7N0P8IB  07  THE  80LAB  STSTBlf.  461 

sten,  the  indiYidiuIfl  suspected  to  compose  which  are  too  close 
together  to  be  divided  by  any  telescope.  He  thinks,  nevertheless, 
that  they  might  disappear  in  perceptible  succession  behind  the 
edge  of  the  moon's  disk.  It  does  not  seem  to  be  easy  to  conceive 
how  such  an  effect  can  be  expected  in  a  case  where  the  most  pow- 
erlvl  telescopes  have  fidled  to  resolve  the  stars. 

2970.   Oceuitatumi  by  Saium'i  rtngi,  —  In  the  case  of  stars 
oeenlted  by  Saturn's  rings,  a  reappearance  and  second  disappearance 
may  be  seen  in  the  open  space  between  the  ring  and  the  planet.     It 
has  been  affirmed  also,  that  a  momentary-  reappearance  of  a  star,  in 
the  space  which  intervenes  between  the  rings,  has  been  witnessed. 
Thifl  observation  does  not,  however,  seem  to  have  been  repeated, 
notwithstanding  the  recent  improvements  in  the  telescope,  and  the 
increased  number  of  observers.     The  passage  of  the  planet,  in  a 
finvonrable  phase  of  the  ring,  through  the  neighbourhood  of  the 
Bilky  way,  which  is  so  thickly  strewed  with  stars,  would  afford  an 
opportunity  of  testing  this,  and  might  also  supply  precise  evidence, 
positive  or  negative,  upon  the  question  of  the  existence  of  more  than 
two  concentric  rings.     K  other  black  streaks  seen  upon  the  surface 
of  the  ring  be,  like  the  principal  one,  real  openings  between  a  mul- 
tiple system  of  rings,  the  stars  sprinkled  in  such  countless  numbers 
over  the  regions  of  the  galaxy,  and  the  adjacent  parts  of  the  firma- 
laent,  would  be  seen  to  flash  between  ring  and  ring,  as  the  planet 
pittes  before  them.     Such  observations,  however,  would  require  in 
tke  telescope  the  very  highest  attainable  degree  of  optical  perfection. 


CHAP.  XVII 

TABULAR  8TN0P8IS  OF   THE   SOLAR   SYSTEM. 

2971.  Planetary  data.  —  Having  explained,  individually,  the 
aieumstances  attending  the  physical  condition  and  motion  of  the 
bodies  of  the  system,  it  remains  to  bring  them  into  juxtaposition, 
to  view  them  collectively,  and  to  supply,  in  tabulated  forms,  those 
QDmerical  data  which  at  any  given  time  determine  their  positions 
and  motions. 

Snch  data  may  be  resolved  into  three  classes :  — 

I.  Those  which  determine  the  orbit. 

II.  Those  which  determine  the  place  of  the  body  in  the  orbit. 
UL  Those  which  determine  the  conditions  which  are  independent 

of  the  oMt 


ASTROKOMY. 


Form  of  ihe 
erstooii  (2 


?  ihe/orm,  magnibuit,  andpanium  fif 
rbils  of  the  plancU. 
irhit  deUrmincd  hy  thr.  eretrntricity.  —  It 
1  ellipse  depends 


the 


t  the  form  of 
t,itj;  all  ellipses  with  the  same  eccentricity,  however  thej 
r  differ  in  magnitude,  having  the  same  form, 
uet  a  =  the  mean  distance,  c  =  the  distance  of  the  centre  of 
orbit  from  the  centre  of  tho  sun,  and  e  =  the  ewentricitj.    We 
U  then  have 


a]        of  0,  in  the  oases  of  all  tho  prinotpal  planets,  Uer- 
,  are  lesa  than  ■^.    In  the  case  of  Merour;,  it  u  aboat 
a  larger  planets  jV 

<  e  of  the  planetoids,  the  eccentric! tics  are  subject  to 

I  ana  (..^eptional  variation,  amounting  in  one  case  to  },  and  in 
■"  being  loss  than  A. 
3.  Magnitude   deifrmintd   b)/  wmi'OxU    major. —  Aa   the 
ricity  determines  the  form,  the  semi-axia  determines  the  mag- 
uii.uae,  of  the  orbit.     This  quantity  forms  in  other  respects  a  very 
important  planetary  element,  since  upon  it  is  dependent  alao,  by  the 
Barmonio  law,  the  periodic  time,  and,  ooiiae<]DeDtly,  the  mean  >» 
gular  and  mean  linear  velocity  in  the  orbit. 

2974.  Position,  of  the  plane  of  the  orbit.  —  The  plane  of  lb* 
orbit  must  always  pass  through  the  centre  of  the  sun,  which  i^ 
therefore  the  common  point  at  which  the  planes  of  all  the  planetaiy 
.  orbits  intersect.  But  to  define  the  position  of  the  plane  of  any 
orbit  something  more  is  necessary.  If  the  piano  of  the  earth's 
orbit  be  provisionally  assumed  as  a  fixed  plane  (which,  however,  it 
is  not,  as  will  appear  hereafter),  tho  positions  of  the  planes  of  tb< 
orbits  of  the  planets,  severally,  with  relation  to  it,  will  be  deter 
mined,  1st,  by  the  angle  at  which  they  intersect  it,  and,  £ndly,  bj 
the  direction  of  the  line  of  intersection. 

2976.  Indinationg  of  Ike  orbit*.  — The  angles  which  the  phoM 
of  planets'  orbits  form  with  the  plane'  of  the  ecliptic  are  gcnenillv 
less  than  3°.  Of  tho  principal  planets.  Mercury  forms  an  eiception 
to  this,  having  an  inclination  of  7°.  The  pinnefoids  are  also  eiwp- 
tional,  the  orbit  of  one  having  an  inclination  of  34 1°;  the  incljai- 
tions  of  the  others  varying  between  16°  and  1°. 

2976.  Line  of  noilct. —  The  inclination  is  ntit  enough  to  deter- 
mine the  position  of  the  plane  of  the  orbit,  for  it  ia  evident  that  as 
infinite  variety  of  difTerent  planes  may  be  inclineil  at  (ho  same  angle 
to  the  ecliptic.  If,  however,  the  direction  of  the  line  of  intersection 
of  the  plane  of  the  orbit  with  the  plane  of  the  ecliptic  (which  line 
nut  always  pass  through  the  centre  of  the  bdo)  be  also  defined, 


TABUI.AR  SYNOPSIS  OF  THB  SOLAR  STSTBM.  468 

the  poation  of  the  plane  of  the  orbit  will  be  determined.  This 
line  of  intersection  is  called  the  h'ne  of  nodes^  being  the  direction 
in  which  the  nodes  of  the  planet's  orbit  are  seen  from  the  snn.  If 
an  observer  be  imagined  to  be  stationed  at  the  centre  of  the  sun,  he 
will  be  in  this  line,  and  the  nodes  will  be  viewed  by  him  in  opposite 
directions  along  this  line,  the  ascending  node  (2625)  being  viewed 
in  one  direction,  and  the  descending  node  in  the  other. 

2977.  Longitude  of  atcending  node,  —  It  has  been  onstomary 
to  define  the  direction  of  the  line  of  nodes  by  the  angle  which  the 
direction  of  the  ascending  node,  seen  from  the  snn,  makes  with  the 
direction  of  the  "  first  pomt  of  Aries/'  or^  what  is  the  same,  by  its 
heliocentric  longitude. 

The  poution  of  the  plane  of  the  orbit  is,  therefore,  determined 
hj  its  inclination  and  the  longitude  of  the  ascending  node, 

2978.  Longitude  of  perihelion,  —  These  data,  however,  are  still 

insufficient  to  determine  the  position  of  the  orbit.     They  would  be 

nfficient  if  the  orbit  were  circular,  since  a  circle  is  symmetrical  with 

idation  to  its  centre.     But  the  orbit  being  an  ellipse,  the  major 

axis  may  have  an  infinite  variety  of  different  directions,  all  of  which 

shall  pass  through  the  sun's  centre,  and  all  of  which  shall  be  in  the 

■me  plane.     After  defining,  therefore,  the  position  of  the  plane  of 

the  orbit|  it  is  necessary  to  determine  the  position  of  the  orbit  upon 

that  plane,  and  this  is  determined  by  the  direction  of  its  major  axis, 

joit  as  the  plane  itself  was  determined  by  the  direction  of  the  line 

of  nodes,  and  as  the  latter  was  determined  by  the  heliocentric  lon- 

gitode  of  the  ascending  node;  the  position  of  the  orbit  upon  its 

plane  is  determined  by  the  heliocentric  longitude  of  perihelion 

(2608). 

2979.  Five  elements  which  determine  the  orbit,  —  The  orbit  of  a 

friaaet  is,  therefore,  determined,  in  form,  magnitude,  and  position^ 
vj  the  five  following  data,  which  are  called  its  elements  :  — 

1.  The  semi-axis,  or  mean  distance a 

2.  The  eccentricity e 

8.  The  inclination i 

4.  The  longitude  of  the  ascending  node r 

5.  The  longitude  of  perihelion rt 

mie  eccentricity  is  sometimes  expressed  by  the  angle  ^,  of  which 
i  is  the  sine,  which  is  called  the  "  angle  of  eccentricity." 

2980.  Elements  subject  to  slow  variation  —  Epoch.  — If  the  ele- 
lients  of  the  orbit  were  invariable,  they  would  bo  always  known 
when  once  ascertained.  But  it  will  appear  hereafter,  that  although 
for  short  intervals  of  time  they  may,  withcPut  sensible  error,  bo 
R«rded  as  constant,  some  of  them  are  subject  to  slow  variations, 
wmdh|  after  long  intervals,  such,  for  example,  as  centuries^  oomr 


Hjirti 

TlrtorLi  (CUd) 


PrOBcrrplDa  ■ 

JUPITER 

HATUBS 


ASTKONOMT.  ^^H 

TABLE  L  ^^ 

Db.U  which  determuie  Ihe  magnltnid 


cwessdo 

01SS7SIT 

(rsoaoon 


nt7,  tnd  on  th*  fiwadlntdtTi  April  ei 


UBDLAE  srHOPSia  or  the  solas  btbtsil 

TABLE  L 
DB  of  th«  PlADttuT  Orbita. 


-,-. 

Jsa;;?i°^. 

V.;&V.t"' 

tp-ct 

' 

« 

* 

u.T.ruii. 

; 

; 

u 

6T 

S3 

;« 

X 

42 

1  J«.=.^,  1300. 

B 

» 

Tl 

U 

U 

123 

43 

a 

•' 

n 

D 

0 

0 

0 

in 

DO 

2B 

" 

' 

« 

» 

M 

M2 

M 

51 

" 

s, 

12 

M 

W 

U 

lU 

, 

M 

21)  Jul  J,  im 

K 

X 

m 

u 

u 

m 

24 

11 

20Jnlj,lMi 

3 

17 

no 

M 

28 

M 

IB 

ii 

2H.S,iH«al>,r,lB»a. 

« 

IS 

IM 

23 

u 

sw 

44 

3 

3-0NoT.IIll»r,llM. 

U 

» 

111 

H 

u 

135 

42 

32 

39-4ipril,185L 

M 

ai 

131 

31 

M 

16 

13 

20 

130Jd]7,1B32. 

» 

» 

ua 

U 

e 

41 

20 

23 

8-0  Juno,  1S62 

U 

s 

110 

ao 

u 

3S 

49 

43 

210  ll^cb,  1831 

w 

u 

a 

a 

us 

71 

33 

U 

4-0  Jnot,  1832. 

« 

u 

KT 

33 

ST 

ai8 

2 

29 

M 

u 

lU 

M 

M 

311 

3 

ei 

no  JdIj,  18S2. 

n 

T 

S» 

29 

31 

301 

tb 

19 

0-0  JuBUT,  1831. 

a 

T 

«3 

IT 

to 

lis 

IT 

17 

1311  MH=h,  1881 

6 

U 

M 

61 

S3 

US 

23 

68 

130  JolT.  1962. 

ts 

10 

■m 

U 

I> 

« 

13 

14 

lJ-0  0clobn,IS6J. 

1 

n 

IM 

36 

43 

11 

2! 

B 

Sl-0  Much,  1*6X 

a 

K 

IM 

3 

U 

STI 

se 

» 

1-0  M.J.  ISM. 

u 

38 

140 

M 

S3 

IB 

iii 

t3 

lO-OJalj.lMl 

u 

IB 

SOS 

SO 

3 

IM 

1 

49 

M  Octabw.  IBja. 

la 

IS 

an 

0 

« 

31 

10 

IS 

^■iStpu-ab^r.mi 

u 

»» 

as 

_ 

1 

: 

19-4 

a4D«.l»],U.T,Bgi. 

u 

- 

n 

H 

- 

I 

^ 

33 

I  JMuiirr.  1800. 

» 

H 

in 

u 

T 

a« 

3 

30 

« 

a 

"L 

M 

A 

1B7 

30 

" 

■ 

i 

WM  ASTKOKOHT. 

plrtet;  diBon  ibe  orbits.  These  yariatioas  bare  been  calctilibJ 
with  rarprinog  prociEion,  and  are,  moreover,  found  to  W  pnigdn), 
■Ithtnigh  thur  periods  are  in  general  of  suvli  ipBgnhaia  m  ts 
■WpMa  not  only  the  limita  of  buama  life,  but  thoK  dC  ifl  hMB 

BiDM,  tharafon>,  the  planetary  objects  sre  thus  nhjwt  to%A> 
bat  eoBsluit  ehnge,  it  is  ncccsaarj  in  sfsigaing  tbnr  iiliiwiili  K 
urigo  alao  the  dbte  at  nhieb  the  orbits  had  these  daraoBli.  Vtm 
lbs  ntM  it  which  the  elementa  BeTcrall;'  vary  am  kaown^  Acr 
tdim  at  KDj  aaRigned  data  being  given,  their  value*  ■!  apf  «lb(r 
dal^  anterior  or  pasl^rior,  can  be  determined. 

Tbt  date  at  which  the  elemcDls  of  the  orbits  have  had  Oianfan 
ungned  to  then  U  technically  called  the  Erocii. 

298L  TabU  o/  ifut  ehmentt  of  Oie  orbitt.  — In  ths  pwAg 
labia  m  given  the  elemcDls  of  the  planetary  orUls,  aeivnHliil 
the  epochs  aasignpd  in  tbc  last  colaran.  Those  of  the  nun  iMsd; 
diicovered  planets  must  be  regarded  a«  provisionil,  and  aalfllt  Id 
■uch  corrections  v.s  future  obBcrrationa  mny  suggest. 

Tbc  elements  arc  taken  from  tbc  tables  pablishe<l  h;  the  Fi«Kh 
Board  of  liOngitwle,  with  the  exception  of  those  of  the  reesotiT 
discovered  planetoid  Lutetia,  ihe  elcffleals  of  which  m  Bfw, 
proviuonallj,  from  those  calculated  by  iM.  George  Kumker,  Jan., 
of  Hamburg.  {Comptes  Reiidus  de  I'Aeud.  dts  So.  t.  sXtT.  p- 
810.) 

To  illustrate  the  relative  mean  distaoccs  of  the  planela  fnun  tb< 
ann,  and  from  each  other,  n'e  have  delineated,  ncarlj  il  ikir 
proper  proportiona,  the  mean  distances  of  the  principal  pWMli^aBd 
the  phtoetoida  or  asteroids,  in^^.  815. 

II.  Dota  to  determine  Ihe  place  of  thepkmeL 

2982.  By  (he  rporh  and  the  ffiran  dat/jf  motion.— -Hm  wti^ 
being  defined  in  magnilade,  form,  and  position,  it  is  nraMVX** 
supply  the  data  by  nbicb  the  position  of  the  planet  ia  it  tl  but 
assigned  time  may  be  faund.  It  will  be  sufficient  fur  this  to  aaR^ 
the  position  which  the  planet  had  at  the  epoch,  and  the  poiodi.' 
tine,  from  which  ihe  mcao  daily  motion  of  the  plauet  oan  be  in. 
ferred.  By  means  of  this  motion,  the  mean  place  of  the  jidsDetfu 
any  given  time  anterior  or  posterior  to  the  epoch  can  be  dettr- 
mined. 

2983.  The  rqunihii  of  the  centrt.  —  To  God  the  true  phee  of 
the  planet,  a  further  ci>rrcction,  however,  is  necessary.  The  angnlif 
Telocity  of  the  planet  referred  to  the  sun  is  not  uTiifonn,  being 
greatest  at  perihelion  and  least  at  apbeliim.  Thedilltrvnco  b«tireFD 
the  position  which  the  ^Wet  ^tiM\4  \i«.n&,  «k  «&&  from  tb«  iss,  if 

its  BD^lar  motion  were  MKAor[n,kTi&  ^i.^^'Hoi^^wiadS^'Sei^V 


UBOEAB  8TB0P8IS  OF  TUE  SOLAK  BTBTEH. 


457 


ealled  tlie  "eqaatlna  of  the  centre,"  and  ta- 
bles are  compatcd  hj  which  thia  oorrectiou 
for  each  pl&eet  may  be  made,  so  that,  the 
mean  pliice  of  tbe  planet  in  its  orbit  being 
determioed,  the  true  place  may  be  found. 

2984.  Table  of  the  data  necenary  to  (fo. 
termine  the  p/iicr.  of  /lie  planet.  — In  the  fol- 
lowing tablu  are  given  tbe  data  which  are 
necessary  to  determine  the  mean  place  of 
each  of  the  pluneiB  fur  any  given  time.  In 
the  first  column  is  given  tbe  mean  longitude 
of  the  planet  at  tbe  epoch  assigned  in  Table 
L,  and  in  tlio  second  colmnn  is  given  the 
mean  daily  increment  of  hcliocentrio  longi- 
tude. 

The  siDERF.AL  PERIOD,  or  the  time  which 
the  planet  takes  to  make  a  complete  revoln- 
tion  round  the  sun,  is  given  in  days  and  years 
in  tbe  third  and  fourth  columns. 

If  the  equinoctial  points  were  fixed,  the 
riderca]  period  would  he  equal  to  tho  interval 
between  two  successive  returns  of  the  planet 
to  the  same  equinoctial  point.  But  the  eqni- 
noctial  points  are  subject,  as  will  appear  here- 
after, to  a  very  slow  retrograde  motion,  in 
Tirtue  of  which  the  first  point  of  Aries,  from 
which  right  ascensions  and  longitudes  are 
measured,  moves  annually  ^om  east  to  west 
upon  the  ecliptic  through  a  gpace  a  little 
less  than  a  degree.  A  planet,  therefore,  de- 
parting from  the  vernal  equinoctial  point, 
and  moving  constantly  from  west  to  east,  will 
return  to  that  point  before  it  completes  its 
revolution,  inasmuch  as  that  point  moving  in 
the  contrary  direction  meets  it  before  its  return 
to  the  point  of  departure. 

It  follows  from  this,  that  the  interval 
twcen  two  suecciisive  returns  to  tbe  veroai 
equinoctial  piiiiit  is  a  little  less  tban  the  side- 
real period.  This  interval  is  called  tbe  eqiii- 
Korlial peri-Jil,  and  is  given  in  the  fiflb  colomu 
Of  Table  II. 

The  synoilic  period  is  given  in  tbe  last 
column. 

2985.  Table  of  extreme  and  mean  dw- 
taHcn/nm  mn  anil  earth. — ^lo  Ta\)\«\.,*» 


ASTBO^OMT. 

TABLE  II. 

rtiich  detoriniDe  tbe  plic«i  or  the  Flaneti 


in  tbair  iMpeoliv*  Orblti  i( 


•-iSS" 

-"411 

■"                  1 

• 

» 

»-,.        1  .,-_^ 

TTMt 

1 

si 

"T..... 

m 

100 
3IB 

XK 

1« 

sg 

XH 

« 
aw 

M 
311 

3 

2B 

1! 

lJ92-;3fl 
30U3M 

1  or  sea  I  w 

S!16WM04 

lOODO 

3MMI 

'3100 

auo 
f 

ll-M 

luat 

USSS" 

ii! 

laM'ST 

ffiS 

UM-O 

ll»0-l 

ISSW 
9D4» 

»MBM*7J 

M*lli— 

XuoomU. 

^™ - 

»-■■" 

WPITB»_...." 

BAnrKN 

aKPTDNK 

mean  diatances  a  of  tbe  several  plaoets  from  the  sua  are  expressed 
in  Dumbers,  of  nlitcb  tbe  earth's  mean  distaoce  is  the  unit.  It  t> 
necessary,  hoireTcr,  to  compute  tbe  actual  mean  diEtsnces  lo  eome 
kcionn  units,  such  aa  miles.  To  oblatD  these  it  is  ouly  Deeessar; 
to  multiply  tbe  actual  meun  iliatHDCca  of  the  earth  in  miles  bj  tlie 
numbers  in  the  column  a  of  Tiible  I. 

It  it  also  necessary  to  assi^'u  tbe  ocloal  limits  of  tbe  VBryioK  dl>- 
lances  of  the  planets  as  nell  from  tbe  earth  as  from  the  sun.  Tbeie 
■re  easily  dctcrtuined  by  the  data  in  Table  I. 

2986.  Perihelion  <ind  aphtUon  dislancei,  — Let  tbe  extienw  iDtl 
mean  distances  of  the  earth  from  the  sun,  eipreased  in  milliouuf 
inilei^  be 


TABULA&  SYNOPSIS  0¥  THE  SOLAR  STSTBM.  469 

d   s  mean  distance 
cf  =  least  distance 
cf  '  =  greatest  distance : 

11  tlien  have^  according  to  what  has  been  alreadj  explained 
•▼edy 

=95,        cf  =  95  X  (1  —  c),        (f"  =95  X  (1  +  e), 

ae  of  e  in  the  case  of  the  earth  being  0  0 1679226. 
the  mean  and  extreme  distances  of  a  planet  from  the  sun  be 
manner  expressed  by  d,  d',  d"  in  millions  of  miles,  and  we 
iTe 

96a,      i/  =  95a  X  (1  — e),      D"  =  95a  X  (1  +  «). 

distance  s  of  a  planet  from  the  earth  at  superior  conjunction 
({oal  to  the  sum  of  the  distances  of  the  earth  and  planet  from 
,  we  shall  have 

8  =  D  +  rf. 

II  yaiy,  because  the  distances  from  the  sun  vary.  It  will  be 
^  when  the  earth  and  planet  are  both  in  aphelion,  and  least 
hey  are  both  in  perihelion.  If  6",  therefore,  express  the 
'*f  and  8'  the  least  possible,  distance  of  the  planet  when  in 
ition,  the  mean  being  expressed  by  s,  we  shall  have 

fi"  =  d"  -f  d"        s'  =  d'  +  d!. 

iistanoe  of  an  inferior  planet  from  the  earth,  when  in  inferior 
lion,  is  found  by  subtracting  the  planet's  distance  from  the 
m  the  earth's  distance.  If  o  express  the  mean  distance  of 
let  in  inferior  conjunction  from  the  earth,  we  shall  have 

0  =  rf  —  D. 

distance  will  vary  according  to  the  relative  positions  of  the 

the  elliptic  orbits,  and  will  evidently  be  greatest  when  the 

in  perihelion  and  the  planet  in  aphelion.     If  o"  and  o'  then 

,  as  before,  the  greatest  and  least  possible  distances  of  the 

n  inferior  conjunction,  we  shall  have 

o"  =  cf '  —  d'        o'  =  d  "  d". 

iistance  of  a  superior  planet  in  opposition  is  found  by  sub- 
the  earth's  from  the  planet's  distance ;  and  it  may  in  like 
be  shown  that  the  mean  and  extreme  distances  of  the  planet 

ntkm  from  the  earth  will  be 

0-T>  —  d        o"  =  l/'  —  d'        o'  =  1/  —  cf' . 

le  following  table  the  mean  and  extreme  distances  of  the 
inccessively  from  the  sun  and  earth  are  given  as  computed 
9  several  formulas.  The  method  of  computation  is  indicated 
mA  of  each  column.     (See  Table  on  next  pagd.) 


ASTHuNOMT. 

TABLE  ni. 
DUUuces  from  the  Sun  &ad  from  tha  Earih  in  mtlliaiig  of  MUca. 


- 

.— .r«I«.                       1 

*'"P- 

— 

*..g-J--«»  1 

»«-. 

...»,. 

.-. 

«.. 

a—. 

w 

u- 

M^ 

"*" 

rk 

-- 

-!!•■  +  » 

-oV 

-D+i 

:& 

-^ 

:i: 

= 

S1W4 

BIB'tt 
Ml** 

I 

Dtaw 

U1-3B 
9M    7 

au'78 

Ma-18 

M  M 
2M-3S 

4M-SI 

la-Ti 

30M1 
5B    IB 

3ia  0 

SM-O 

S»TB 

aB78 

MO- 
MS- 

S787T 
2»1M7 

MM 

ax    0 

tail 

4««a 

«■«: 

im-w 

lOTH 

rMEi 

1 

»HI 

«f'a 

Itirs 
SMI 

iSJ 

1      TtSi): 

sr^ 

P»1Ih 

See; 

NRPTUNB  

JMSM 

J32»ll 

Ksa-w 

tttr» 

III.    Condilioni  affecting  the  phytical  and  m«han\cal  lialt  of  fik 

jilanet  indepenJcnt/y  of  itM  orbit. 

2987.  Id  the  preceding  cluipfpre  wo  have  explained  and  illn»- 
tratcd  tlio  methods  bj  wliR*h  tli(.>  real  magniludes,  ntaases,  densitieB, 
diuTDal  rolxlioD,  oblateness,  and  gupcrficiai  gravity  of  the  plueti 
are  severallj  determioed.  These  data  and  some  others  are  brooEht 
tcu^ether  and  arraoged  ia  juilapoBitioo,  being  expre!<sed  DDmericuI;, 
with  relation  to  the  most  gcoerullj  useful  imila  in  Table  IV. 

The  methods  of  computing  m.iny  of  the  qaantities  and  magnitiido 


lASDLAB  BYaoPSn  Or  IHB  SOUa  8E8TBM.  Ml 

TABLE  IT. 
Dfttft  kffeetiiiB  tb*  naaM,  wluoh  ue  independuit  of  Its  Orbit 


t    ..       IMU     1,KD         U-t  ■-]  It^  DIU  ('fll  0  in  (KM 

niltt    <-iu  n,»D         I'l  ('•  t-1        c-wo       Mi'm         un-xn       ti-m 
iiiiCEajm     i*nt         itn*!         ii\n    iuiihie  u^ocsos  hhbi-ooo swU'Oa 


Km. 

^.. 

"jE 

l-;"'  H.n.k..    "'i".""  1^ 

4- 

'  f 

I- 

nm 

^,'' 

a.. 
m. 

~z 

arTTT 

^ 

irtt 

Il4« 

it-U 
Ml 

14)0    » 
QltB     « 

T      1-tl     tl  ll    II     ! 1 

4  o-o   H  »r  M  M  n    0  -y, 

ltd    M  u     0                  Y       \^ 

pvcn  in  the  several  columns  of  Table  IV,  hove  been  already  ei- 
plained.     Some  of  llicni,  however,  rcijuirc  furtber  elncidatioa. 

2988.  Mfihod  of  computing  thf.  extreme  and  mean  apparmS 
diamfteri.  —  The  real  diameters  8  being  ascertained  by  the  melhodi 
explained  in  (*2299),  the  estremo  TamCion  of  the  apparent  diamelft 
may  be  found  from  a  comparison  of  the  real  diameter  nith  the 
eztrene  and  mean  distAnces  d",  d',  d,  given  in  Table  III.  W° 
have  thus  (2294) 

«!'  =  i,  y,  206265,     *'  =  ~    X  206265,     «  =  i-  x  206265, 
d'  d'  d 

29fi9.  Sar/aea  and  volumei.  — The  surface  of  the  earth  oodsibU 
of  197  millions  of  aqunre  miles,  and  its  volume  of  259,800  tnillionf 
of  cubic  miles.  Let  these  numbers  be  expressed  respcctiTely  by  r! 
and  k".  Since,  Ibcn,  the  surfaces  of  spheres  are  as  the  Bt^naj^ 
and  their  volumes  as  the  cubes,  of  their  diameters,  if  &'  expceM  tba 
surface  and  A"  the  volume  of  a  planet  related  to  those  of  the  earth 
at  an  unit,  and  A"  the  volume  in  billions  of  cubic  miles,  we  absU 


TABULAE  8TN0P8IS  OF  THE  SOLAR  SYSTEM.  468 

2990.  The  maues.  —  The  masses  of  the  pUnets  in  relation  to  the 
■an  being  aseertained  by  the  several  methods  explained  in  (2633), 
ei  »eg,,  and  the  ratio  of  that  of  the  sun  to  the  earth  being  ascer- 
tained to  bo  354936  to  1,  let  A'"  express  the  mass  related  to  that 
of  the  earthy  and  S'"  to  that  of  the  snn  as  the  nnit.  We  shall  then 
have 


354936' 


By  which  A'"  may  be  inferred  from  X'". 

The  actual  weight  of  the  earth  in  trillions  of  tons  being  6069 
(2394),  let  the  weight  of  any  other  mass  in  trillions  of  tons  be  ^"^ 
and  we  shall  have 

«"'  =  A'"  X  6069. 

2991.  77^  densities,  —  The  mean  densities  being  the  qaotients 
obtained  by  dividing  the  volumes  by  the  masses,  and  the  mean 
density  of  the  earth  related  to  that  of  water  as  the  unit  being  5*67 
(2393),  let  the  mean  density  of  any  of  the  other  bodies  related  to 
that  of  the  earth  as  the  unit  be  Xj  and  related  to  water  a/,  and  wo 
ihall  have 

A'" 

X  =  —,y        of  =  X  X  5-67. 

A 

2992.  Certain  data  not  exactly  ascertained.  —  It  will  be  useful 
to  observe  that,  in  the  determination  of  several  of  these,  the  results  of 
the  observations  and  computations  of  astronomers  are  to  a  certain 
ezteot  at  variance,  and  a  corresponding  uncertainty  attends  such 
data,  as  well  as  all  conditions  which  depend  on  them  or  are  derived 
by  ealcalation  from  them.  This  is  more  especially  the  case  with 
the  masses  of  those  planets  which  are  unaccompanied  by  satellites, 
and  consequently  with  the  densities  which  are  ascertained  by 
dividing  the  masses  by  the  volumes. 

2993.  Eocample  of  the  masses  and  densities  of  some  planets, — 
As  an  example  of  the  character  and  extent  of  these  discrepancies, 
we  rive  the  following  estimates  of  the  masses  of  some  of  the  prin- 
cipu  planets  expressed  as  fractions  of  the  mass  of  the  sun.  The 
eolnmn  E  contains  the  values  assigned  by  Professor  Enck^,  from  a 
eomparison  of  all  the  authorities,  except  that  of  Neptune,  which  is 
riven  on  the  authority  of  Professor  Pierce.  The  column  F  contains 
the  values  adopted  by  the  French  Board  of  Longitude,  and  the 
eolumns  L  and  M  the  values  given  in  the  treatises  lately  published 
in  Oennony  by  Professors  Littrow  and  Mfidler. 


i 


ASTROi^OMY. 


K 

». 

^ 

». 

Slim 

SSTo 

-w7 

*.Ta 

MtU 

7Z'..:::::::. 

It  will  be  observed  that  in  Table  IV,,  as  well  as  in  the  preceding 
tftbles,  ibe  qaaDtities  are  in  all  cases  reduced  to,  and  cxprcBsed  in, 
those  actual  Blaodard  meajuros  and  weights  with  whicb  all  penoos 
■re  familiar.  The  utility  of  this  waa  very  foroiblj  cipreased  and 
very  happily  illustrated  by  the  Astronomer  Royal,  ia  the  popakr 
lectures  delivered  by  him  at  Ipswich. 

2994.  fnlensily  of  mlar  li'i/hl  and  hrat.  —  Since  the  intensity  of 
•olar  radiation  decreases  as  the  square  of  the  distance  from  the  mo 
decreases,  if  y  expresses  its  iotenaity  at  the  mean  disbracs  of  any 
planet  relative  to  ils  intensity  at  the  earth  as  the  unit,  we  shall  biTS 


2995.  Superficial  gravity. — The  superficial  gravity  of  a  spherical 
body  being  in  proportion  to  its  mass,  divided  Dy  the  aqoare  of  ib 
•emi-diameter,  and  the  height  through  which  a  body  hha  npon  the 
surface  of  the  earth  in  ooe  second  being  16'08  feet,  let  g'  expren 
the  superGcial  gravity  of  a  spherical  body  related  to  that  of  tba 
earth  as  the  unit,  and  let  /'  express  the  height  throngh  which  a 
body  submitted  to  it  would  &U  in  ooe  second,  and  we  shall  have 


-  i«' 


/•■- 


i  X  1601 


2996.  Orbital  velocities.  —  It  is  easy  to  show  that  it  fbllowa  as  ■ 
necessary  consequeuce  of  the  harmonic  law,  that  the  mean  orbital 
velocities  of  the  planets  are  in  the  inverse  ratio  one  to  another  of 
the  square  roots  of  the  distances;  for  since  these  Telocities  aie  pro- 
portional to  the  circumferences,  or,  what  is  the  same,  the  aemi- 
diameters  of  the  orbits,  divided  by  the  periods,  thoy  are  prapartioul 

to  — ;  but  since,  by  the  harmonic  lav,  P*  ia  proportioiuJ  to  (^,  ^ 

velocities  will  be  proportional  to  ~=^,  or,  what  is  the  same,  to  -rxr 

...  '^'*'  '*'*'' 

that  19,  iDversely  proportional  to  the  square  roots  of  tbe  mean  dis- 
tances. 
This  being  anderttood,  and  the  mean  orbital  velooi^  of  tbe  earth 


TABULAR  SYNOPSIS  OF  THE  SOLAR  SYSTEM.     465 

ezpresBed  in  miles  per  hour  being  68,890,  let  y  be  the  mean  velocity 
of  a  plmoet  related  to  that  of  the  earth  as  the  unit,  and  v'  its  mean 
felocity  in  miles  per  hour,  and  we  shall  have 

v=  -J,        y  =  vx  68890; 

and  since  the  ratio  of  miles  per  hour  to  feet  per  second  is  that 
of  5280  to  3600,  if  y"  be  the  velocity  in  feet  per  second,  we  shall 
have 

//      628 
360 

2997.  Superficial  velocity  of  rotation.  —  The  superficial  velocity 
of  a  planet  at  its  equator  in  virtue  of  its  diurnal  rotation  is  found 
by  comparing  the  circumferences  of  its  equator  with  the  time  of  its 
rotation.  By  the  elementary  principles  of  geometry,  the  circum- 
ference of  a  circle  whose  diameter  is  d,  is  d  X  3*1415,  and  if  t  ex- 
press the  time  of  rotation  in  hours,  we  shall  have  for  v,  the  velocity 
of  rotatkm  in  miles  per  hour 

a  X  31415 

T  ' 

which  may  be  reduced  to  feet  per  second,  as  before,  by 

.  528 

^  =  ^^360- 

2998.  Solar  gravitation.  —  The  general  law  of  gravitation  sup- 
plies easy  and  simple  means  by  which  the  force  of  the  sun's  attrac- 
tion at  the  mean  distance  of  each  of  the  planets  may  be  brought 
into  immediate  comparison  with  the  known  force  of  gravity  at  the 
waihce  of  the  earth. 

Let  this  latter  force  be  expressed  by  g.  It  will  decrease  in  the 
same  ratio  as  the  square  of  the  distance  of  the  body  affected  by  it 
increases.  The  distance  of  the  sun  beiug  24,000  semi-diameters 
of  the  earth,  the  intensity  of  the  attraction  which  the  earth's  mass 
would  exert  at  that  distance  would  be 


24000  X  24000  ""  576,000000  * 

Bot  the  mass  of  the  sun  being  354,936  times  that  of  the  earth,  it 
will  at  the  same  distance  exert  an  attraction  354,936  times  greater. 
The  intensity  of  the  attraction,  therefore,  which  the  sun  exerts  at 
the  earth's  mean  distance  will  bo 

354936  _     ff 

^  ^  24000*  ""  1626 ' 

ind  the  intensity  of  its  attraction  at  the  mean  distance  of  the  other 
planets  being  still  inversely  as  the  squares  of  the  distances^  will  ba 


ASTRONOMY. 


Hf  dividing  this  by  a*.     So  that  if  a  expreBS  this  attrectiou, 
i£e  height,  !□  thomanJtlia  of  an  ial^b,  tbroagh  which  a  body 
ed  at  each  distance  nauld  full  in  odo  sccodJ,  ne  shall  have 


"1626  a" 


)  X  12  X  o  =  192960  o. 


P»Titftte  to  die  I 
•biob  on  the  ear 


Bt  the  numbers  given  in  the  column  q,  it  ia  tbcro  to  be  undir- 
Btood  that  a  mass  of  matter  which,  placed  upon  tho  eurface  of  the 
earth,  would  weigh  the  number  of  pounds  expressed  b;  the  deaomi- 
natora  of  the  fractions  severally,  would,  if  submitted  only  to  the 
"l  attrMtion  at  the  reapective  mean  diataneea  of  tho  planets, 
nith  the  force  of  one  pound.  Tboa,  a  moss 
s  earth's  surface  would  weigh  1626  lbs.  would  weigh 
wly  ona  pound  if  exposed  to  the  sun's  attraction  in  tho  absence  of 
Um  oartb.  In  like  manner,  a  maas  which  upon  the  earth's  surface 
irouU  iragli  1467333  lbs.,  or  655  tons,  would,  if  exposed  to  the 
Nn'a  attraotion  at  the  mean  diatanco  of  2Jeptune,  weigh  only  one 
poand,  to  estremelj  is  the  iuteDsit;  of  eolar  attraction  enfeebled 
by  the  enormous  increase  of  distance. 

The  nnmben  given  in  the  column  f  have  a  more  absolute  sense, 
and  express  in  thnusandths  of  an  inch  the  actual  spaces  through 
which  a  body  would  be  drawn  in  one  second  of  lime  by  the  snn's 
attraction  at  the  mean  distances  of  the  planets  severally. 


IV.  Tabulated  Elements  of  thb  Satellites. 

2999.  The  elements  of  the  orbits,  and  other  physical  data  relating 
to  the  satellites  of  Uranus,  Jupitor,  and  Saturn,  so  far  as  they  have 
been  discovered,  are  given  in  Tables  V.,  VI.,  and  VII.  After  the 
explanations  which  have  been  given  above  respecting  the  correspond- 
ing data  of  tho  primary  planets,  no  difficulty  will  D«  found  in  oom- 
pKhending  those  tables,  and  the  manner  of  computing  thom. 

TABLE  V. 

Elements  oT  the  Uraniau  Sjstem. 


gSxii'^E-'-J't----- 

M 

^ 

**  ■'* 

§ 

St 

... 

m 

TABXSLASL  SYNOPSIS  Of  TilS  SOLAR  SYSTBM. 


467 


TABLE  VL 
ElementB  of  the  Jovian  System. 


L 

IIL 

III. 

17. 

ii.r.a. 

ILT.  0. 

M.T.  0. 

M.  r.  a. 

1  Jan.  VOL 
I-7W1 

1  Jan.  1801. 
S-551S 

1  Jan.  ISOl. 
7-IS46 

1  Jan.  I80L 
164888 

laiBJiittPB  (teri)     .... 

it«aK<tioa  .....•• 

ISft" 

615" 

S46" 

666" 

boM  Jiip*tar  i*  wt-Aniiitft 

6-0486 

8-629S 
4-SS500 

163602 
660000 

85-8981 

IIUOOO 

••          to  Baa  .    •    • 

Souil 

SomU 

:■■              .         ^    ^    .    .    • 

0 

0 

and 
Tari<bl« 

and 
▼anahla 

"»-•••••*• 

f      i'  -  ^aa  frvw •*'f b 

I"  164 

I'"070 

l"-747 

1"-4S6 

••           ••             Jtt,  Iter  - 

»'    40" 

ly    30' 

18'     16' 

6'    68" 

(HSe 

0-0239 

0-096 

00828 

»a«-  •  .... 

2308 

aot» 

3878 

8861 

1 

1 

1 

1 

^Mtk%  a  1 

^^■■M 

1736 

1284 

34 

70 

1 

1 

1 

1 

(■pifMr%«l 

67800 

43100 

11300 

984iO 

1 

1 

1 

1 

.Bv1k'k«l 

46-6 

33-d 

U3 

85-6 

1 

1 

1 

1 

W^lm\  a  1 

8-75 

6-6& 

2-63 

4-48 

rfKij.BiltpVlMW-     •     • 

8W78 

30716 

21513 

17748 

••        fael  per  Mcood      •    . 

S08ti6 

46153 

3S052 

90082 

1 

1 

1 

1 

MlBv»r4tJapitar,t*r.  ft  mm  I 

~u' 

Ifi 

90 

ttti 

•     lUI  Im1m<  ia  1  Heond 

I9-8S 

6-46 

SI46 

0-748 

■«  of  OTtNi  to  a  fixed  p'uc 

t»CKll 

OO    0-    0^ 

OO    67'    60" 

Oo    U*    20" 

Oo    14'    68" 

n  •!   th«    isad    pfataa    to 

•^aqMtor.    ...... 

OP    »    6" 

fp    I'    6" 

00    6'    2' 

0»    24'    4" 

rvtngrada  ramlblioa  of  aoitct, 

»614S 

Mi^rsoo 

681-0000 

TABLE  VIL 
Elementa  of  the  Satumian  System. 


L 

II. 

Kacaiadw. 

III. 
TWli)t. 

IV. 
Diooa. 

V. 
Rhaa. 

VI. 
T!aa. 

VIU 
Hyparioa. 

VIII. 
JapatM. 

II.T.  0. 

X.  T.  0. 

X.T.  0. 

M.  T.  0. 

M.  T.  0. 

X.  T.  0. 

K.  T.  0. 

X.  T.  0. 

•       •       • 

•hi'hw 

1780O 
08a 

1-370 

1836-0 
1-888 

1836-0 
2738 

18360 
4-517 

1830*0 
15-846 

89-5? 

I78IH) 
78-830 

IM)     . 

•  •        * 

i#  pen- 

•  «        • 

34-4 
8-3807 

43-1 
4-3125 

63"'4 
6-3386 

88"  4 
6-8308 

96"-6 
9-6528 

22i"-4 
82-1450 

280'? 
26- ? 

648e 

64*368 

186020 

i 

16IT80 

? 

? 

800836 
0-04? 

64°? 

296500 
008? 

420? 

35S225 

0-Oi? 

850  ? 

r0440 
2560  88' II'- 

lOSOOOO 

? 

? 

9414680 

i 
} 

lip,  iBet 
l»»a>d» 

84988 

61813 

1 
KKlt 

30976 

46325 

1 
I6-6 

27778 

40723 
1 

24516 

36S67 

1 

20763 

30152 

1 
Sl-48 

13636 

19608 

1 
438 

18216 

17980 

1 
700 

7888 

11880 

I 
8708 

t     .    . 

85-46 

4i-:7 

a«  ia 

♦       •        • 

«apac* 

18'IJ 

t.i068'4r- 

«704l'36" 

7-^ 
1133  43-46' 

4-62 

3J70  40*  48" 

937 

3630440" 

0-441 
137021'  94" 

o«:f 

> 

0088 
9680  triT' 
\ 

cnAP.  XVIII. 


I.   COME! 


^ 


3000.  Prffienci!  a/  thf  atlroaoTnrr.  —  For  the  civil  and  politint 
hislorian  the  past  alone  has  osistence  —  the  present  he  rare)/ ap- 
prehends; the  future  never.  To  the  bistorinn  of  science  it  is  pl^^ 
tnitted,  bowercr,  to  penetrate  the  depths  of  put  and  future  with 
ei]ual  clenrncss  ond  certainty  :  facts  to  come  sre  to  him  as  present, 
and  nnt  unfrequeatly  more  assured  ihan  facts  which  are  paHod. 
Although  this  elcar  perception  of  fauses  and  consequences  cbano- 
leriBes  the  whole  domain  of  physical  science,  and  clothes  the  natnn! 
philatopher  with  powers  denied  to  the  political  and  moral  inquirer, 
yet  foreknowledge  is  eminently  the  privilege  of  the  Bstronomer. 
Nature  bus  raised  the  curlaia  of  futuntj,  and  displayed  before  bim 
the  Buccession  of  her  decrees,  so  far  as  they  affect  tite  physical 
universe,  for  counlless  ages  to  corne  ;  and  the  revelations  of  which 
ebc  has  made  bim  the  icstrument,  are  supported  and  verified  by  a 
never-ceasing  train  of  predictions  fulfilled.  He  "  shows  ns  the 
things  which  will  bo  hereafter,"  not  obscurely  shadowed  out  in 
figures  and  in  parables,  as  must  necessarily  be  the  case  with  other 
reveUiious,  but  altcuded  with  tho  most  minute  precision  of  time, 
place,  and  tircnmstanee.  He  converts  the  hours  as  tboy  roll  into 
an  ever-present  miracle,  in  atteslalion  of  those  laws  which  bis  Creator 
through  him  has  unfolded  ;  the  sun  cannot  rise  —  the  moon  cannot 
wane  —  a  star  cunnot  twinkle  in  the  firmament,  without  being 
witness  to  the  truth  of  his  prophetic  records.  It  has  pleased  tho 
"  Lord  and  Governor  "  of  the  world,  in  his  inscrutable  wisdom,  to 
baffle  our  inquiries  into  the  nature  and  proximate  cause  of  that  wor- 
derfol  faculty  of  intellect  —  that  image  of  bis  own  essence  which  be 
has  conferred  upon  us;  nay,  the  springs  and  wheelwnrk  of  animil 
and  vegetable  vitality  are  concealed  from  our  view  by  an  impene- 
trable veil,  and  the  piide  of  philosophy  is  bumbled  by  the  spcclado 
of  the  physiologist  binding  in  fruitless  ardour  over  the  dissection  of 
the  human  brain,  and  peering  in  equally  unproductive  inquiry  over 
the  gambols  of  an  animalcule.  But  how  nohly  is  the  darkness 
whieh  envelopes  metaphysical  inrjuinca  CoropeDsated  bv  ibe  fiooJ 
of  light  which  is  shed  upon  the  physical  creation  !  There  >I1  is 
harmony,  and  order,  and  mnjcsty,  and  beauty.  From  the  chaoa  of 
social  aud  political  phenomena  exhibited  in  human  records — phe- 
nomena unconnected  to  our  imperfect  vision  hy  aoj  disooverablo 
hw,  a  irar  of  passions  and  prejudices,  governed  by  do  appucDt 


COMETS.  489 

purpose,  tending  to  no  apparent  end,  and  scttiDg  all  intelligible 
order  at  defiance  —  how  soothing  and  yet  how  elevating  it  is  to  turn 
to  the  splendid  spectacle  which  offers  itself  to  the  habitaal  contem- 
plation of  the  astronomer  I  How  favourable  to  the  development  of 
all  the  best  and  highest  feelings  of  the  soul  are  such  objects  I  tho 
only  passion  they  inspire  being  the  love  of  truth,  and  the  chiefest 
pleasure  of  their  votaries  arising  from  excursioDs  through  the  im- 
poung  scenery  of  the  universe  —  sceuery  on  a  scale  of  grandeur  and 
magnificence,  compared  with  which  whatever  we  are  accustomed  to 
call  anblimity  on  our  plauet  dwindles  into  ridiculous  insiguifi- 
eancy.  Most  justly  has  it  been  said,  that  nature  has  implanted  in 
our  boaoma  a  craving  after  the  discovery  of  truth ;  and  assuredly 
that  glorious  instinct  is  never  more  irresistibly  awakened  than  when 
our  notice  is  directed  to  what  is  going  on  in  the  heavens.  ''  Quo- 
mam  eadem  Natura  cupiditatcm  ingenuit  hominibus  veri  inveniendi, 
qood  faoillime  apparet,  cum  vacui  curis,  etiam  quid  in  coelo  fiat, 
scire  avemuff;  his  initiis  inducti  omnia  vera  diligimus;  id  est, 
fidelia,  simplicia,  constantia ;  turn  vana,  falsa,  fallcntia  odimus."  * 

3001.  Strikingly  illustrated  by  cometary  discovery.  —  Such  re- 
flections are  awakened  by  every  branch  of  the  science  which  now 
engages  ns,  but  by  none  so  strongly  as  by  the  history  of  cometary 
diKovery.  Nowhere  can  be  found  so  marvellous  a  series  of  phe- 
nomena foretold.  The  interval  between  the  prediction  and  its  ful- 
filment has  sometimes  exceeded  the  limits  of  human  life,  and  ono 
generation  has  bequeathed  its  predictions  to  another,  which  has  been 
filled  with  astonishment  and  admiration  at  witnessing  their  literal 
accomplishment. 

8002.  Motion  of  comets  explained  by  gravitation,  —  In  the  vast 
IrameWork  of  the  theory  of  gravitation  constructed  by  Newton, 
places  were  provided  for  the  arrangement  and  exposition  not  only 
of  all  the  astronomical  phenomena  which  the  observation  of  all  pre- 
ceding generations  had  supplied,  but  also  for  a  far  greater  mass 
which  the  more  fertile  and  active  research  of  the  generations  which 
focceeded  him  have  furnishod.  By  this  theory,  as  we  have  seen, 
all  the  known  planetary  motions  were  explained,  and  planets  pre- 
viooely  unseen  were  felt  by  their  effects,  their  places  ascertained, 
and  the  telescope  of  the  observer  guided  to  them. 

But  transcendently  the  gretitest  triumph  of  this  celebrated  theory 
waa  the  exposition  it  supplied  of  the  physical  laws  which  govern  the 
motions  of  comets,  as  distinguished  from  those  which  prevail  among 
the  planets. 

8003.  Conditions  imposed  on  the  orbits  of  bodies  which  are  sub- 
jfci  to  the  attraction  of  grnvitntion,  —  It  is  proved  in  the  propo- 
dtions  demonstrated  in  the  first  book  of  Newton's  Prinoipia,  wfiich 


*  Cic.  de  Fin.  Ron.  et  Mnl   ii.  14. 
III.  40 


470 


ASTRONOVY. 


propositions  form  in  substance  the  grooniiwarlE  of  the  endte  thuij 
of  gruvitutitin,  that  a  body  which  is  under  tho  tnflaence  of  ■  entnl 
force,  the  iutensity  of  which  decreases  as  the  square  of  the  dislaiiN 
iocreuses,  must  move  in  one  or  other  of  the  curvea  known  to  geo- 
meters as  the  "  COMC  SECTIONS,"  being  those  which  «re  formed  bj 
the  intersection  of  the  surface  of  t>  cone  b;  ft  plane,  and  thtt  the 
centre  of  attraction  must  be  in  the  fdci:s  of  the  ciure ;  and  in  oidcr 
to  prove  that  such  curves  arc  compatible  with  no  other  law  of  attne- 
Uou,  and  may  therefore  be  taken  as  conclusive  evidence  of  the  ciiM- 
cnce  of  this  law,  it  is  further  demonstrated  that  whenever  a  bodj  it 
observed  to  move  round  a  centre  of  attraction  in  anj  one  of  thwe 
curves,  that  centre  being  ita  focus,  the  law  of  the  attraction  will  be 
that  of  gravitation;  that  ia  to  saj,  it«  intensity  will  vary  in  ttie  iii- 

verse  proportioo  of  the  Wjautcf 

the  distance  of  the  moving  bodj 
from  the  centre  of  force. 

Subject  to  tbcae  limitatioo^ 
however,  a  body  may  men 
round  ihc  sun  in  any  orbit,  u 
any  distance,  in  any  plane,  and 
in  any  direction  wbalever.  1:  " 
may  describe  an  ellipse  cf  anj 
eccentricity,  from  a  perfect  rit- 
cle  to  the  most  el'iugated  oi-«l. 
This  ellipse  may  be  in  uovplaoe, 
from  thut  of  the  ecliptic  lo  ODe 
at  ri^lit  angles  to  it,  and  ibe 
body  may  muve  in  sutli  ellipiC) 


cither 


I  the  a 


the  earth  o 
reclion.  Or  tbo  Lmly  iliu=\ub- 
ject  to  bolur  allr;icti<jii  niuy  niovv 
in  a  parabola  with  i:s  point  ef 
perihelion  at  uuy  diMaoce  whi;- 
evcr  from  the  sun,  either  graiiri;: 
its  very  surface  or  swtcj.ing  U- 
yond  the  orbit  of  .Ni'plune,  it, 
in  Hue,  it  uiay  swet-p  round  lit 
eun  in  un  bjiwrMa,  enteriuj 
and   leaving  lliu  syrteui   iu  Ewj 


To  rcndi.r  thes 


•xpii. 


ivhich  are  of  tho  great.st  'luUn^l 


C0MBT8  471 

ill  iS^.  816,  the  fonns  of  a  yeiy  eooeDtrio  ellipse,  ah  a  h'y  a  para- 
boU  apjf^  and  an  hyperbola  a  h  h',  having  $  as  their  common 
focus,  and  it  will  be  convenient  to  explain  in  the  first  instance  the 
relative  magnitude  of  some  important  lines  and  distances  connected 
with  these  orbits. 

8004.  UUipHc  orbit — Ellipses  or  ovals  vary  without  limit  in 
their  eccentricity.  A  circle  is  regarded  as  an  ellipse  whose  eccen- 
tricity is  nothing.  The  orbits  of  the  planets  generally  are  ellipses, 
bat  having  eccentricities  so  small  that,  if  described  on  a  large  scale 
in  their  proper  proportions  on  paper,  they  would  be  distinguishable 
from  circles  only  by  measuring  accurately  the  dimensions  taken  in 
different  directions,  and  thus  ascertaining  that  they  are  longer  in  a 
certain  direction  than  in  another  at  right  angles  to  it  A  very 
eccentric  and  oblong  ellipse  is  delineated  in^</.  816^  of  which  a  a' 
is  the  major  axis.     The  focus  being  «,  the  periholion  distance  d  is 

•  a,  and  the  aphelion  distance  d!  is  «  a',  the  mean  distance  a  being 

•  e,  or  half  the  major  axis.  The  eccentricity  e,  being  expressed  by 
the  numerical  ratio  of  the  distance  of  the  focus  s  from  the  centre  c 
to  the  semi-axis,  we  shall  have 

B  C 

—  =  e,  8  c  =  a  X  e, 
a 

It  is  evident  from  what  has  been  just  stated,  then,  that  we  shall 
kave 

d  =  a  —  a  X  e  =  a  X  (1  —  c), 

tad  consequently 

d 
a  =  = — 


c' 


ad  also 

<f  =  a  +  aXe=aX  (l  +  c)  =  rfx 


l  +  e 


1  -c' 

Hence  it  is  evident  that,  if  the  perihelion  distance  and  eccentricity 
k  given,  the  semi-axis  a  and  the  aphelion  distance  d'  can  be  com- 
fited. 

By  the  properties  of  the  ellipse,  the  distance  of  any  point  from 
tte  ibcns  s  can  be  computed,  if  the  perihelion  distance  d,  the  eccen- 
tneitj  «,  and  the  angular  distance  of  the  point  from  perihelion  be 
pren.  Let  a  express  this  angular  distance,  which  is,  in  fact,  the 
v^le  formed  by  two  lines,  one  d,  drawn  from  s  to  a,  and  the  other 
tfrom  8  to  the  actual  place  of  the  body  in  the  ellipse.  It  is  proved 
m  geometry  that  the  value  of  z  may  be  determined  in  all  cases  by 
tbe  formula, 

y  1  +  e 

z  =  d  X  z ; 

1  +  €  X  COS.  a 

tbl  ii  to  saj;  if  the  perihelion  distance  be  first  mult\]^U^  X^'j  ^<^ 


ASTUONUllV.  ^^1 

ntridt;  increased  by  1,  and  tLe  prodsct  tlieii  divided  by  Su 
nber  foutid  b;  adding  lo  1  the  product  of  Lbe  eccentncilf  and 
eosiae  of  the  angular  diaUoee  of  llio  bodj  from  perihelion,  the 
.Jtiea;  fill  bu  the  dist.intw  uf  the  body  from  the  focus  t. 
From  thia  gpriera.1  furuiulu,  therefore,  the  cxpresaioD  for  the  difr- 
te  of  the  body  frum  the  fociu  in  every  position  can  be  found. 
u  at  90°  from  perihelion  we  have 

COS.  a  =  COS.  90°  =  0, 
tnd  therefore  the  dieUnce  i  (^  which  we  shall  call  /,  is 

1  =  J  X  (1  +  •). 
If  vre  auppoBe  a  =  180",  we  shall  reproduce  the  espressloa  for  th« 
aphelion  distnoce  <!',  for  cos.  180°  =  —  1 ;  and  therefore 

,f=,ix>i-;. 

It  will  be  Diefol  also  to  obaerve  &mX  the  coi.  » ie  po^Tf  when  •  ii 
lew.  Hid  nentiva  when  >  ia  gre>l«r,  than  90°. 

The  nnmDer  which  ie  ezpreued  by  <  ii  necawirily  \nm  tbu  If 
snoe  it  is  a  fiactioo  whow  nnmerator  «  c  ia  len  than  ita  denonuulot 
c  a.  The  more  eccentric  the  ellipse  is,  tiie  more  nearlj  eqna!  will 
(  c  be  to  c  a,  and  consequently  the  more  nearly  eqiud  to  1  will  be 
the  eccentricity  e. 

The  diatancc  I,  being  greater  thaa  the  perihelion  distance  d,  in 
the  ratio  of  1  +  e  to  1,  it  will  therefore  be  always  less  than  twiee 
this  distance,  inasiouch  as  1  -f-  «  is  always  less  than  2;  bat  tiu 
more  eccentric  the  ellipse  is,  the  more  nearly  will  I  approach  te 
twice  the  perihelion  distance  d.  Thus,  for  example,  if  e  =  0-999, 
we  should  have  I  ^^d  X  1-999,  which  falls  short  of  twice  the  peri- 
helion distance  by  not  more  than  the  1000th  part  of  that  dislauoe. 

The  curvature  of  the  ellipse  continually  increases  from  the  mean 
distance  to  perihelion,  and  oonsequently  decreases  from  perihelion 
to  the  mean  distance,  being  eqtial  at  equal  angular  <<!»'»«*«»■  from 
perihelion  as  seen  from  tbe  sun. 

It  is  evident  that  if  a  body  move  in  a  very  eccentric  ellipse,  md 
as  that  represented  in  Jig.  816,  whose  plane  ooinoides  exactly  or 
nearly  with  tbe  common  plane  of  tbe  planetary  orbits,  it  may  inter 
sect  tbe  orbits  of  several  or  all  of  the  planets,  as  it  is  represented  to 
dc  in  the  cgure,  although  its  mean  distance  from  the  snn  may  be 
less  than  the  mean  distance  of  several  of  those  which  it  tbna  inter- 
secta.  The  aphelion  distance  of  such  a  body  may,  therefore,  greatly 
exceed  that  of  any  planet,  while  its  mean  distance  may  be  len  than 
that  of  the  more  distant  planets. 

3005.  PuTaholic  orhiu. — Tbe  form  of  a  paraboUe  orbit  having 
the  same  perihelion  distance  as  the  elliptic  orbit  is  repn.eeoted  al 
app,  in  ^.  iil6.    This  orbit  oonsista  of  two  indeftialB  b      '  ~ 


COMETS.  '^''^ 

nmilar  in  form,  which  unite  at  perihelion  a.  Departing  from  this 
point  on  opposite  sides  of  the  axis  a  a'j  thei^  curvature  regularly  and 
impidlj  decreases,  being  equal  at  equal  distances  from  perihelion. 
The  two  .branches  have  a  constant  tendency  to  assume  the  direction 
and  form  of  two  straight  lines  parallel  to  the  az<s  a  a'.  To  actual 
parmlleliam,  and  still  less  to  convergence,  these  branches,  however, 
never  attain,  and  consequently  they  can  never  reunite.  They 
extend,  in  fine,  like  parallel  straight  lines,  to  an  unlimited  distance 
without  ever  reuniting,  but  assuming  directions  when  the  distance 
firom  the  focus  bears  a  high  ratio  to  the  perihelion  distance,  which 
are  practically  undistinguishable  from  parallelism. 

It  is  demonstrated  in  geometry,  that  if  d  express  the  perihelion 
distance  and  z  the  distance  of  the  body  at  the  angular  distance  a 
from  the  perihelion,  we  shall  have 

_        2d 

z  —  ^  • 

1  +  COS.  a 

that  is  to  say,  the  distance  z  is  found  by  dividing  twice  the  peri- 
helion distance  by  1  added  to  the  cosine  of  the  angular  dbtanoe 
from  perihelion.' 

It  mnst  be  mentioned,  however,  that  when  a  is  greater  than  90^, 
the  oonne  is  negative,  and  its  value  must  then  be  subtracted  from  1 
to  obtain  the  divisor. 

To  find  the  distance  I  of  the  body  at  90^  from  perihelion,  let 
%  =  90^,  and  consequently  cos.  a  =  0.     Therefore 

that  18  to  say,  the  distance  at  90^  from  perihelion  is  twice  the 
perihelion  distance. 

One  parabolic  orbit  differs  from  another  in  its  perihelion  distance. 
The  less  this  distance  is,  the  less  will  be  the  separation  at  a  given 
distance  fit>m  s  between  the  parallel  directions  to  which  the  indefinite 
branches  p;/  tend.  This  distance  may  have  any  magnitude.  The 
body  in  its  perihelion  may  graze  the  surface  of  the  sun,  or  may  pass 
tt  a  distance  from  it  greater  than  that  of  the  most  remote  of  tho 
phnetSi  so  that,  although  it  be  subject  to  solar  attraction,  it  would  in 
that  ease  never  enter  within  the  limits  of  the  solar  system  at  all. 

A  body  moving  in  such  an  orbit,  therefore,  would  not  make,  like 
0D6  which  moves  in  an  ellipse,  a  succession  of  revolutions  round  the 
son  3  Dor  can  the  term  periodic  time  be  applied  at  all  to  its  motion. 
It  enters  the  system  in  some  definite  direction,  such  asp'p,  as  indi* 
eated  bj  the  arrow,  from  an  indefinite  distance.  Arriving  within 
the  sensible  influence  of  solar  gravitation,  the  effects  of  this  attraction 
are  manifested  in  the  curvation  of  its  path,  which  gradually  increases 
as  its  distance  frt>m  the  sun  decreases,  until  it  arrives  at  perihelion, 
whan  tba  attraotiye  force,  and  consequently  the  curvatvirfh,  ^\Xa[\Ti 


AeTKOSOsrr. 

The  extreme  velocity  which  the  body  attuns  at  thii 
la  prodooM,  ia  virtu^  of  the  ioertia  of  the  maviog  mass,  a  ccd- 
igjU  foroB,  vhich  counteracts  the  gravitutiaa,  and  the  body,  after 

jttng  perihelioD,  begins  to  retreat;  the  solar  grsvitattoo  and  the 
vumtnre  of  it>  path  dccre.-iBiDg  together,  until  it  ieeues  from  th« 
fjftem  ia  &  dircctioa  pp',  as  indicated  by  the  atrows,  which  is 
Muly  a  Btrught  line,  asd  parallel  to  that  in  which  it  entered,  lo 
aooh  an  orbit  a  body  therefore  viaits  the  eystem  but  once.  It  enters 
IB  k  oertun  direction  from  an  indefinite  distance,  and,  paeung 
tkrom^h  iti  perihelion,  issues  in  a  parallel  direction,  passing  to  an 
unlimited  distance,  never  to  return. 

SOM.  ^perhoUc  orti(ji.  —  This  class  of  orbits,  like  the  pra- 
Mu,  eoBoat  of  two  indefinite  branches,  which  unite  at  peribelian, 
which  at  eqoal  distances  from  perihelion  have  equal  curvatares,  and 
which,  as  the  dttitaoue  from  perihelion  increases,  approach  indefi- 
Bjtely  in  diieotion  and  form  to  straight  liuea ;  but^  nnlike  the  pais- 
bolio  orbits,  the  straight  lines  lo  whose  direction  the  two  branches 
^prozimata  are  divergent  and  not  parallel. 

Bqoh  n  oiUt  having  the  same  perihelion  distance  as  the  ellipH 
and  parabola,  is  represented  by  aKh,',Jtg.  816. 

If  s  express,  as  beforo,  the  distaoce  of  the  body  from  *,  when  itd 
angular  distance  from  perihelion  is  a,  and  if  e  express  a  cerUia 
number,  which,  instead  of  being  less,  as  in  the  case  of  the  ellipse, 
is  greater  than  I,  we  shall  have 

1  +  .■  .y  COS.  «.• 

a  formula  identical  with  that  wbieh  expresses  the  valae  of  z  in  the 
ease  of  the  ellipse,  the  difference  being  merely  in  the  relation  which 
the  number  e  bears  to  1. 

It  is  easy  to  perceive  that  when  the  perihelion  distance  ia  the 
same,  the  value  of  i  for  any  proposed  angukr  distance  from  peri- 
helion is  greater  in  the  hyperbola  ibsn  in  the  ellipse,  and  that  iti 
value  in  the  parabola  is  intermediate,  bciag  less  than  in  the  hy< 
perbola  and  greater  than  in  the  ellipao. 

The  parabola  is,  therefore,  included  between  the  ellipse  and 
hyperbola,  and  tiic  le^s  the  namber  e  falls  short  of  1  for  the  ellipse, 
and  exceeds  it  for  the  hyperbola,  the  nearer  will  the  three  orbits  ba 
in  relation  to  each  other  at  those  parts  which  are  not  very  fti 
removed  from  perihelion. 

The  distance  /  of  the  body  wbieh  moves  in  the  bjpctbola  at  90° 
from  perihelion,  ia 

i=d(l  +  e), 
Hm  name  as  for  tli<t  ellipse.    If  I  expien  this  dislaM*  tat  llw  ellqas^ 


QOMBTS  475 

t  tot  ike  panboky  and  T  for  the  hyperbola,  and  ^  ezpreBS  the  value 
of  e  for  the  hyperbola,  we  shall  have 

I  =  rf  X  (1  +  0 

f  =2d 

r  =  dx  (1  +  Oj 

and  eonaeqnenUj  the  distancea  between  the  parabola  and  each  of 
the  other  orbits  at  90^  from  perihelion,  measured  in  the  direction 
oft/r,  wiUbe 

r  —I  z=dx  (\  —  e) 

r  —  V^dx  (e'— 1). 

It  18  evident,  therefore,  that,  whatever  be  the  fraction  by  which 
«  fidls  short  of  1,  and  by  which  ff  exceeds  1,  the  same  will  be  the 
frmction  of  the  perihelion  distance  by  which  the  parabola  at  this 
pMnt  is  separated  from  the  other  orbits. 

It  will  be  recollected  that,  when  a  exceeds  90^,  the  cos.  a  becomes 
negative,  and,  consequently  we  would  then  have 

1  4-c 


«  =  rf  X 


1  —  e  X  cos. 


Now,  as  the  cos.  a,  which  is  0,  when  a  =  90^  increases,  the  product 
e  X  COS.  a,  which,  after  passing  90^,  is  very  minute,  will  also  in- 
crease, and,  consequently,  the  divisor  1  —  e  X  cos.  a  will  decrease. 
This  will  evidently  cause  a  proportionate  increase  of  z.  As  the 
prodoet  e  x  cos.  a  approaches  to  1,  the  divisor  decreasing,  the  value 
<tf  s  rapidly  increases )  and  when  e  x  cos.  a  becomes  actually  =  1, 
a  becomes  infinite. 

The  geometrical  interpretation  of  this  analytical  contingency  is, 
that  each  branch  of  the  orbit,  in  receding  from  the  centre  of  attrac- 
tioo  ff,  approaches  indefinitely  to  coincidence  with  certain  straight 
Iinesy  which  make,  with  the  direction  of  perihelion,  an  angle,  the 
eoaiiie  <^  which  has  such  a  value,  that  e  X  cos.  a  =  1,  that  is,  an 

MB^  whose  cone  is  — . 

If  two  straight  lines,  therefore,  be  drawn  from  s,  making  an 

angle  with  the  axis  a  o^,  whose  cosine  is  — ,  these  lines  will  be  the 

directions  into  which  the  two  branches  of  the  hyperbolic  orbit  have 
a  constant  tendency  to  run.  They  will,  therefore,  be  the  limit  of 
the  divergence  of  the  branches  h  h'. 

It  is  evident,  therefore,  that  the  more  the  number  e  exceeds  1, 
the  greater  will  be  the  angle  of  divergence  of  the  two  branches  h  h!j 
and  the  less  it  exceeds  1,  the  nearer  will  the  hyperbolic  branches 
hV  approach  to  the  parabolic  branches /^j?'. 

In  tha  Jig,  816,  the  orbits  circular,  elliptic,  parabolic,  and  hy^t> 


A8TROH0MT. 

BTO  neoesmiily  represeat«d  as  bnng  all  in  tbe  flame  plane.    It 

.,  however,  bo  underatood,  that  so  far  aa  any  conditions  are 
A)sed  upon  tbcm  by  tbe  Ian  of  gravilAtJon,  tbey  may  severa!]y 
in  nay  planer  whatever,  ioclined  each  to  tbe  otber,  at  any  angles 
ntef  er,  frma  0°  to  90°,  with  their  mutual  iotcraectioa  or  lines  of 

Jes  in  any  direction  whatever,  and  that  the  bodies  may  mova  in 

these  several  orbits,  in  any  directions,  how  opposed  Boever  to  each 
other. 

3007.  Planeli  i^feree  in  (heir  molioni  order  not  exacted  by  the 
law  of  gramtalion.  —  When  the  theory  of  gravitation  was  first  pro- 
poanded  by  its  illustrious  author,  no  other  bodies,  save  the  pliuets 
and  satellites  then  discovered,  were  knotrn  lo  move  under  the  in- 
fluence  of  such  a  central  attniction.     These  bodies,  however,  tap- 

Elicd  no  example  of  the  play  of  that  celebrated  theory  in  its  fiiil 
ititude.  Tbey  obeyed,  it  is  true,  its  laws,  but  they  did  much  more. 
They  displayed  a  degree  of  harmoDyand  order  far  exceeding  what 
tbe  law  of  gravitation  ciacled.  Fermitl«d  by  that  law  to  move  in 
any  of  the  three  ctosecs  of  conic  sections,  their  paths  were  eicla- 
Bively  eiliptJcul ;  permitted  to  move  in  ellipses  infiniioly  various  in 
their  eccentricities,  they  moved  exclusively  in  such  aa  differed  almost 
insensibly  from  circles;  permitted  to  move  at  dixtanccs  subordinated 
to  no  regular  law,  they  move  in  a  aeries  of  orbits  at  distanoes  in- 
creasing in  a  regular  progression ;  permitted  to  move  at  all  cono^- 
able  angles  with  the  plane  of  the  ecliptic,  their  paths  are  inclined  to 
it  at  angles  limited  in  general  to  a  few  degrees;  permitted,  in  fine, 
to  move  in  either  direction,  they  all  agreed  in  moving  in  the  diieoUoa 
in  which  the  earth  moves  in  its  annual  course. 

Accordance  so  wondrous,  and  order  bo  admirable,  conld  not  be 
fortuitous,  aod,  not  being  enjoined  by  the  conditions  of  the  law  of 

SBvitatioD,  must  either  be  ascribed  to  tbe  immediate  dictates  of  the 
mnipotent  Architect  of  the  universe  above  all  general  lawa,  or  to 
some  general  laws  superinduced  upon  gravitation,  which  had  escaped 
the  sagacity  of  tbe  discoverer  of  that  principle.  If  the  former  rap- 
position  were  adopted,  some  bodies,  different  in  their  physical  cha- 
racters from  the  planets,  primary  and  secondary,  and  playing  differ- 
ent parts  and  fulfilling  different  functions  in  the  economy  of  the 
universe,  might  still  be  found,  which  would  illustrate  the  play  of 
gravitation  in  its  full  latitude,  sweeping  round  the  son  in  all  fomii 
of  orbit,  eccentric,  parabolic,  and  hyperbolic,  in  all  planes,  at  all 
distances,  and  indifferently  in  both  directions.  If  the  latter  rappo- 
sition  were  accepted,  then  no  other  orbit,  save  ellipses  of  small 
eccentricity,  with  planes  coinciding  nearly  with  that  of  the  ecliptic, 
would  he  physically  possible. 

3008.  Comets  observe  no  fitch  order  I'li  tlieir  motion*. — The 
theory  of  gravitation  bad  not  long  been  promulgated,  nor  u  yet 
been  generally  accepted,  when  the  means  of  its  further  imiSoatioo 


COMSTS.  477 

were  might  in  the  moUon  of  comets.  Hitherto  these  bodies  had 
been  regarded  as  exceptional  and  abnormal,  and  as  beiog  exempt 
altogether  from  the  operation  of  the  law  and  order  which  prevailed 
in  a  manner  so  striking  amon^  the  members  of  the  solar  system. 
So  little  attention  had  been  given  to  comets,  that  it  had  not  been 
eertainly  ascertained  whether  they  were  to  be  classed  as  meteoric  or 
cosmioal  phenomena ;  whether  their  theatre  was  the  regions  of  the 
atmosph^^  or  the  vast  spaces  in  which  the  great  bodies  of  the  nni- 
verse  move.  Their  apparent  positions  in  the  heavens  on  varioos 
oooasioDs  of  the  appearances  of  the  most  conspicuous  of  them,  had 
nevertheless  been  from  time  to  time  for  some  centuries  observed 
and  recorded  with  such  a  degree  of  precision  as  the  existing  state 
of  matrononical  science  permitted ;  and  even  when  their  places  were 
not  astronomioally  ascertained,  the  date  of  their  appearance  was  gene- 
lally  preserved  in  the  historic  records,  and  in  many  cases  the  con- 
stellations through  which  they  passed  were  indicated,  so  that  the 
memns  of  obtaining  at  least  a  rude  approximation  to  their  position 
in  the  firmament  were  thus  supplied. 

8009.  Thejf  move  in  conic  sections^  with  the  gun  for  the/ocut.  — 
Sach  observations,  vague,  scattered,  and  inexact  as  they  were,  sup- 
plied, however,  data,  by  which,  in  several  cases,  it  was  possible  to 
eompnte  the  real  motion  of  these  bodies  through  space,  their  posi- 
tiona  in  relation  to  the  sun,  the  earth,  and  the  planets,  and  the 
paths  they  foUowed  in  moving  through  the  system,  with  sufficient 
approximate  accuracy  to  conclude  with  certainty  that  they  were  one 
or  other  of  the  conic  sections,  the  place  of  the  sun  being  the  focus. 

This  was  sufficient  to  bring  these  bodies  under  the  general  opera- 
(ioD  ci  the  attraction  of  gravitation. 

It  still  remained,  however,  to  determine  more  exactly  the  specific 
charaeter  of  these  orbits.  Are  they  ellipses  more  or  less  eccentric  ? 
or  parabolas  ?  or  hyperbolas  ?  Any  of  the  three  classes  of  orbits 
would,  as  has  been  shown,  be  equally  compatible  with  the  law  of 
gravitation. 

3010.  DifficuUy  of  atcertaining  in  uihat  species  of  conic  section 
a  oomU  moves.  —  It  might  be  supposed  that  the  same  course  of  ob- 
servation as  that  by  which  the  orbit  of  a  planet  is  traced  would  be 
applieable  equally  to  comets.  Many  circumstances,  however,  attend 
this  latter  class  of  bodies,  which  render  such  observations  impossi- 
ble,  and  compel  the  astronomer  to  resort  to  other  means  to  determine 
their  orlntt. 

A  spectator  stationed  upon  the  earth  keeps  within  his  view  each 
of  the  other  planets  of  the  system  throughout  nearly  the  whole  of 
its  coarse.  Indeed,  there  is  no  part  of  the  orbit  of  any  planet  in 
whiehi  at  some  time  or  other,  it  may  not  be  seen  from  the  earth. 
Every  point  of  the  path  of  each  planet  can  therefore  be  observed ; 
and,  althongfi  without  waiting  for  such  observation^  its  coarse  migjht 


nPP  ASTKOKOXT. 

f  }»  ietermmeS,  yet  it  is  Tnalcrial  liere  to  attend  to  tlie  ^t,  tbltflV' 
I  whole  orbit  may  he  submitted  to  direct  obscrration.  The  diflMrt* 
r  pUnetfi,  alsD,  present  peculiar  fefttures,  by  wbicb  each  ma7lwffif> 
tioguished.  Thus,  as  b»B  been  csplaincd,  thej  are  obserred  tol« 
Bpbericat  bodies  of  various  mamiitudeg.  Their  surfuces  are  marked 
by  peculiar  modea  of  light  andsbade,  which,  althoogh  ruiablc  and 
ehifting,  elill,  in  each  cose,  posseaa  some  prevailing  and  permaiwal 
cbaractera  by  nbicb  tbc  identity  of  the  object  may  be  eatablish^j, 
even  were  there  do  other  means  cf  detcrmioing  it. 

Unlike  planets,  comets  do  not  present  to  as  those  indiridiul 
cbamelers  above  mentioned,  by  which  their  identity  may  be  del» 
mined.  None  of  them  have  been  satisfactorily  atwertiined  la  U 
Bpberical  bodicR,  nor  indeed  to  have  any  definite  shape.  It  is  cerUii 
that  many  of  them  possess  no  solid  matter,  but  are  mass«  em- 
eisting  of  some  nearly  transparent  substances ;  others  are  w  so- 
rounded  with  this  apparently  vaporous  matter,  that  it  is  impo«Ut| 
by  any  means  of  obscrvatioD  which  we  possess,  to  discover  wbethi 
this  vapour  enshrouds  within  it  any  solid  mass.  Tbe  sanie  vaponr 
which  thus  envelopes  ibo  body  (if  such  there  be  wiihin  it)  alw 
conoeala  from  uH  its  features  and  indii-idual  character.  Even  tb« 
limits  of  the  vapour  itpelf,  if  vapour  it  be,  are  subject  to  gnal 
cbange  in  each  individual  comet.  Within  a  few  days  they  are  sone- 
times  observed  to  increase  or  diminish  some  hundred-fold.  A  comet 
appcnring  at  distant  intervals  presents,  therefore,  no  very  obviou 
means  of  recognition.  A  like  extent  of  surrounding  vapour  wdoU 
evidently  be  a  fallible  test  of  identity;  and  not  less  iDconclnaiTC 
-  would  it  be  to  infer  diversity  from  a  different  extent  of  nebulosilj. 
If  a  comet,  like  a  planet,  revolved  round  tbe  sud  in  an  nrbil 
nearly  circular,  it  might  be  bccd  in  every  part  of  its  path,  and  In 
identity  might  thus  be  established  independently  of  any  pwoliar 
characters  in  its  appearance.  But  such  is  not  tbe  coarse  whicb 
comets  are  observed  to  take. 

In  general  a.  coniet  is  visible  only  throughout  an  arc  of  iis  orbit, 
which  eitends  to  a  certain  limited  distance  on  each  side  of  iu  poi- 
hclion.  It  first  becomes  apparent  at  some  point  of  its  path,  soeb  u 
3i  ^  '*'^  i/'ffi'J-  816;  it  approaches  the  sua  and  disappears  after  il 
passes  a  corresponding  point  g,  <^  or  ^'  in  departing  from  the  roil. 
The  aro  of  its  orbit  in  which  alone  ii  is  visible  would  therefore  be 
gag,^a^,  ory'af. 

It  this  arc,  extending  on  either  aide  of  perihelion,  could  alwayi 
be  observed  with  the  same  precision  as  are  the  planetary  orbits,  it 
would  be  posaihic,  by  the  properties  of  the  conic  sections,  to  dot«^ 
mine  not  only  the  general  character  of  the  orbit,  whether  it  be  ID 
ellipse,  or  parabola,  or  an  hyperbola,  but  even  to  ascertain  the  indi- 
vidual  curve  of  tbe  one  Vmiio'c  \.W(iV.Wt  xavkieb  the  comet  mom, 
JO  that  the  oonne  it  £o\low«&W<n«  ii^  >»'»'(»' 'vibi«^'«».~«^«> 


COMETS.  479 

tbat  which  it  pursues  aflter  it  ceases  to  be  visible,  would  be  as  cer- 
tainly and  precisely  known  as  if  it  could  be  traced  by  direct  obser- 
TatioD  throughout  its  entire  orbit 

3011.  Hjfperhciic  and  parahoUc  comets  not  periodic,  —  If  it  be 
aaoertained  that  the  arc  in  which  the  comet  moves  while  it  is  visible 
it  part  of  an  hyperbola,  such  %s  gag,  it  will  be  inferred  that  the 
eomety  coming  from  some  indefinitely  distant  region  of  the  universe, 
has  entered  the  system  in  a  certain  direction,  h' h,  which  can  be 
inferred  from  the  visible  arc  g  ag,  and  that  it  must  depart  to 
another  indefinitely  distant  region  of  the  universe  following  the 
direction  hh\  which  is  also  ascertained  from  the  visible  vnegag. 

If,  on  the  other  hand,  it  be  ascertained  that  the  visible  arc,  such 
MMsfa^y  be  part  uf  a  parabola,  then,  in  like  manner,  by  the  pro- 
perties of  that  curve,  it  will  follow  that  it  entered  the  system  coming 
from  an  indefinitely  distant  region  of  the  universe  in  a  certain  di- 
rection p'p,  which  can  be  inferred  from  the  visible  arc^a^,  and 
that  after  it  ceases  to  be  visible,  it  will  issue  from  the  system  in 
another  determinate  direction,  pp',  parallel  to  that  which  it  entered. 

The  comet,  in  neither  of  these  cases,  would  have  a  periodic  cha- 
racter. It  would  be  analogous  to  one  of  those  occasional  meteors 
which  are  seen  to  shoot  across  the  firmament  never  again  to  reap- 
pear. The  body,  arriving  from  some  distant  region,  and  coming, 
aa  would  appear,  fortuitously  within  the  solar  attraction,  is  drawn 
from  its  course  into  the  hyperbolic  or  parabolic  path,  which  it  is 
■een  to  pursue,  and  escapes  from  the  solar  attraction,  issuing  from 
the  system  never  to  return.  The  phenomenon  would  in  each  case 
be  occasional,  and,  in  a  certain  sense,  accidental,  and  the  body  could 
not  be  said  properly  to  belong  to  the  system.  So  far  as  relates  to 
the  comet  itself,  the  phenomenon  would  consist  in  a  change  of  the 
direedoQ  of  its  course  through  the  universe,  operated  by  the  tempo- 
ruy  action  of  solar  gravity  upon  it. 

3012.  Elliptic  comets  periodic  like  the  planets.  —  But  the  case  (is 
very  different,  the  tie  between  the  comet  and  the  system  much  more 
intimate,  and  the  interest  and  physical  importance  of  the  body 
tranaeendently  greater,  when  the  arc,  Buch  as  g"  ag^'y  proves  to  be 
part  of  an  ellipse.  In  that  case  the  invisible  part  of  the  orbit  being 
inferred  from  the  visible,  the  major  axis  a  a'  would  be  known.  The 
comet  would  possess  the  periodic  character,  making  successive  revo- 
lutions like  the  planets,  and  returning  to  perihelion  a  after  the 
proper  periodic  time,  which  could  be  inferred  by  the  harmonic  law 
from  the  magnitude  of  its  major  axis. 

Such  a  body  would  then  not  be,  like  those  which  follow  hyper- 
bolic or  parabolic  paths,  an  occasional  visitor  to  the  system,  con- 
nected with  it  by  no  permanent  relation,  and  subject  to  solar  gravi- 
tation only  accidentally  and  temporarily.  It  would,  on  the  contrary, 
be  as  permanent,  if  not  as  strictly  regular,  a  member  of  ih&  «^%V^YKi 


Mi  AB-ntONOXT. 

/ 

■■  an^of  the  planets,  thongli  inTested,  u  irill  presently  appear,  inA 
an  eztreinclj  different  physical  cbsractcr. 

It  will,  therefore,  be  easily  conoeived  with  what  profonnd  ioteresi 
eoDiets  were  regarded  before  the  tfaeorj  of  gravitation  had  been  jti 
firmly  established  or  generally  ace^pted,  and  while  it  was,  go  lo 
apeak,  upon  ila  trial.  These  bodies  were,  in  (act,  looked  for  as  tha 
will) esses  whose  te^itimony  must  decide  ils  hte. 

3013.  BiJlcuUies  aHmtlwg  Ihe  amli/fia  of  ccmietnry  motiotu.^ 
DifficulticB,  however,  which  aeemed  almost  insurmountable,  opposed 
fhemaelvcs  to  a  saliirfiictDryand  conclusive  analysis  of  their  motiou 
Many  causes  rendered  the  observations  npon  their  apparent  plaoei 
fi^  in  number  and  deficient  in  precision.  The  arcs  g  a  ij,  ^  a  if, 
and  t/'aij"  q{  the  three  classes  of  orbit,  in  any  of  which  tbey  migiil 
move  wiihont  any  Ttolation  of  the  law  of  grsvilation,  were  vwj 
nearly  coineident  in  the  neighbourhood  of  the  place  of  pcribelion  a. 
It  was,  for  example,  io  almost  all  the  cases  which  presenteid  thcn- 
eelves,  powiblo  to  conceive  tliree  different  curves,  an  eccenlris 
ellipse,  rach  as  a  fi  a'  6',  a  parabola,  such  as  jf  p  o,  and  an  hyper- 
bola, such  as  h'ha,  BO  related  that  the  arcs  3  iff,  ff'a^.ioi 
^'  Bff,  would  not  deviate  one  from  another  to  an  extent  exceediof 
the  errors  inevitable  in  cometary  observations.  Thus  any  oae  of 
the  three  curves  within  the  liraila  of  the  visible  path  of  ihe  cornel 
might  with  equal  fidelity  represent  its  tourse.  In  such  cases, 
therefore,  it  was  impossible  to  infer,  from  the  observations  alnne, 
whether  the  comet  belonged  10  the  class  of  hyperbolic  or  pambolio 
bodies,  which  have  no  periodic  character,  or  to  the  elliptic,  which 
bas. 

3014.  Periodicity  alone  proiKt  the  rtliptic  charader. — The  rfia- 
racter  of  periodicity  itself,  which  belongs  exclusively  to  elHpCn 
orbits,  supplied  the  means  of  surmounting  this  difficulty.  If  loj 
observed  comet  have  an  elliptic  moiion,  it  must  return  to  perihelion 
after  completing  its  revolution,  and  it  must  have  been  visihiB  od 
former  returns  to  ihat  position.  Not  only  ought  it  to  be  expected, 
therefore,  that  such  a  comet  would  re-appear  in  future,  afWr 
absences  of  etjual  duration  (depending  on  ils  periodic  time),  hat 
that  ila  previous  relurns  to  perihelion  would  be  found  by  searching 
among  the  recorded  appearances  of  such  objecrs  for  any,  the  dalM 
of  whose  sppeamucc  might  correspond  wiih  the  supposed  periol, 
and  whose  apparent  motions,  if  observed,  might  indicate  a  real 
motion  iu  an  otbil,  identical,  or  nearly  so,  with  (bat  of  the  comet  in 
ijuescion. 

If  the  molion  of  such  a  body  were  not  effecl«l  by  any  other  forca 
except  the  solar  atlr:ictioQ,  it  would  re-appear  aflw  each  sueccssiw 
reviilntion  ut  exactly  the  Mme  point;  would  follow,  while  visible, 
exactly  the  same  are  -f  a  ;/■ ;  would  move  in  the  same  plane,  inclined 
It   the  same  hiijlc  tu  the  ecliptic,  the  nodes  retaining  the  same 


COMETS.  481 

id  wonld  am^e  at  its  perihelion  at  exactly  the  same  point 
!r  ezaotlj  equal  intervals. 

[though  the  disturbing  actions  of  the  planets  near  which 
asSy  in  departing  from  and  returning  to  the  sun,  must  be 
to  be  much  more  considerable  than  when  one  planet  acts 
ber,  as  well  because  of  the  extreme  comparative  lightness 
net,  as  of  the  great  eccentricity  of  its  orbit,  which  some- 
ally  or  nearly  intersects  the  paths  of  several  planets,  and 
those  of  the  larger  ones,  yet  still  such  planetary  attrao- 
inly  disturbances,  and  cannot  be  supposed  to  e&oe  that 
irhich  the  orbit  receives  from  the  predominant  force  of 
Dse  mass  of  the  sun.  While,  therefore,  we  may  be  pie- 
the  possibility,  and  even  the  probability,  that  the  same 
>met,  on  the  occasion  of  its  successive  re-appearances,  may 
Kth  ^'  a  ^'  in  passing  to  and  from  its  perihelion,  differing 
Ltent  from  that  which  it  had  followed  on  previous  appear- 
in  the  main  such  differences  cannot,  except  in  rare  and 
1  cases,  be  very  considerable,  and  for  the  same  reason  the 
between  its  successive  periods,  though  they  may  di&Ti 
subject  to  any  very  great  variation. 
Periodicity  J  combined  with  the  idefUity  of  the  paths  uihile 
uMishes  identity. — If  then,  on  examining  the  varions 
lose  appearances  have  been  recorded,  and  whose  places 
lie  have  been  observed,  and  on  computing  from  the  appa- 
«  the  arc  of  the  orbit  through  which  they  moved,  it  be 
.  two  or  more  of  them,  while  visible,  moved  in  the  same 
presumption  will  be  Uiat  these  were  the  same  body  re-ap- 
ler  having  completed  its  motion  in  an  elliptic  orbit ;  nor 
is  presumption  of  identity  be  hastily  rejected  because  of 
Dce  of  any  disdirepancies  between  the  observed  paths,  or 
dity  of  the  intervals  between  its  successive  re-appearanceS| 
such  discrepancies  can  fairly  bo  ascribed  to  the  possible 
es  produced  by  planets  which  the  comet  might  have  en- 
in  its  path. 

Uany  comets  recorded — few  observed,  —  Many  comets, 
bave  been  recorded,  but  not  observed.  Historians  have 
,  and  even  described  their  appearances,  and  in  some  cases 
aited  the  chief  constellations  through  which  «uch  bodies 
hough  no  observations  of  their  apparent  places  have  been 
i  by  which  any  close  approximation  to  their  actual  paths 
Doade.  Nevertheless,  even  in  tbese  cases,  some  clue  to 
ification  is  supplied.  The  intervals  between  their  appear- 
le  is  a  highly  probable  test  of  identity.  Thus  if  comets 
arly  recorded  to  have  appeared  at  intervals  of  fifty  years 
istanoe  affording  evidence  of  the  diversity  of  these  objects), 
it  be  assomed,  with  a  high  degree  of  pTobabV!&V]«\i;^\)^ 

41 


ASTRONOMY. 
leccsMve  retunu  of  >n  elliptjo  oomet  having  ifaat  inleml  u  its 

a. 

.017.  Claisificalion  of  the  comaary  ortiU.  —  The  appearanMS 
aboat  400  comets  bad  been  recorded  in  the  annala  of  varioBi 
Dtries  before  the  end  of  the  BcveotGeiith  centurj,  th«  epoch  n^ 
nuiised  by  the  discoveries  and  researches  of  Ncwtoo,  In  most  taae*. 
however,  the  only  ciroumataDco  recorded  was  tbo  appearance  of  the 
object,  accompanied  in  many  ioBtanccB  with  details  bearing  evident 
marks  of  essggeratioa  respeuting  it«  magnitude,  form  and  tplendoor. 
In  Bomc  few  chscr,  the  coDBtcllations  through  which  the  object  passed 
successively,  with  the  Deeessary  dates,  are  luentiuocd,  and  in  eoiiK, 
fewer  ^li,  ob^ervntiaiis  of  a  roagh  kind  have  been  handed  down. 
From  sucb  scnoty  data,  eagerly  sought  for  in  the  wor)(s  preserved  in 
different  cooDtrieB,  sufficieoC  materials  have  been  collected  for  the 
eompulation,  with  more  or  less  approximation,  of  the  elements  of 
the  orbita  of  about  wxty  of  the  400  comole  above  mcnlioocd. 

Since  (he  time  of  Newton,  Ualley,  and  their  contemporaries, 
observers  have  been  more  active,  and  have  had  the  command  of 
instmimmta  of  considerable  and  oonatantly  increaaiog  power;  m 
that  every  comet  which  has  been  visible  from  the  northeni  herni- 
Bphere  of  the  earth  since  that  time,  baa  been  observed  with  cae- 
tinnally  increasing  precision,  and  data  have  been  in  all  cases  ob- 
tained, by  which  the  elenienta  of  the  orbits  have  been  calcalated. 
Since  the  year  1700,  accordingly,  about  140  have  been  observed, 
the  elements  of  the  orbits  of  which  have  been  ascertained  with  great 
precision. 

It  appears,  therefore,  that  of  the  entire  number  of  comets  wliici 
have  appeared  in  the  firmament,  the  orbits  of  about  200  have  been 
ascertained.  Of  this  number,  forty  have  been  ascertained,  some 
conclusively,  others  with  more  or  less  probability,  to  revolve  ia 
elliptical  orbits. 

Seven  have  passed  tbrongh  the  system  in  hyperbolae,  and  coo- 
aequently  will  not  visit  it  again,  unless  tbej  be  thrown  into  otha 
orbits  by  some  disturbing  force. 

One  hundred  and  sixty  have  passed  tbrongh  the  system  either  in 
parabolic  orbits,  or  in  ellipses  of  such  extreme  eccentricity  as  to  b« 
undiBtinguishable  from  parabolas  by  any  data  supplied  by  the 
observations. 

n.  Elliptic  Com 

3018.  Ennki's  amid.  —  In  1818,  a  comet  was  observed  at  Mat- 
BoiUes,  on  the  26lh  of  November,  bj  il.  Pons.  In  the  following 
January,  its  path  being  calcula,ted,  M.  Arago  immediately  recog- 
nized it  as  ideulical  with  one  which  bad  appeared  in  ISOd.    Sub- 


COMETS. 


488 


wquentlj,  M.  Eiick4  of  Berlin  succeeded  in  calculating  its  entire 
orbit — inferring  the  invisible  from  the  visible  part  —  and  found 
that  its  period  was  about  twelve  hundred  days.  This  calculation 
was  verified  by  the  fact  of  its  return  in  1822,  since  which  time 
the  comet  has  gone  by  the  name  of  Enckt's  comet,  and  returned 
reealarly. 

It  mmj  be  asked,  How  it  could  have  happened  that  a  comet  which 
made  its  revolution  in  a  period  so  short  as  three  years  and  a  quarter, 
should  not  have  been  observed  until  so  recent  an  epoch  as  1818  ? 
Tliis  is  explained  by  the  fact  that  the  comet  is  so  small,  and  its 
light  BO  feeble  even  when  in  the  most  favourable  position,  that  it 
mn  ooly  be  seen  by  the  aid  of  the  telescope,  and  not  even  with  this, 
except  under  certain  conditions  which  are  not  fulfilled  on  the  oo- 
eMion  of  every  perihelion  passage.  Nevertheless,  the  comet  was 
obaerved  on  three  former  occasions,  and  the  general  elements  of  its 
path  recorded,  although  its  elliptic^  and  consequently  periodic  cha- 
iMter,  WIS  not  recognised. 

On  comparing,  however,  the  elements  then  observed  with  those 
of  the  comet  now  ascertained,  no  doubt  can  be  entertained  of  their 


8019.  Tahle  of  the  t^emenU  of  the  orbit  —  In  the  following  table 
are  given  the  elements  of  the  orbit  of  this  comet,  as  computed  from 
the  observations  made  upon  it  at  each  of  ita  three  appearances  in 
1786y  1795,  and  1805,  before  its  periodic  character  was  discovered, 
lad  at  its  eleven  subsequent  appearances  up  to  1852. 


TABLE  I. 
Elements  of  the  Orbit  of  £nck4*s  Comet  to  1852. 


M«B 

Earb's 

tridty. 

ib|. 

« 

• 

rw 

trVQ 

OMM 

n» 

f-iiao 

0'H'« 

t-iiai 

aS4M 

Kit 

>Jl4t 

04486 

Ml 

MriHi 

o-vus 

KS 

••tm 

0«M9 

let 

tn» 

0*^46 

Ml 

f-iiif 

(►••4M 

ll» 

f«/»7 

0  8450 

M» 

tlfll 

O^fiC 

■Ml 

J-Otf 

0-*>448 

IMt 

2l2lh 

0MT4 

IHA 

ait4T 

01147» 

Ml 

t-flU 

o-Mn 

PkriMifla 
Ouuaee. 


0«M« 
0aS44 
0-3401 

OJass 

0<}|U) 
0'»«4t 
0*S45A 
034  4 
0St44 
0»t40 
0  3450 
0-A»l 
0-J37I 
0>a374 


DultBOB. 

Looffi'iidc 
PeriMion. 

Loogitud* 

of 

AKendinf 

^o«to. 

iMlimika 

(1-1- •) 

» 

V 

i 

o      »     " 

O        '       " 

Q        t        ft 

i-OftlS 

156  38 

334     8 

13  86 

4  0BI6 

168  41  20 

334  39  88 

13  42  80 

4HM4) 

156  47  84 

334  80  10 

IS  SS  30 

4'0>l2» 

166  59  12 

334  83  19 

IS  36  M 

4I0M 

157   II  44 

334  25     0 

13  80  17 

4' 1017 

157   14  31 

334  n  30 

13  81  84 

4  1023 

157   17  53 

334  89  3(2 

13  80  34 

4-IU0 

167  31     1  1  334  38     » 

13  82    • 

4  tOiO 

157  23  89  ;  3M  34  59 

13  21    15 

4  lOM 

1^7  tl     4 

3il  Stf  41 

IS  81  88 

A-amn 

I-.7  29  27 

334  39   10 

13  80  88 

4I0I0 

157  44  21 

9M    10  34 

13    7  94 

4  023 

157  47     f 

:t3l  22   12 

4'0U» 

157  51     2 

334  21  21 

13    7  U 

Time  of  Pvribtlks 


Jan.  80. 
Dm.  81. 
Not.  81. 
Ju.  87. 
May  88. 
Stpt.  ML 
Jaa.  8. 
UvfVL 
Auc  88. 
Dw.  18. 
April  It. 
Aiiff.8. 
Nov.  26. 
Mv.  14. 


81 

10 

18 

< 

S3 

6 

18 

S3 

8 

8 

0 

It 


7 
44 

8 
18 
16 
48 

3 
84 

48 
S7 
95 
II 


3+  0 
80 


The  motion  of  this  comet  is  direct;  and  its  period  in  1852  was 
3-29616  years,  which  is  subject  to  a  slight  variation. 
It  ii  evident  that  between  1786  and  1795  there  w«t«  tti^ 


bctwet 


ASTROKOMT. 


between  1795  and  1805  two,  tad,  in  fine,  between  1805  ind  18U 

three,  unoWrved  reluroB  to  poribelion. 

It  appears,  tbercfure,  that,  ezceptiog  tbe  ovul  form  of  the  orVt, 
the  motion  of  tbia  body  difiera  in  noiiiiog  from  Ib&t  of  ■  pitnet 
whose  mean  distance  from  the  sun  ia  that  of  tbe  nearest  of  tbe  pit- 
netoids.  Ita  ecccntricilj  is  guct,  however,  that  when  in  periheliim 
it  ia  within  the  orbit  of  Mercury,  and  when  in  aphelion  it  it  ootil^ 
tbe  most  dlHtant  of  tbe  planetoids,  and  at  a  distance  from  the  sin 
equal  to  four-fiftha  of  that  of  Jupiter, 

3020.  Indicalioia  of  the  fffectt  of  a  resitting  mallum.  —  A  firt 
nllogetbcr  anomatons  in  the  motions  of  tbe  bodies  of  the  nilu 
sygtem,  and  indicating  a  conEe(|uenc«  of  the  highest  phjscal  ia- 
portanee,  bas  been  disclosed  in  the  observation  of  tbe  motion  of  tUi 
oomct.  It  has  been  found  that  its  periodic  time,  and  consequentlj 
its  mean  dislanee,  undergaca  a  slow,  Kradual,  and  apparently  regnlir 
decrease.  The  decrease  is  small,  but  not  at  all  unoerttua.  It 
amounted  to  about  a  day  in  ten  revolutions,  a  qnantity  which  coaU 
not  by  any  means  be  placed  to  the  account  cither  of  errors  alobsa- 
TatioQ  or  of  calculatioa ;  and,  besidea,  this  increase  ia  inoeanat, 
whereas  errors  would  affect  tbe  result  somctimea  one  way  and  MBfr 
times  the  other.  The  period  of  the  comet  between  1786  and  1T95 
was  l-lOSi  days;  between  1795  and  1805  it  was  1207A  dija; 
between  1805  and  1819  it  was  1207A  days;  in  18i5  it  was  ISWJ 
days ;  and,  in  fine,  in  1852  it  was  1201  days. 

Tho  magnitude  of  the  orbit  thus  constaDtly  decreasing  (for  llie 
cube  of  its  greater  axis  must  decrease  in  the  same  proportion  u  (he 
■cjnarc  of  the  period),  the  actual  path  followed  by  the  comet  mast 
be  a  sort  of  elliptic  spiral,  the  succcssivo  coils  of  which  are  very  doec 
together,  every  succesaive  revolution  bringing  the  comet  nearer  Mul 
nearer  to  the  sun. 

Such  a  motion  could  not  arise  from  tbe  disturbing  action  of  tb» 
planets.  These  forces  have  been  taken  strictly  into  account  in  Uie 
computation  of  tbe  cpbcmerides  of  the  comet,  and  there  ia  ttiil 
found  this  residual  phenomenon,  which  cannot  be  placed  to  tbei 
account,  but  which  is  exactly  the  effect  which  would  ariae  froni  aaj 

Ebyaical  agency  by  which  the  tangential  motion  of  tbe  comet  would 
9  feebly  but  coeatantly  resisted.  Such  an  agency,  by  diminiihtDg 
the  tangential  velocity,  would  give  increased  efficacy  to  the  win 
attraction,  and,  consequently,  increased  curvature  to  tbe  comet's  path ; 
BO  that,  after  each  revolution,  it  would  revolve  at  a  less  distaoee 
from  the  centre  of  attraction. 

3021.  The  liimiyii/irous  eiher  imild  produte  $aeh  an  tject,— 
It  is  evident  that  a  resisting  medium,  such  as  the  luminiferous  eth«T 
(1225)  is  assumed  to  be  in  tbe  hypothesis  which  forms  the  basis  of 
Me  undulatory  ibeorj  ol  Vv^l,  wavi\4  ■^Todivee  just  such  a  pbeno- 
neitoii,  and,  acoord'inglj,  l\ie  tn<Aw^  (A  'Cms -^unii. "■*  t^^jAk^  «i,k 


COMETS.  485 

strong  evidence  tending  to  conyert  that  hypothetical  flmd  into  a  real 
pfajsical  agent. 

It  remains  to  be  seen  whether  a  like  phenomenon  will  be  de- 
veloped in  the  motion  of  other  periodic  comets.  The  discovery  of 
these  bodies,  and  the  observation  of  their  motions,  are  as  yet  too 
recent  to  enable  aatronomers,  notwithstanding  their  greatly  mul- 
tiplied namber,  to  prononnoe  decisively  upon  it. 

8022.  OomeU  would  uliimatefy  /all  into  the  nm.  *-  If  the  ex- 
istence of  this  resisting  medium  should  be  established  by  its  observed 
efleets  on  comets  in  general,  it  will  follow  that,  after  the  lapse  of  a 
certain  time  (many  ages,  it  is  true,  but  still  a  definite  interval),  the 
eomets  will  be  successively  absorbed  by  tho  sun,  unless,  as  is  not 
improbable,  they  should  be  previously  vaporized  by  their  near 
approach  to  the  solar  fires,  and  should  thus  be  incorporated  with  hia 
atmosphere.* 

3023.  Why  Uht  efftxts  ore  not  manifested  in  the  motion  of  the 
vfanetM. —  It  may  bo  asked,  If  the  existence  of  a  resisting  medium 
pe  admitted,  whether  the  same  ultimate  fate  must  not  await  the 
planets?  To  this  inquiry  it  may  be  answered  that,  within  the 
limits  of  past  astronomical  record,  the  ethereal  medium,  if  it  exist, 
has  had  no  sensible  effect  on  the  motion  of  any  planet.  That  it 
Bight  have  a  perceptible  efiect  upon  comets,  and  yet  not  upon 
pluetSy  will  not  be  surprising,  if  the  extreme  lightness  of  the 
eomets  compared  with  their  bulk  be  considered.  The  efiect  in  the 
tvo  eases  may  be  compared  to  that  of  the  atmosphere  upon  a  piece 
of  swan's  down  and  upon  a  leaden  bullet  moving  through  it  It  is 
certain  that  whatever  may  be  the  nature  of  this  resisting  medium, 

*  In  the  efforts  by  which  the  human  mind  laboars  after  truth,  it  is  corioos 
te  obeerre  how  often  that  desired  object  is  stumbled  upon  by  accident,  or 
trriTed  at  by  reasoning  which  is  false.  One  of  Newton's  coxgectures  re» 
•peetiiig  eomets  was,  that  they  are  **  the  aliment  by  which  suns  are  sus- 
taiaed;"  and  be  therefore  concluded  that  these  bodies  were  in  a  state  of 
progreasiTe  decline  upon  the  suns,  round  which  they  respectively  swept ; 
tad  that  into  these  suns  they  from  time  to  time  fell.  This  opinion  appears 
Is  have  been  cherished  by  Newton  to  the  latest  hours  of  his  life :  he  not 
wly  eoDsigned  it  to  his  immortal  writings ;  but,  at  the  age  of  eighty-three, 
a  eoBTersation  took  place  between  him  and  his  nephew  on  this  subject, 
vhieh  has  come  down  to  us.  **  I  oannot  say,"  said  Newton,  *'  when  the 
coBMt  of  1680  will  fall  into  the  sun :  possibly  after  five  or  six  revolutions , 
Wt  whenever  that  time  shall  arrive,  the  heat  of  the  sun  will  be  raised  by  it 
to  tneh  a  point,  that  our  globe  will  be  burnt,  and  all  the  animals  upon  it 
*in  peiiaa.  The  new  stars  observed  by  Htpparchus,  Tycho,  and  Kepler, 
■art  have  proceeded  from  such  a  cause,  for  it  is  impossible  otherwise  to 
explain  their  sudden  splendour."  His  nephew  then  asked  him,  **  Why, 
vhcn  he  atated  in  his  writings  that  comets  would  fall  into  the  sun,  did  he 
aol  also  state  those  vast  fires  they  must  produce,  as  he  supposed  they  had 
dona  la  tlie  stars  T"  —  **  Because,"  replied  the  old  man,  **  the  conflagrations 
if  tka  ann  eonoem  ns  a  little  more  directly.  I  have  said,  however,"  added 
h$f  twi""C>  "  enough  to  enable  the  world  to  collect  my  opinion." 

41  * 


486  ASTKOKOVT. 

|t  vill  not,  for  many  hoodrcd  jeara  to  come,  prodoee  the  lUgltat 
L  petceptililo  effect  upon  the  taotiona  of  tlie  plnnela. 

3024.  Correeted  tMimale  of  the  inaa*  of  Mercury.  — TV  mUM 
of  comets  ia  general  are,  aa  vill  be  explaiood,  iocomparablf  rawUd 
than  those  of  the  Btnallest  of  the  planeta;  eo  much  so,  indetJ,  uU 
bear  do  appreciable  ntio  to  Uiem.  A  coneequence  of  thu  u,  ttu 
while  the  effects  of  their  attraction  upon  the  pjuieia  uv  allogrthr 
Inscnfflble,  the  disturbing  effects  of  the  mosses  of  the  planets  upcs 
ttem  are  very  considerable.  These  disturbances,  being  proportkoil 
to  the  disturbing  tnasscs,  may  then  be  agei  as  measures  of  the  lallH, 
Just  as  the  movement  of  the  pith-ball  in  the  Imlaocc  of  torsian  top- 
^lies  a  measure  of  the  pbysical  forces  to  which  that  imCnuneal  ii 
■pplied. 

Enckf'B  eomet  near  its  perifaelion  passes  near  the  orbit  of  SIB^ 
oury;  and  vhea  that  planet  at  the  epoch  of  its  perihelion  happen) 
to  be  near  the  same  point,  a  considcnble  and  measurable  disturtaiM 
is  manifested  in  the  comet's  motion,  which  being  obserTed  aapplici 
■  tuensnro  of  the  planet's  mo^s. 

This  combination  of  the  motions  of  the  planet  and  comet  liKik 
place  under  very  favourable  circumstances,  on  the  occaaion  of  ihe 
perihelion  passage  of  the  oomct  in  1838,  the  result  of  which,  le- 
oordiog  to  the  cslculutions  of  Profe^Bor  Encki^,  was  the  dtscorery  of 
KD  error  of  large  amount  in  (he  previou.s  estimates  of  the  mass  of  tli« 
planet  After  making  every  allowance  for  other  planetary  attractJoos, 
ftnd  for  the  effects  of  the  resiaUng  medium,  the  existence  of  whiob  il 
appears  necessary  to  admit,  it  was  inferred  that  the  rasss  asagotd 
to  Mercury  by  I^place  was  too  great  in  the  proportion  of  12  to  7. 
a  This  question  is  stilt  under  examination,  and  every  succeeding 
perihelion  passage  of  the  comet  will  increase  the  data  by  which  it> 
more  exact  solution  may  be  accomplished. 

3025.  Bkla'i  comft.—Oa  February  2Sth,  1826,  M,  Biela,  lo 
Austrian  officer,  observed  in  Bohemia  a  comet,  which  was  Be«D  il 
Marseilles  at  about  Ihe  same  time  by  M.  QamburL  The  pil^ 
which  it  pursued,  was  observed  to  be  similar  to  that  of  comets  viit^ 
had  appeared  in  17T2  and  1806.  Finally,  it  was  found  that  thij 
body  moved,  round  the  sun  in  an  oval  orbit,  and  that  the  time  of  ile 
revolution  was  about  6  years  and  8  months.  It  has  since  retunuJ 
at  its  predicted  times,  and  has  been  adopted  as  a  member  of  our 
system,  under  the  name  of  Biela's  comet. 

Biola's  comet  moves  in  an  orbit  whose  piano  is  inclined  at  a  null 
angle  to  those  of  the  planets.  It  is  but  slightly  oval,  the  lei^ 
being  to  the  breadth  in  the  proportion  of  about  four  to  three.  WhfB 
nearest  to  the  sun,  its  distance  ia  a  little  less  than  that  of  the  earth; 
and  whun  moat  remote  from  the  sun,  its  distance  somewhat  cxoeolt 
that  of  Jupiter.  TWs  it  Taogcs  fctoni^  *!&«  wi\M  c^icm,  between 
the  orbits  of  Jupilei  wd  t^ie  caiitk. 


COMETS. 


487 


This  comet  had  been  observed  in  1772  and  in  1806;  but  in  the 
elliptic  form  of  its  orbit,  and  consequeDtly  its  periodicity,  was  not  dis- 
eoTcred.  Its  retnm  to  perihelion  was  predicted  and  observed  in  1832, 
in  1846,  and  in  1852 ;  but  that  which  took  place  in  1838  escaped 
oheervation,  owing  to  its  unfavonrable  position  and  extreme  funtness. 

The  elements  of  the  orbit,  deduced  from  the  observations  made 
on  each  of  its  appearances  to  1846  inclusive,  are  given  in  Table  IL 
We  have  not  yet  obtained  calculations  of  its  elements  from  obser- 
vations made  in  1852.  It  was  first  seen  in  that  year  bv  Professor 
Secchi  at  Rome,  on  September  16th,  and  continued  to  oe  seen  for 
throe  weeks.  It  was  preceded  in  right  ascension  about  two  minutes 
of  time  by  a  still  fainter  comet,  whose  real  distance  from  it  must 
have  been  about  a  million  and  a  quarter  of  miles. 

TABLE  II. 
Elements  of  the  Orbit  of  Biela's  Comet  to  1846. 


una 

tridtj. 

Ptrfhelioa 
DbiuiM. 

Aphrlion 
DmUbcc 

or 

Perihalioo. 

Lonfitnde 

of 

AKcndiiiff 

Nod«. 

IndiBalloo 

TuMorpArilwBaa 

• 

• 

d'^mx 

V 

V 

C 

t4n 

94f7l 
94613 

94169 

0-«7e9 
0^4S9 
Ch746B 
»7Sff 
0^M3 

04118 
0-9068 
040  J» 
0-8:98 

o*ue7 

4-73 
643 
6-23 
6*% 
6-19 

O      '      " 

97  81     0 
100  32  S3 

109  45  60 

110  0  85 
109    6  31 

o      •      " 

863  94    0 
SSI    IS   15 
861  88  IS 
8l8  IS  18 
945  47  61 

O      '      " 

17  39    0 
13  36  46 
IS  93   61 
13   IS  47 
IS  39  46 

k.    m. 
Ftb.  8.           10 
Jan.  1.         S3     32 
Mv.  I&      10       3 
Nov.  96.        1      41 
Fab.  11.        0      49 

8026.  Pouihility  of  the  collision  of  Biela's  comet  with  the  earth. 
—  One  of  the  points  at  which  the  orbit  of  Biela's  comet  intersects 
the  plane  of  the  ecliptic,  is  at  a  distance  from  the  earth's  orbit  less 
than  the  sum  of  the  semi-diameters  of  the  earth  and  the  comet  It 
follows,  therefore  (2905),  that  if  the  comet  should  arrive  at  this 
pMnt  at  the  same  moment  at  which  the  earth  passes  through  the 
point  of  its  orbit  which  is  nearest  to  it,  a  portion  of  the  globe  of  the 
earth  must  penetrate  the  comet 

It  was  estimated  on  the  occasion  of  the  perihelion  passage  of  this 
eoroet  in  1832,  that  the  semi-diameter  of  the  comet  (that  body  beiog 
nearly  slobular,  and  having  no  perceptible  tail)  was  21,000  miles, 
while  the  distance  of  the  point  at  which  its  centre  passed  through 
the  plane  of  the  ecliptic,  on  the  29  th  of  October  in  that  year,  from 
the  path  of  the  earth  was  only  18,600  miles.  If  the  centre  of  the 
earth  happened  to  have  been  at  the  point  of  its  orbit  nearest  to  the 
centre  of  the  comet  on  that  day,  the  distance  between  the  centres 
of  the  two  bodies  would  have  been  only  18,600  miles,  while  the 
■enl-diameter  of  the  comet  was  21,000  miles;  and  the  semi-diameter 
of  the  earth  beings  in  round  numbers^  4000  miles^  it  would  follow 


D  «ome 


ASTBosomr. 


-tttt  in  mich  a  mntingcnc;  tho  earth  wnnid  bare  plunged  iBlBlkt 
to  the  ilrpth  of 

21,000  +  4000  —  13,000  =  610(1  mile*, 
t  depth  eicecding  tiiree-fourtha  of  the  earth's  diameter. 

The  poisibtlity  of  aoch  a  eBlastrnplie  having  been  nmaani, 
great  popular  *Iiirm  wan  excited  before  the  eipcct«d  retnni  of  ibt 
comet  in  1S32.  It  was,  however,  shown  that  on  (he  SJlth  (V 
tobor  the  earth  would  ho  about  five  millions  of  miles  from  the  poial 
of  daoger,  and  that  on  the  arrival  of  tho  earth  at  that  poiol  lb 
comet  wodM  have  moved  to  a  atiU  greater  distance. 

3027.  Rni'hilion  ff  BUln't  cwn^t  tnln  tico.  —  One  of  the  tai* 
extniordiDary  pheDomcca  of  which  (be  btstorj  of  aalroooniv  afFoHi 
an;  example,  attended  the  appearance  of  this  comet  in  18-16.  It 
VBB  on  that  occasion  seen  to  resolve  itself  into  two  distinct  onm'tt, 
which,  from  the  litter  end  of  December,  1845,  to  the  epoch  gf  ill 
disappearance  in  April,  1846,  moved  in  distinct  and  iodependcot 
orbits.  I'he  paths  of  these  two  bodies  were  in  sucb  optical  juita- 
position  that  both  were  always  seen  together  in  the  field  of  vie*  «\ 
the  telescope,  and  the  greatest  visuid  angle  between  tbetr  ctatm 
did  not  amount  at  any  time  to  10',  the  Tariation  of  that  iiigia 
arising  principally  from  the  change  of  direction  of  the  visual  line, 
relatively  to  the  line  joining  their  centres,  and  to  the  change  of  tte 
comet's  distance  from  the  e.artb. 

M.  Plantamour,  director  of  the  Ohaervatory  of  Geneva,  calcnlated 
the  orbits  of  these  two  comets,  considered  as  indepcadent  bodiu; 
and  found  that  the  real  distance  between  their  centres  waa,  snbjed 
to  but  little  variation  while  vbihio,  about  tbirty-oinc  semi-fjiameien 
of  (he  earth,  or  two-thirds  of  the  moon's  distance.  The  eomcH 
moved  on  thus  aide  by  aide,  without  manifesting  any  reciprocal  di* 
torhing  action ;  a.  circumstance  no  way  aurpHsing,  considering  ib« 
infinitely  minute  masses  of  such  bodies. 

3028.  ChanijfS  of  apptorance  aflent/iny  the  ti-paralion. — Th* 
original  comet  was  apparently  a  globular  mass  of  nebulous  matlit. 
semi-transparent  at  its  very  centre,  no  appearaoce  of  a  tail  beiojt 
discoverable.  After  tho  separation,  both  comets  had  short  taib, 
parallel  in  their  direction,  and  at  right  angles  to  tho  lino  jninini 
their  centres;  both  had  nuclei.  From  the  day  of  their  separation 
the  original  oomct  decreased,  and  the  companion  increased  io  bright- 
ness until  (on  tho  10th  February)  they  were  sensibly  equal-  AftfT 
this  the  companion  still  increased  in  brightness,  sod  from  the  l-lth 
to  the  Itjtb  was  not  only  greatly  superior  in  brightness  to  tha 
original,  but  had  a  sharp  and  stariike  nucleus  compared  to  a 
diamond  spark.     The  change  of  brightness  was  now  reversed,  the 

original  comet  recovering  iw  Bu^T\i«\\^,'MndttCiyjiring  on  the  18th 
Ibc  same  appearance  as  i\\c  coto^Tttutt  \«A  Vnrai  *»i\\.>^  vi4\i>» 


COMETS.  480 

16th.  After  this  the  companion  gradaally  faded  away,  and  disap- 
peared preyiooslj  to  the  final  disappearance  of  the  original  comet  on 
22nd  April. 

It  was  observed  also  that  a  thin  Inminous  line  or  arc  was  thrown 
across  the  space  which  separated  the  centres  of  the  two  nuclei,  espe- 
cially when  one  or  the  other  had  attained  its  greatest  brightness, 
the  arc  appearing  to  emanate  from  that  which  for  the  moment  was 
the  brighter. 

After  the  disappearance  of  the  companion,  the  original  comet 
threw  out  three  faint  tails,  forming  angles  of  120^  with  each  other, 
one  of  which  was  directed  to  the  place  which  had  been  oocnpied  by 
the  companion. 

It  is  suspected  that  the  faint  comet  which  was  observed  by  Prof. 
Seochi  to  precede  Biela's  comet  in  1852,  may  have  been  the  com- 
panion thus  separated  from  it,  and  if  so,  the  separation  must  be 
permanent,  the  distance  between  the  parts  being  greater  than  that 
which  separates  the  earth  from  the  sun. 

3029.  Faye'%  comet.-^n  the  22nd  November,  1843,  M.  Fajre, 
of  the  Paris  Observatory,  discovered  a  comet,  the  path  of  which 
ioon  appeared  to  be  incompatible  with  the  parabolic  character.  Dr. 
Ooldschmidt  showed  that  it  moved  in  an  ellipse  of  very  limited 
dimensions,  with  a  period  of  7}  years.  It  was  immediately  ob- 
served as  being  extraordinary,  that,  notwithstanding  the  frequent 
letnms  to  perihelion  which  such  a  period  would  infer,  its  previous 
appearances  had  not  been  recorded.  M.  Faye  replied  by  showing 
that  the  aphelion  of  the  orbit  passed  very  near  to  the  path  of 
Jnpiter,  and  that  it  was  possible  Uiat  the  violent  action  of  the  great 
mass  of  that  planet,  in  such  close  proximity  with  the  comparatively 
light  mass  of  the  comet,  might  have  thrown  the  latter  body  into  its 
pnaent  orbit,  its  former  path  being  either  a  parabola  or  an  ellipse, 
with  anch  elements  as  to  prevent  the  comet  from  coming  within 
visible  distance.  M.  Faye  supported  these  observations  by  reference 
to  a  more  ancient  comet,  which  we  shall  presently  notice,  to  which 
a  like  incident  b  supposed  with  much  probability,  if  not  certainty, 
to  have  occurred. 

3030.  Re-appearance  in  1850-1  calculated  hy  M,  Le  Verrier, — 
The  observations  which  had  been  made  in  1843,  at  several  observa- 
tories, but  more  especially  those  made  by  M.  Struve  at  Pultowa, 
who  continued  to  observe  the  comet  long  after  it  ceased  to  be  ob- 
Krred  elsewhere,  supplied  to  M.  Le  Verrier  the  data  necessary  for 
the  ealcnlation  of  its  motion  in  the  interval  between  its  perihelion 
in  1843  and  its  expected  re-appearance  in  1850-1,  subject  to  the 
disturbing  action  of  the  planets,  and  predicted  its  succeeding  peri- 
helion for  the  3rd  of  April,  1851. 

Aided  by  the  formulsB  of  M.  Le  Verrier,  Lieutenant  Stratford 
^\^UtM»H  t  provisional   ephemeris  in  1850,  by  which  obser^eca 


fM  AttTHOIOm* 

Bight  be  enabled  more  easily  to  deteet  tbe  eomeL  whieh  was  tkt 
more  neoesaary  aa  tbe  object  u  extremdj  Cunt  and  email,  and  nol 
e^wble  of  being  seen  except  by  meana  of  the  moat  perfect  teb- 
aoopea.  Bj  meana  of  thia  epbemeri8|  Profeaeor  ChaUia,  of  &n- 
briaffei  found  tbe  oomet  on  uie  night  of  the  28(h  November  ynaj 
uwny  in  the  pUce  aaaigned  to  it  in  the  taUea.  Two  ohaerralioea 
only  were  then  made  npon  it,  wbicb|  however,  were  nSeient  to 
enable  M.  Le  Yerrier  to  give  atili  greater  jnedaion  to  hia  fiirmala, 


by  aeaigning  a  definite  nnmerioal  Taloe  to  a  email  qnantity  which 
befbre  waa  left  indeterminate.  Lientenant  Stratford^  with  the  ftr- 
nrala  thna  oorreoted,  calculated  a  more  extensive  and  exaot  ophoao 
ria,  extending  to  the  last  day  of  March,  and  publiahed  it  in  Janonyi 
1851,  in  the  Nautical  Almanack. 

The  oomet|  thonsb  extremely  fiunt  and  small,  and  conaeqnendy 
difficult  of  observation,  continued  to  be  observed  by  Frafeasor  Challis 
with  the  great  Northumberland  telescope  at  Cambric^  and  by  H. 
Stmve  at  Pultowa,  and  it  waa  finmd  to  move  in  ezaet  aeeorauoi 
with  the  predietiona. 

8081.  Be  Fto/f  comd.— On  the  22nd  August,  1844,  If.  da 
Vioo,  of  tbe  Boman  Observatoi^,  discovered  a  oomet  whose  oibit 
was  soon  afterwards  proved  by  M.  Faye  to  be  an  ellipse  of  moderate 
eccentricity,  with  a  period  of  about  5}  years.  It  arrived  at  its 
perihelion  on  the  2nd  of  September,  and  con  tinned  to  be  observed 
nntil  the  7th  of  December.  The  return  of  this  comet  to  perihelion 
was  predicted  for  March,  1851 ;  but,  owing  most  probably  to  its 
apparent  proximity  to  the  sun,  it  was  not  seen.  It  will  be  more 
£ivourably  situate  on  its  next  return  in  1855.  Dr.  Brunnow  has 
computed  the  effects  of  the  planetary  perturbations  upon  it;  so  that 
an  ephcmeris  of  its  positions  in  the  heavens  for  that  year  will  be 
placed  in  the  hands  of  observers.  It  will  pass  through  its  perihelion 
on  the  6th  August,  1855. 

M.  Le  Yerrier  has  made  some  computations,  which  render  it 
somewhat  probable  that  a  comet  which  passed  its  perihelion  in 
August,  1678,  is  identical  with  that  discovered  by  De  Vico. 

3032.  Brorsens  comet  — On  the  26th  of  February,  1846,  M. 
Brorsen,  of  Kiel,  discovered  a  faint  comet,  which  was  soon  found 
to  move  in  an  elliptic  orbit,  with  a  period  of  about  5}  years.  Its 
position  in  the  heavens  not  being  favourable,  the  observations  upon 
it  were  few,  and  the  resulting  elements,  consequently,  not  asoe^ 
taincd  with  all  the  precision  that  might  be  desired.  Its  re-appear- 
ance on  its  approach  to  the  succeeding  perihelion,  was  expected  from 
September  to  November,  1851.  It  escaped  ol^rvation,  however, 
owing  to  its  unfuvoumblc  position  in  relation  to  the  sun.  Its  next 
perihelion  passage  will  take  place  in  1857. 

3033.    B* Arrest's  comet.  — On  the  27th  of  June,  1851,  Dr. 
D'Arrcstf  of  the   Iicipsic  Observatory,  discovered  a  faint  cornet^ 


COMETS.  491 

which  M.  Villarceaaz  proved  to  move  in  an  elliptic  orbit,  with 
a  period  of  abont  6}  years.  The  next  perihelion  passage  of 
this  comet  will  take  place  in  the  end  of  1857,  or  the  beginning  of 
1858. 

3034.  Elltptic  camel  of  1743.  —  A  revision  of  the  recorded 
obeeirations  of  former  comets  bj  the  more  active  and  intelligent 
laal  of  modem  mathemaUcians  and  computers,  has  led  to  the  dis- 
covery of  the  great  probability  of  several  among  tbem  having 
revolved  in  elliptic  orbits,  with  periods  not  differing  considerably 
from  those  of  the  comets  above  mentioned.  The  ^ct  that  these 
comets  have  not  been  re-observed  on  their  successive  returns 
through  perihelion,  may  be  explained,  either  by  the  difficulty  of 
observing  them,  owing  to  their  unfavourable  positions,  and  the  cir- 
cumstance of  observers  not  expecting  their  re-appearance,  their 
periodic  character  not  being  then  suspected ;  or  because  they  may 
have  been  thrown  by  the  disturbing  action  of  the  larger  planets  into 
orbits  such  as  to  keep  them  continually  out  of  the  raugc  of  view  of 
terrestrial  observers. 

Among  those  maybe  mentioned  a  comet  which  appeared  in*1743| 
and  was  observed  bv  Zanctti  at  Bologna ;  the  observations  indicate 
an  elliptic  orbit,  with  a  period  of  about  5|  years. 

8085.  Ettiptic  comet  of  1766. — ^This  comet,  which  was  observed 
1^  Meaner,  at  Paris,  and  by  La  Nux,  at  the  Isle  of  Bourbon,  re- 
raved,  aeoording  to  the  calculations  of  Burckhardt,  in  an  ellipse 
with  a  period  of  5  years. 

8036.  LexeWs  comet. — The  history  of  astronomy  has  recorded 
(me  singular  example  of  a  comet  which  appeared  in  the  system,  made 
two  revolutions  round  the  sun  in  an  elliptic  orbit,  and  then  disap- 
peiied,  never  having  been  seen  either  before  or  since. 

This  comet  was  discovered  by  Messier,  in  June,  1770,  in  the 
constellation  of  Sagittarius  between  the  head  and  the  northern 
\  extremity  of  the  bow,  and  was  observed  during  that  month.  It 
I  dinppeared  in  July,  being  lost  in  the  sun's  rays.  After  passing 
-  through  its  perihelion,  it  re-appeared  about  the  4th  of  August,  and 
f  eoDtinued  to  be  observed  until  the  first  days  of  October,  when  it 
^    faally  disappeared. 

\        AU  the  attempts  of  the  astronomers  of  that  day  failed  to  deduce 

\     the  path  of  this  comet  from  the  observations,  until  six  years  latci, 

^     in  1776,  Lexell  showed  that  the  observations  were  explained,  not, 

y     u  had  been  assumed  previously,  by  a  parabolic  path,  but  by  an 

ellipse,  and  one,  moreover,  without  any  example  at  that  epoch, 

which  indicated  the  short  period  of  5}  years. 

It  was  immediately  objected  to  such  a  solution,  that  its  admission 

i     would  involve  the  consequence  that  tho  comet,  with  a  period  so 

I     riiort^  and  a  magnitude  and  splendour  such  as  it  exhibited  in  \XV^^ 


\ 


lift  AsmMroKT. 

ami  liKTC  lea  frequently  aeen  on  Ibrmer  retnnu  to  pci&dtal( 
wbarcM  no  noon]  of  my  such  appeanuioe  was  found. 

Tb  tbb  lezell  replied,  b;  showing  that  the  elemenla  of  ill  tM, 
^srind  from  tlw  oMerrationa  made  ia  1770,  w«re  such,  tlul  ai  in 
BTBYioM  nbalkili,  in  1767,  the  comet  most  hxte  passed  withjo  t 
oiltHWa  oc  the  planet  Jupitor  fiftj-eight  tinaea  less  ibaa  its  di^tasM 
fton  Ibe  m;  lOd  that  congcqaeDtly  it  most  then  have  nvUinal 
an  attnetioa  tmm  the  vrcat  ms£8  of  that  planet  more  than  ihnt 
limei  TUttn  meigGtio  than  that  of  the  snn ;  that  conseqaentl;  it 
«■■  thrown  ont  uf  the  whit  in  which  it  previoiisly  moved  inle  Ibt 
elliptic  orbit  in  which  it  actually  moved  io  1770 ;  that  its  orbit  pn- 
Tionaly  to  1767  was,  according  to  all  probnblUtj,  a  psraboU;  lod, 
in  fine,  that  ocmiequently  moviog  in  an  clliptio  orbit  from  17^  ta 
1770,  and  heviiig  the  periodicity  conseqaent  on  each  motion,  it 
MTerthelca  nored  only  for  the  first  time  in  its  new  orbit,  and  hid 
nenr  come  williin  the  sphere  of  the  sun's  attraction  twToie  tin 
epoch. 

Lczell  further  stated,  that  since  the  comet  passed  throngb  iti 
aphelion,  which  nearly  intersected  Jupiter's  orbit,  at  interrali  flf 
6|  years,  and  it  encountered  the  planet  near  that  point  in  1767,  Ai 
period  of  tie  planet  being  somewhat  above  11  years,  the  phaal 
after  a  single  revolution  and  the  oomet  after  two  revolntiou  mart 
necessarily  again  encounter  each  other  in  1779 ;  and,  that  nnei  ikl 
orbit  was  sach  that  the  comet  must  in  1779  pass  at  a  distaaotfiv 
Jnpiter  500  times  less  than  its  dislsnce  from  the  sun,  it  mnrtiaSf 
from  that  planet  an  action  260  times  greater  than  the  snn'a  altai* 
tion,  and  that  therefore  it  would  in  all  probability  be  again  Ann 
into  a  parabolio  or  hyperbolic  path ;  and,  if  so,  that  it  would  d^Hl 
for  ever  from  our  system  to  visit  other  spheres  of  attraction.  LenL 
therefore,  anticipated  the  finsl  disappearaace  of  the  comet,  wUa 
sotnally  took  place. 

In  the  interval  Lclveeu  1770  and  1T79,  the  comet  rctantediMl 
to  perihelion ;  but  its  position  was  such  that  it  was  above  the  hoiin 
only  during  the  day,  and  could  not  iu  the  actual  state  of  Bcienee  bt 
observed. 

8037.  Analytis  n/  Lnjiface  applied  to  LexeWicnmel,  —  At  this 
epoch  analytical  science  had  not  yet  supplied  a  definite  BolnlioD  of 
the  problem  of  cometary  disturbauccs.  At  a  later  period  the  fp» 
tion  was  resumed  by  Loplace,  who,  in  his  celebrated  work,  the  i 
Jiicanitpie  Cileile,  gave  the  genera!  solution  of  the  following  prob- 
lem : 

"The  actual  orbit  of  a  comet  being  given,  what  waa  ite  orbit  be- 
fore, and  what  will  be  its  orbit  after  being  submitted  to  any  givea 
disturbing  action  of  a  ^\Miel  iieBx  vbicb  it  passes  1 " 

3038.  /rt(>rbabe/oT£\16Taiao^Vl'\(S«olcdi<a«A\i^fci^ 
»uix.  —  Applying  dus  to  \\»ft  ■yitfowiw  wKdL\«xiS£.«.vniA^'<A, 


COMETS.  403 

iBBamiDg  as  data  the  obeerratioDS  recorded  in  1770^  Laplace  showed 
that  before  snstainiDg  the  disturbing  action  of  Jupiter  in  1767^  the 
eomet  must  have  moved  in  an  ellipse,  of  which  the  semi-axis  major 
was  18-298,  and  oonsequently  that  its  period,  instead  of  beinff  5 } 
jears,  must  have  been  48^  years ;  and  that  the  eccentricity  of  the 
orbit  was  such,  that  its  perihelion  distance  would  be  but  httle  less 
than  the  mean  distance  of  Jupiter,  and  that  consequently  it  could 
nerer  have  been  visible.  It  followed  also,  that,  after  suffering  the 
disturbing  action  of  Jupiter  in  1779,  the  comet  passed  into  an 
elliptio  orbit|  whose  semi-axis  major  was  7*3;  that  its  period  was 
eooaeqiiently  20  years;  and  that  its  eccentricity  was  such,  that  its 
perihelion  distance  was  more  than  twice  the  distance  of  Mars,  and 
thml  in  such  an  orbit  it  could  not  become  visible; 

8039.  Revision  of  these  researches  hy  M.  Le  Verrter.  —  This  in- 
Ycatigation  has  recently  been  revised  by  M.  Le  Yerrior,*  who  has 
shown  that  the  observations  of  1770  were  not  sufficiently  definite 
■ad  accurate  to  justify  conclusions  so  absolute.  He  has  shown 
that  the  orbit  of  1770  is  subject  to  an  uncertainty,  comprised  be- 
tween certain  definite  limits ;  that  tracing  the  consequences  of  this 
to  the  positions  of  the  comet  in  1767  and  1779,  these  positions  are 
tabject  to  still  wider  limits  of  uncertainty.  Thus  he  shows  that| 
eompatibly  with  the  observations  of  1770,  the  comet  might  in  1779 
paas  either  considerably  outside,  or  considerably  inside  Jupiter's 
orbit,  or  mighty  as  it  was  supposed  to  have  done,  have  passed  actually 
within  the  orbits  of  his  satellites.  He  deduces  in  fine  the  following 
feneial  conclusions :  — 

1.  That  if  the  comet  had  passed  within  the  orbits  of  the  satellites, 
il  must  have  fallen  down  upon  the  planet  and  coalesced  with  it ;  an 
loeident  which  ho  thinks  improbable,  though  not  absolutely  im- 
posrible. 

2.  The  action  of  Jupiter  may  have  thrown  the  comet  into  a 
panbolio  or  hyperbolic  orbit,  in  which  case  it  must  have  departed 
fiom  onr  system  altogether,  never  to  return,  except  by  the  conse- 
quence of  some  disturbance  produced  in  another  sphere  of  attraction. 

8.  It  may  have  been  thrown  into  an  elliptic  orbit,  having  a  great 
nil  and  long  period,  and  so  placed  and  formed  that  the  comet  could 
Bever  become  visible ;  a  supposition  within  which  comes  the  solu- 
tioD  of  Laplace. 

4.  It  may  have  had  merely  its  elliptic  elements  more  or  less 
Bodified  by  the  action  of  the  planet,  without  losing  its  character  of 
ihort  periodicity ;  a  result  which  M.  le  Verrier  thinks  the  most  pro- 
lable,  and  which  would  render  it  possible  that  this  comet  may  still 
be  identified  with  some  one  of  the  many  comets  of  short  period, 

*  See  Mem.  Acad,  doi  Sciences,  1847, 1848. 

in.  42 


h;ivc  lifi'u  an  cllip.-c,  wlnwe  iniiji'r  asia  was  ctiusiJi'rjb) 
that  ivhii'h  I,aplaie  JL.lufod  fruui  Hiq  iiiPuffitici.t  oW 
Mussier.  lie  sliuwa  that,  before  that  tpoeb,  tbe  pcrihdi 
of  the  coniet  could  not,  uoUcr  any  possible  suppoaitioc 
cocded  three  times  tbe  earth's  mean  dislaoco,  and  moi 
vas  JDcluded  between  1}  and  2  times  ibat  distance;  ai 
Bcmi-oxis  major  of  tbe  orbit  could  not  have  exceeded  4 
earth's  mean  distance,  a  magnitude  3  times  less  than  tb 
to  it  by  the  caloulationa  of  I^place. 

3040.  Proceii  bff  uihich  the  id-enlificafioti  of  •periodic  y 
he  decided.  — It  must  not,  however,  be  aupposed  that  it 
to  compare  the  actual  elements  of  each  periodio  come 
eovercd,  with  the  clemenia  given  ia  the  table  of  M.  Lo  T 
to  infer  the  absence  of  identity  from  their  dikcordance 
inference  would  only  be  rendered  valid  by  ahovring  tl 
Qgcs,  the  comet  in  qucstiou  had  suffered  no  serious  distni 
by  which  the  elements  of  its  orbit  could  be  considcrab 
To  decide  the  question  a  much  more  laborious  and  diffit 
must  lie  encountered;  a  process  from  which  the  uutirin 
M.  Lo  Vcrrier  has  not  shrunk.  It  is  necessary,  in  fine,  i 
factory  and  conclusive  solution  of  such  a  problem,  that  I 
couiet  in  question  should  be  traced  back  through  all 
revolutions  up  to  1779,  that  al!  the  disturbances  which 
from  the  planets  which  it  encountered  in  that  interval  b 
and  asceriaiaed,  and  that  by  such  means  the  orbit  whi 
have  had  previous  to  such  disturbances,  in  1779,  be  < 
Such  orbit  would  then  be  conipared  with  the  table  of  poE 


COMETS.  495 

eomets  of  Fayc,  Do  YicOy  and  Brorscn ;  tracing  back  their  histories 
daring  their  unseen  motions  for  three-quarters  of  a  century,  and 
ascertaining  the  effects  of  the  disturbing  actions  which  thej  roust 
fieverallj  have  sustained  from  revolution  to  revolution,  until  ho 
brought  them  to  the  epoch  of  1770.  On  comparing  the  orbits  thus 
determined  with  those  of  the  table  of  possible  orbits  of  LexelFs 
comet,  he  has  shown  that  none  of  them  can  be  identical  with  it,  how- 
ever strongly  some  of  the  elements  of  their  present  orbits  may  raise 
■uch  a  presumption. 

3042.  Prcbahle  identity  of  De  Vico's  comet  tcith  the  comet  of 
1678.  — The  comet  of  De  Vico  having  presented  striking  analogies 
with  a  comet  which  was  observed  by  Tycho  Brahe  and  Rothmann 
in  1585,  and  one  observed  by  La  Hire  in  1678,  M.  Le  Verricr  has 
applied  like  principles  to  the  investigation  of  these  questions. 

MM.  Laugier  and  Mauvais  observed  that  the  elements  of  Do 
Yieo's  comet  presented  such  a  resemblance  to  that  of  Tycho  Brahe, 
as  almost  to  decide  the  question  of  their  identity.  M.  Le  Verrier, 
tncing  back  the  comet  of  De  Vico  to  1585,  has  shown  that  its 
orbit  at  that  epoch  was  so  different  from  that  of  the  comet  of 
Tycho,  as  to  be  incompatible  with  any  plausible  inference  of  their 
identity.* 

He  has  shown,  however,  by  like  reasoning,  that  there  is  a  high 
degree  of  probability  that  the  comet  of  Do  Vico  is  identical  with 
that  observed  by  La  Hire  in  1678. 

8043.  Blaviplan's  comet  of  1810.  —  M.  Blainpan  discovered  a 
eomet  at  Marseilles  on  28th  November,  1810,  which  was  observed 
at  Milan  until  25th  January,  1820.  The  observations  reduced  and 
cilciilated  by  Prof.  Encko  gave  an  elliptic  orbit  with  a  period  a  little 
abort  of  5  years.  Clausen  conjectures  that  this  comet  may  be  idcn- 
tieal  with  that  of  1743.     It  has  not  been  seen  since  1820. 

3044.  I'un/s  comet  of  1810.  —  A  comet  was  discovered  by 
M.  Pons  on  June  12th,  1810,  which  was  observed  until  July  10th. 
Ph>f.  Encke  assigned  to  it  an  elliptic  orbit,  with  a  period  of  5} 
years. 

3045.  Pigott*$  comet  of  1783.  —  A  comet,  discovered  by  Mr. 
Pigott  at  New  York  in  1783,  was  shown  by  Burckhardt  to  have  an 
dbptic  orbit,  with  a  period  of  5}  years. 

SQ46.— i'eter«'«  comet  of  1846.  — On  the  20th  June,  1846,  a 
eomet  was  discovered  at  Naples  by  M.  Peters,  which  was  subse- 
quently observed  at  Rome  by  De  Vico,  and  continued  to  be  seen 
until  21st  July.  An  elliptic  orbit  is  assigned  to  this  comet,  with  a 
period  of  from  13  to  16  years,  some  uncertainty  attending  the  obser- 
vationj*.  The  rc-appearauce  of  this  comet  may  bo  expected  in  1850, 
18fi0. 

*  M^m.  Acad,  des  Sciences,  1847. 


ini  ASIRONOHT. 

8047-   Ti^ruiar  e;p\opti.»  of  the  orhiti  o/the  eonub 
Klthin  Snturit's:  orhil. — In  TuLIb  III.  w«  Lavc  gtica 

of  the  thirteen  comets  above  mentjoucd. 


i 


.0  Cometj  vrhicli  rerolTt  wilhai  H 


^  '£r 


J^n'ijm 


3048.  Diagram  of  tlte  orbit*. — In  Jig.  817,  the  orbits  of  tbCM 
tbirtecD  comets,  brought  to  a  eomnioii  pliiDe,sre  reprcscaled  roo^f 
bat  in  their  proper  proportions  and  ralutive  positions,  so  aa  to  Mt 
hibit  to  the  eye  their  Beveral  elliptieitiea,  and  the  rel&tive  direo^OBl 
of  their  Bxea.*  All  the%  bodies,  without  one  exception,  Kvolt*  b 
the  coQinion  direction  of  the  planets. 

3049.  Planetary  characlcr  fi/Oiei'r  orhils. — It  is  not  alone,  how- 
ever, in  the  direction  of  thi'ir  motiona  that  the  orbila  of  (facMS  bo&a 


^OSIETS. 


jkw*  ■■  AiMkgr  to  &eM  «(  tk*  flaitb  TbeirididiBalMBB.iritfa 
>aM  awBptioB,  an  whUa  tke  Gaili  nf  tkcse  of  tbe  plaocts.  Theii 
MOBlltdoitiai,  thoogh  iaoomfuMj  g^ntm  thaa  those  of  tho  ptuie», 
■n,  u  will  pnaratly  ffft  InoMBfiaibly  less  than  those  of  &i: 


r  «miatl~  }»t  diMonmi.  Hmu  iMan  diatancca  aod  periods 
{with  the  CTiiiplinn  of  tha  lut  tm  ia  the  table,}  are  withiit  the 
Jtautiof  thooeof  the  pluotgidi. 

SOfiO.  FlmuftifjF  dMraettr of  Aew  otMl— Ha  tamamibmtt 
4he  Bmnban  a^  in  Tsbk  UL  with  i3um  wUA  wlH  U  pfaa 
iMMftar,  in  the  tablM  of  the  elemanto  of  otlwr  sU^tit  flMMlq 
tiM  eompeiiaoD  of  thodiegniuttf  thararitemlh  tbonof  ol 
will  diow  in  ■  striking  niuner,  to  how  gnat  an  extest  tta  'anu 
at  thie  groap  of  ooaieta  ponMa  the  plmla^  chanetar.  Bm^ 
moving  nand  the  nn  in  the  eommoo  dinetun,  tbair  "■Hi'm^w 
wth  a  angle  ezeeptiMi,  an  within  the  Umita  of  thoM  of  the  ' 
le  tut  their  cooenlridlite  ham 


li  ia  tnie  that  their  cooenlridlita  ham  an  otdn  of  n  ^ 
paater;  bnt  on  the  othw  hand,  it  will  beaeen  praaa&j  Aatd 
HO  inoomiiaiaUj  haa  than  the  oooentrioitiaa  of  all  a" 
flometa  yet  tUaomred.     Ili«ir  tacaa  dirtaaoea  and 
Aam  ID  diraot  analogy  with  the  fdamtada. 

Uodente  u  are  the  eccentricities  as  oompand  with  Oum  of 
Other  comets,  thej  are  sufficieatlj  great  to  impart  a  decoded  oml 
form  to  the  orbits,  and  to  produce  oonBiderable  differenoee  bctwem 
the  perihelion  and  aphelion  diBtaaccB,  ae  will  be  apparent  hj  in- 

rtJDK  the  nnmbera  id  the  colnmna  rP  and  (f.  It  ^tpean  Iff 
e,  mt  while  the  perihelion  of  Enck^'s  comet  lies  within  fiw 
orbit  of  Mercury,  its  aphelion  lies  ootside  the  orbit  of  the  miMt 
remote  of  the  plaaetoids,  and  not  far  within  that  of  Jnpiter.  Hm 
perihelion  of  Biela's  comet,  in  like  maimer,  lies  between  the  orinls 
of  the  earth  and  Venus,  while  its  aphelion  lies  ontside  that  of 
Jnpiter.  In  the  case  of  Face's  comet,  the  least  eocentrie  of  the 
gronp,  the  perihelion  lies  near  the  orbit  of  Mars,  and  the  a|Jteli(iii 
Qntaide  that  of  Jupiter. 

It  most  be  remembered  that  the  elliptic  form  of  these  orbili  hu 
only  been  verified  bj  observations  on  the  eucocssive  returns  to  peri- 
helion of  the  first  five  comets  in  the  table.  The  elliptio  eletnenlt 
of  the  others  may,  so  fiir  as  is  at  present  known,  hare  been  e&oed 
bj  disturbing  causes. 

The  angular  motions  at  the  mean  and  extreme  distances  fma  the 
Ban,  given  in  the  columns  a,  a'  and  a"  have  been  compnted,  co  the 
principles  already  explained,  by  the  formnlio 


1,296,000  ,  a' 

n»  same  unmbers  which  express  those  angular  i ,  _ 

express  in  all  cases  the  intensities  of  solar  light  and  heat  in  th« 


COMET&  499 

ieienl  podtions  of  tlie  oomet;  asd  also  the  apparent  motion  of 
ihe  BODi  aa  seen  from  the  comet;  and  a  comparison  of  these  with 
the  oorreapondinff  numbers  related  to  any  of  the  planets,  will 
fllnstrmte  in  a  atnking  manner  how  different  are  the  physical  condi- 
tknia  by  which  these  two  classes  of  bodies  are  affected ;  and  this  will 
be  more  and  more  strikingy  when  the  other  groups  of  comets  have 
been  noticed. 

Taking  the  comet  of  Encke  as  an  example,  it  appears  that  while 
iti  mean  daily  motion  is  1076"  or  18',  its  motion  in  aphelion  is  only 
S'y  and  in  perihelion  nearly  13^.  Its  motion  in  perihelion,  the 
light  and  heat  it  receives  from  the  sun,  and  the  apparent  motion  of 
the  son  as  seen  from  it,  arc  therefore  severally  more  than  150  times 
greater  in  perihelion  than  in  aphelion. 

in.  Elliptio  Comets,  whose  mean  distances  are  nearly 

EQUAL  TO  THAT  OP  UrANUS. 

8051.  Comets  of  long  periods  first  recognised  as  periodic. — ^It 
might  be  expected,  that  comets  moving  in  elliptio  orbits  of  small 
dimensions,  and  consequently  having  short  periods,  would  have 
been  the  first  in  which  the  character  of  periodicity  would  be  dis- 
eofered.  The  comparative  frequency  of  their  returns  to  those  posi- 
tMNif  near  perihelion,  where  alone  bodies  of  this  class  are  visible 
from  the  earth,  and  the  consequent  possibility  of  verifying  the  fact 
of  periodicity,  by  ascertaining  the  equality  of  the  intervals  between 
their  anocessive  returns  to  the  same  heliocentric  position,  to  say 
nothing  of  the  more  distinctly  elliptio  form  of  the  arcs  of  their 
wbits  in  which  they  can  be  immediately  observed,  would  afford 
■bong  ground  for  such  an  expectation ;  nevertheless  in  this  case,  as 
haa  happened  in  so  many  others  in  the  progress  of  physical  know- 
ledge, the  a<^tual  results  of  observation  and  research  have  been  di- 
rectly contrary  to  such  an  anticipation ;  the  roost  remarkable  case 
of  A  oomet  of  large  orbit,  long  period,  and  rare  returns,  being  the 
fint,  and  those  of  small  orbits,  short  periods,  and  frequent  returns, 
the  last  whose  periodicity  has  been  discovered. 

3052.  Newton's  conjectures  as  to  the  ejcistenre  of  comets  of  long 
periods, — ^It  is  evident  that  the  idea  of  tho  possible  existence  of 
eometa  with  periods  shorter  than  those  of  the  more  remote  planets, 
and  orbits  circumscribed  within  the  limits  of  the  solar  system,  never 
oeenrred  to  the  mind  either  of  Newton  or  any  of  his  contemporaries 
or  immediate  successors. 

In  the  third  book  of  his  principia,  he  calls  comets  a  species  of 
planets,  revolving  in  elliptic  orbits  of  a  very  oval  form.  But  he 
continues,  ''I  leave  to  be  determined  by  others  the  transverse 
diameters  and  periods,  by  comparing  comets  which  return  after  long 
imiarvab  of  time  to  the  same  orbits." 


A8TR0N0IJT. 

ntereBting  to  observe  the  avidity  with  which  minds  of  i 

^Jn]c^  snatch  at  such  gcaeralisations,  even  when  but  slen- 

louoded  upon  facts.     These  coDJeeturea  of  Newton  were  scfia 

■  adopted  by  Vullaire  :  "  Fl  y  a  quelque  apparence,"  says  he, 

a  essay  on  comets,  "  qn'on  cnanaitni  un  jour  un  ecTtain  nombre 

L-es  autrcs  pku^tee  qui  sous  le  Dom  de  com^tes  t 

luus  lutour  du  aoleil,  mnis  U  nc  faut  pas  esp^rer  qu' 

sent  toutes." 

And  again,  elsowhere,  on  tho  same   'ubject : — 

"ComEt  !i1  du  lonnen 


ItemOBlci,  uhk-uui.  i  nitTO  dcf  JOUTS." 

3053.  HnV'n't  reicarrhcx.  nrdinnry  as  these  oonjeetUTM 
must  have  appeared  at  the  ,  r  were  Hoon  strictly  Tvah'Md, 
Halley  undertoulc  the  kboui  ..'  fining  the  cinm Distances  at- 
tending all  the  comets  previously  ivounled,  with  a  view  to  diitcover 
whether  any,  and  which  of  them,  appeared  to  follow  the  same  path. 
He  found  that  a  comol  which  bad  been  observed  by  himwlf,  by 
Newton,  and  their  contemporaries  in  16K2,  followed  a  path  while 
ViEible,  which  coincided  so  nearly  with  tho^  of  couieta  which  had 
been  observed  in  IG07,  and  in  1531,  aa  to  reuder  It  eitreuielj  pro- 
bable that  these  objecia  were  the  same  identical  oomet,  revolving  in 
BQ  elliptic  orbit  of  such  dimcni ions,  as  to  cause  itfi  return  to  pentw* 
lion  at  intervals  of  75-76  years. 

The  comet  of  1682  had  been  well  observed  by  La  Hire,  Picard, 
Heveliua,  and  Flamatead,  whose  observations  supplied  all  the  data 
necessary  to  calculate  its  path  while  visible.  That  of  1607  had 
been  observed  by  Kepler  and  LongomoDtanua ;  and  that  of  1531, 
by  Pierre  Apian  at  Ingolatadt,  the  observations  in  both  cases  being 
sufficient  for  the  deter miuation  of  the  path  of  the  body,  with  all  tlx 
accuracy  necessary  for  its  identification. 

3054.  Ilolle^  predicfs  iU  re-appearance  in  1758-9.  —  Of  Ihs 
identity  of  the  paths  while  visible  on  each  of  these  appearaiwM 
Halley  entortaincd  no  doubt;  and  announced  to  the  world  the  di*- 
GOvery  of  the  elliptic  motion  of  comets,  as  the  result  of  oombtned  ' 
observation  and  calculatinn,  and  entitled  to  as  much  cooGdenee  u 
any  other  consequence  of  an  established  physical  law ;  and  pre- 
dieted  the  re-appearance  of  this  body,  on  its  saccceding  retara  to 
pcrihclioD  in  1758-9.  He  observed,  however,  that  as  in  the  in- 
terval between  1C07  and  1682  the  comet  passed  near  Japiler,  ila 
velocity  must  have  been  augmented,  and  consequently  its  period 
■hortened  by  the  action  of  that  planet.  This  period,  therefore, 
having  been  only  seveoty-fivo  years,  be  inferred  that  the  following 
period  would  probably  be  eeveoty-si<  years  or  upwards;  «nd  oodm- 


OOMBTS.  •  601 


qncDtly  that  the  oomet  ought  not  to  be  expected  to  appear  until  t1 
end  of  1758,  or  the  beginning  of  1759.     It  is  impossible  to  imagii 


the 
imagine 
any  quality  of  mind  more  enviable  than  that  which,  in  the  existing 
Atate  of  mathematical  physics,  could  have  led  to  such  a  prediction. 
The  imperfect  state  of  science  rendered  it  impossible  for  Halley  to 
offer  to  the  world  a  demonstration  of  the  event  which  he  foretold. 
''  He  therefore/'  says  M.  de  Pontecoulant,  ''  could  only  announce 
these  felicitous  conceptions  of  a  sagacious  mind  as  mere  intuitive 
perceptioiuiy  which  must  be  received  as  uncertain  by  the  world,  how- 
ever he  might  have  felt  them  himself,  until  they  could  be  verified 
by  the  process  of  a  rifforous  analysis.'^ 

Subsequent  researches  gave  increased  force  to  Halley's  prediction ; 
for  it  appeared  from  the  ancient  records  of  observers,  that  comets 
bad  been  seen  in  1456"*"  and  1378,  whose  elements  were  identical 
with  those  of  the  comet  of  1682. 

8054.  Great  advance  of  mathematical  and  physical  science* 
kliceeii  1682  and  1759.  —  In  the  interval  of  three-quarters  of  a 
eentuiy  which  elapsed  between  the  announcement  of  Ualley's  pre- 
dietioD  and  the  date  of  its  expected  fulfilment,  great  advances  were 
Bade  in  mathematical  science;  new  and  improved  methods  of  in- 
veatigatioD  and  calculation  were  invented ;  and,  in  fine,  the  theory 
of  gravitation  was  pursued  with  extraordinary  activity  and  success 
Affcngh  its  consequences  in  the  mutual  disturbances  produced  upon 
ttie  motions  of  the  planets  and  satellites,  by  the  attraction  of  their 

*  The  appearance  of  this  comet  in  1456,  was  described  by  contemporary 
■athorities  to  have  been  an  object  of  " unheard-of  magnitude;"  it  was  ao- 
eoBpanied  by  a  tail  of  extraordinary  length,  which  extended  over  sixty 
degTMS  (a  third  of  the  heayens),  and  continued  to  be  seen  during  the  whole 
of  the  month  of  June.  The  influence  which  was  attributed  to  this  appear- 
taeo,  renders  it  probable  that  in  the  record  there  exists  more  or  less  of 
aaggeration.  It  was  considered  as  the  celestial  indication  of  the  rapid 
■eecn  of  Mohamme<l  II.,  who  had  taken  Constantinople,  and  struck  terror 
kto  the  whole  Christian  world.  PopeCalixtus  II.  levelled  the  thunders  of 
tin  Church  against  the  enemies  of  his  faith,  terrestrial  and  celestial,  and 
ia  the  same  bull  exorcised  the  Turks  and  the  comet ;  and  in  order  that  the 
■■■oiy  of  this  manifestation  of  his  power  should  be  for  ever  preserved,  he 
ttduned  that  the  bells  of  all.  the  churches  should  be  rung  at  midday  —  a 
eastom  which  is  preserved  in  those  countries  to  our  times.  It  must  be 
liflutted  that,  notwithstanding  the  terrors  of  the  Church,  the  comet  pur- 
nied  its  course  with  as  much  ease  and  security  as  those  with  which  Mo- 
hamned  converted  the  church  of  St.  Sophia  into  his  principal  mosque. 
I  The  extraordinary  length  and  brilliancy  which  was  ascribed  to  the  tail 
vpoB  this  occasion,  have  led  astronomers  to  investigate  the  circumstances 
lader  which  its  brightness  and  magnitude  would  bo  the  greatest  possible ; 
and,  upon  tracing  back  the  motion  of  the  comet  to  the  year  145C,  it  has 
been  found  that  it  was  then  actually  under  the  circumstances  of  position 
with  respect  to  the  earth  and  sun  most  favourable  to  mngnitudo  and  pplcn- 
doar.  So  far,  therefore,  the  resalts  of  astronomical  calculation  corroborate 
the  rcoords  of  histOTy. 


ABTRONOMT. 

me  upon  anotber.     As  the  epoch  of  the  eipectcd  retorn  of 

omet  to  its  perihelioQ  approached,  therefore,  the  gcieodfic  world 

ived  to  divest,  as  far  as  possible,  the  prediction,  of  that  vsgaeocas 

loh  necessirily  attended  it,  owing  to  the  imperfect  state  of  science 

the  time  it  was  made,  aad  to  calcakte  the  exact  efieols  of  those 

piaaetB  whose   masses  were  sufficieatly  greal;   in   BCcelenxUng  or 

retardiog  iU  motion  while  passing  them. 

8056.  Exact  path  of  the  cornel  on  it*  raum  and  time  of  iu 
perihelion  calculated  and  predicted  by  Clairaut  and  Lalandx. — 
Tbia  innniry,  which  presented  great  mathemiticol  difficaltics,  uid 
involved  enormous  arithmetical  labour,  was  nndcrtiLketi  b;  Cburant 
and  Lalande :  the  former,  a,  mathematician  irnd  oatural  philosopher, 
who  had  already  applied  with  great  success  the  principles  of  gravi- 
tation to  the  motions  of  tbo  moon,  oudertook  the  purely  analylicil 
part  of  Ibe  JDves ligation,  which  consisted  in  csUblisbing  certsia 

fenorat  algebraical  formula,  by  wb  icb  the  disturbing  actions  exerted 
y  the  plunets  on  the  comet  wore  expressed ;  and  Lalande,  an  emi- 
nent practical  astronomer,  undertook  the  labour  of  the  nrichmetkal 
oompulations,  in  which  he  was  assisted  by  a  lady,  Madame  Lepanle, 
whose  name  has  thua  become  celebrated  in  tlje  ano^ils  of  science. 

These  elaborate  calculations  being  completed,  Clairant  pnMnted 
the  result  of  their  joint  labours,  in  a  memoir,  to  the  Academy  of 
Sciences  of  Paris,*  in  which  he  predicted  the  next  arriTil  of  the 
comet  at  perihelion,  on  the  18th  April,  1759 ;  a  date,  however, 
which,  before  the  re-appearance  of  the  comet,  he  found  reaaiHi  to 
ohange  to  the  11th  of  April,  and  assigned  the  path  which  the 

*  When  it  is  conaidered  thut  tlie  period  of  Hallej'B  oom«t  U  aboat  mtw- 
^-five  jears,  enil  tbftt  every  portioD  of  iticaurae  Tar  two  anacettive  periodi 
wu  necessary  to  be  calculated  aeparatel;  in  this  w*j,  Mine  notioa  lur 
be  fonaed  oC  tlie  labour  encouatefed  by  Lalaade  and  Madame  Lepaota. 
••During  six  aiontba,"  says  Lalande,  "we  calcula(«d  from  momilig  to 
night,  Bomelimes  even  at  meals;  the  coDsequence  of  which  wif,  Uial  1 
contracted  nn  illness  which  chnnged  m;  constitution  for  the  rtmuodn  of 
nv  lire.  The  assistance  rendered  bj  Madame  Lepaate  was  such,  tbat 
without  her  we  never  could  have  dared  to  undertake  this  eDormona  labour, 
in  which  it  was  necessarj  to  calculate  the  distance  of  each  of  the  t<o 
planets,  Jupiter  and  Saturn,  from  the  comet,  and  their  attraction  npoD 
that  body,  separntcly.  for  every  successive  degree,  and  for  150  yean." 

The  name  of  Madame  Lepaute  does  not  appear  in  CUiraut's  memoir;  • 
•appTession  which  Lalaude  attributes  to  the  influence  eieraised  by  another 
lady  to  whom  Clairaut  was  attached.  Lalande,  however,  quotes  letter*  at 
Clairaut,  \a  which  he  speaks  ia  lerms  of  high  admiration  of  •'  la  aavaala 
Miculatrice."  Tlie  labours  of  Ibis  lady  in  the  work  of  calculation  (for  «hs 
also  assisted  Lulnnde  in  constructing  tiis  Kphtmeridta)  at  length  so  weak- 
ened her  sight,  that  she  was  compelled  to  desist.  5he  died  in  1788.  while 
attending  on  her  husband,  who  hud  become  insane.  See  the  articles  on 
eomets,  by  Professor  de  Morgan,  in  the  Companion  to  lit  BritiA  Almmt— 
'  voar  1833. 


COMETS.  503 

comei  would  follow  while  visible,  as  determined  by  the  following 
data:  — 

bcUnaikm.        Long,  of  node.       Long,  of  perih.         Perlhel.  diit       Dlrectioii. 

17**  87'  53<>  bV        803<>  W  0-68       retrograde. 

8057.  Remarkable  anticipation  of  the  discovery  of  Uranitu,  -^ 
In  annoanciDg  his  prediction  Clairaut  stated,  that  the  time  assigned 
for  the  approaching  perihelion  might  vary  from  the  actual  time  to 
the  extent  of  a  month ;  for  that  independently  of  any  error  either 
in  the  methods  or  process  of  calculation,  the  event  might  deviate 
more  or  less  from  its  predicted  occurrence,  by  reason  of  the  attrao- 
ticm  of  an  undiscovered  planet  of  our  system  revolving  heyond  the 
9rhit  of  Saturn.  In  twenty- two  years  after  this  time,  this  conjeo- 
tnre  was  realised  by  the  discovery  of  the  planet  Uranus,  by  the  late 
Sir  William  Hcrschclli  revolving  round  the  sun  one  thousand  mil- 
lions of  miles  beyond  the  orbit  of  Saturn ! 

8058.  Prediction  of  IlaUey  and  Clairaut  fulfilled  by  re-appear- 
amee  of  the  comet  in  1758-9.  —  The  comet^  in  fine,  appeued  in 
Deoember  1758,  and  followed  the  path  predicted  by  Clairaut,  which 
diflbxed  bat  little  from  that  which  it  had  pursued  on  former  appear- 
■noeSy  as  will  be  seen  by  a  comparison  of  the  elements  as  given 
above  with  those  nnce  ascertained.  It  passed  through  perihelion 
oa  the  13th  March,  within  22  days  of  the  time^  and  within  the 
limit  of  the  possible  errors  assigned  by  Clairaut. 

8058.  Disturbing  action  of  a  planet  on  a  comet  explained.  — 
The  general  effects  of  a  planet  in  accelerating  or  retarding  the  mo- 
tioo  of  a  comet  are  easily  explained,  although  the  exact  details  of  the 
diatorbanoes  are  too  complicated  to  admit  of  any  exposition  here. 

Let  ^fjig'  818,  represent  the  place  of  the  disturbing  planet,  and 
0  that  of  tne  comet  The  attraction  of  the  planet  on  the  comet 
will  then  be  a  force  directed  from  o  towards  p,  and  by  the  principle 

of  the  composition  of  forces  is  equivalent 
to  two  components,  one  c  m  in  the  direc- 
tion of  the  comet's  path,  and  the  other 
On  perpendicular  to  that  path.  If  the 
motion  of  the  comet  be  directed  from  o 
towards  m,  it  will  be  accelerated;  and 
if  it  be  directed  from  c  towards  m',  it 
will  be  retarded  by  that  component 
Fig.  81S.  of  the  planet's  attraction  which  is  di- 

rected from  c  to  m.  The  other  com- 
ponent c  m  being  at  right  angles  to  the  comet's  motion,  will  have 
no  direct  effect  either  in  accelerating  or  retarding  it. 

It  appears,  therefore,  in  general,  that,  if  the  direction  ot  the 
Qomet's  motion  c  m  make  an  acute  angle  with  the  Uue  o  T^  di\)i.^\i 
U>  the  fhnetf  the  planet's  attraction  will  accelerate  it  *,  oiidi  \i  \V& 


r 


ASTB^NOinr. 


flection  0  tn'  malie  an  obtiuo  angle  nitli  the  lioeB  C  F,  it  inQ 

rolard  it. 

TLis  being  understood,  the  disturbing  action  of  »  plaaet  snrfi  u 

Jupiter  or  Katiim  on  a  comet  Buch  as  Ilntley'a  may  be  cuilj  com- 

orcheudcd.  la  jig.  819,  the  orbit  of  tbe  comet  is  represented  »t 
A  f  P  i/'  in  ita  proper  proportions,  a  p 
being  the  major  axis,  p  tbe  place  of 
perihelion,  a  that  of  aphelion,  and  h 
that  of  the  focus  in  which  the  gun  ii 
placed.  The  email  circle  described 
round  s  rcprescnla  in  its  proper  pro- 
portions tbe  orbit  of  the  earth,  niom 
distance  ia  about  twice  that  of  the 
comet  when  the  latter  is  st  perihe- 
lion. The  circle  pp'p"  repreecul*  in 
its  proper  proporliona  the  orbil  uf  Ju- 
piter, which,  for  illustration,  we  shall 
consider  as  die  disturbing  plane L 

It  will  be  apparent  on  tbe  men 
inspection  of  the  diagram,  that  lines  | 
drawn  from  the  planet,  whatcTer  ba 
its  place,  to  any  point  whatever  of  the  | 
comet's  path  bclwccn  its  aphelion  A  ( 
and  the  point  m',  where  it  arrives  ai 
the  orbit  of  the  planet  in  approaching 
the  Eun,  wiil  make  acute  angles  iriih 
tbe  direction  of  tbe  comet's  motion, 
and  that,  consequently,  the  comet  wilt 
be  Bccelcraled  by  tbe  action  of  th* 
planet.  In  like  manner  it  ia  appareal 
that  linea  drawn  frora  the  planet, 
whatever  be  its  place,  to  any  pcdnl 
whatever  of  ihe  comet's  path  hetweca 
ind  the  aphelion  A,  will  make  ob- 


Fig.  819. 


toBe  angles  with  the  direction  of  the 

3nently,  the  comet  will  be  retarded  by  the  action  of  the  planet  ia 
eparting  from  tho  sun,  from  m  to  a. 
In  that  part  of  tho  comet's  path  which  lies  within  the  pTanel'i 
orbit,  the  action  of  tho  planet  alternately  aceelcmtes  and  retards  it, 
according  to  their  relative  position-  If  the  planet  be  at  j>,  suppose 
po  drawn  so  as  to  be  at  right  angles  to  the  path  of  tho  comeL 
Witween  m'  and  o  the  action  of  the  planet  at^  will  accelerate  the 
comet,  aud  after  the  comet  passes  ■  it  will  retard  it.  In  like  mao- 
Der  if  the  planet  be  at  p",  it  wilt  first  retard  the  motion  of  the  comet 
prooeoding  from  m'  towards  a,  and  will  continue  to  do  so  until  the 
lino  of  dircotion  becomes  perpendicular  to  that  of  tbo  comet's  mo- 
tioa.  afler  which  \l  ^v\U  aAcAc'ra.v^  'it.- 


COMETS.  605 

It  appears,  therefore,  that  daring  the  period  of  the  oomet,  the 
&tarbiDg  action  of  the  planet  is  subject  to  several  changes  of  direo- 
tion,  owing  partly  to  the  change  of  position  of  the  comet  and  partly 
to  that  of  the  planet;  and  the  total  effect  of  the  disturbing  action 
of  the  planet  on  the  oomet's  period  is  found  by  taking  the  differenco 
between  the  total  amount  of  all  the  accelerating  and  all  the  retard- 
iDff  actions. 

In  the  case  of  the  planet  Jupiter  and  Halley^s  comet,  the  former 
makes  nearly  seven  complete  revolutions  in  a  single  period  of  the 
eomet;  and  consequently  its  disturbing  action  is  not  only  subject  to 
several  changes  of  direction,  but  also  to  continual  variation  of  in- 
tendty,  owing  to  its  change  of  distance  from  the  comet 

Small  as  the  arc  in'  p  m  of  the  comet's  path  is  which  is  included 
within  the  orbit  of  Jupiter,  the  fraction  of  the  period  in  which  this 
arc  18  traversed  by  the  comet  is  much  smaller)  as  will  be  apparent 
by  considering  the  application  of  the  principle  of  equable  areas 
(2599)  to  this  case.  The  time  taken  by  the  comet  to  move  over 
the  arc  m'  P  m  is  in  the  same  proportion  to  its  entire  period,  as  the 
area  included  between  the  arc  nt'  pm  and  the  lines  m!  s  and  m  s  is 
to  the  entire  area  of  the  ellipse  a  p. 

To  simplify  the  explanation,  the  orbit  of  the  comet  has  here  been 
supposed  to  be  in  the  plane  of  that  of  the  disturbing  planet.  If  it 
be  not,  the  disturbing  action  will  have  another  component  at  right 
angles  to  the  plane  of  the  comet's  orbit,  the  effect  of  which  will  be 
a  tendency  to  vary  the  indication. 

3060.  JE^ect  of  the  perturbing  action  of  Jupiter  and  Saturn  on 
HaUt^B  comet  between  1682  and  1759. — The  result  of  the  investi- 
gation by  Clairaut  showed,  that  the  total  effect  of  the  disturbing 
action  of  Jupiter  and  Saturn  on  Halley's  comet  between  the  peri- 
Iwlions  in  1682  and  in  1759,  was  to  increase  its  period  by  618  days 
as  compared  with  the  time  of  its  preceding  revolution,  of  which  in- 
crease, 100  days  were  due  to  the  action  of  Saturn,  and  518  to  that 
of  Jupiter. 

Clairaut  did  not  take  into  account  the  disturbing  action  of  the 
earth,  which  was  not  altogether  incoosiucrablc,  and  could  not  allow 
for  those  of  the  undiscovered  planets  Uranus  and  Neptune.  The 
effects  of  the  action  of  the  other  planets,  Mars,  Venus,  Mercury, 
and  the  planetoids,  are  in  these  cases  insignificant 

3061.  Calculations  of  its  return  in  18*^5-6. — In  the  interval  of 
three-quarters  of  a  century  which  preceded  the  next  re-appearance 
of  this  comet,  science  continued  to  progress,  and  instruments  of  ob- 
servation and  principles  and  methods  of  investigation  were  still 
further  improved;  and,  above  all,  the  number  of  observers  was 
tptktXj  augmented.  Before  the  epoch  of  its  return  in  1835,  its  mo- 
boos,  and  the  effects  produced  upon  them  by  the  disturbing  action 
of  tlie  several  planets,  were  computed  by  MM.  BamomaU)  ^QiiW 

Ui.  ^3 


ASTROSOMT, 

mt,  Kosenberger,  uid  Lebroann,  vho  aerersHj  pretiiAed  id 

al  at  periholion  : — 

Dnmoijcnii 4lh  Not.  1885. 

Ponlecoulant  7lh 

Boseuberger IIIli         " 

LeLmmin 2Btli         ■' 

3062.  PrediHiom /ul//rtd.— These  predictions  were  all  pnblieW 
before  July  1885.  The  comet  was  seen  at  Rome  on  tLe  &tU  J^a- 
ffust,  in  a  position  wHIul  one  iJrgrcf.  m  the  plaoe  assigned  to  it  fuc  I 
Hiat  day,  in  the  pphcmoria  of  M.  Rosenbcrgsr.  On  the  20th  Au- 
gust, it  became  visible  to  a!l  observers,  and  pursued  the  course,  with 
very  little  dcvislion,  which  had  been  aa^igaed  to  it  in  the  epbeniB- 
rides,  nrlTing  ot  its  perihelion  on  the  16th  Nov.,  being  ver;  nearlj 
a  mean  between  the  four  epochs  aasigneil  in  the  prediotJDus. 

After  this,  paaaing  south  of  tbe  equator,  it  was  not  viaihie  in 

''hem  latitudes,  but  (Mmtinued  to  be  ieeu  id  tbe  soutbem  faetni- 
re  until  the  5tb  of  May  18^f>,  when  it  dually  disappeared,  not 

.J  to  retom  uutil  tbe  ji'ear  1911. 

d063.  Tabular  tyiwpsU  of  the  moticm  of  HaUey't  comet, — In 
Table  IV.  ia  given  a  Bynopsia  of  the  elements  of  the  orbit  of  this 
comet,  deduced  from  the  obserTtitions  made  on  each  of  ila  seyea 
Buccessive  returns  to  periholion,  between  l'S~S  and  1835  iucliulTe. 

TABLE  17.  I 

of  Hiillcj'B  Comet  to  1835.  1 


It  appears  that  the  mean  dJetance  of  this  comet  is  about  eighteen 
times  that  uf  the  earth,  aud  that  it  is  C0Di>»1uently  a  little  less  than 
the  mean  distance  of  Urunus.  When  in  perihelion,  its  distance 
from  the  sun  is  about  half  the  earth's  distance,  while  its  distance  in 
aphelion  ia  above  thirty-five  times  the  earth's  distance,  and  therefore 
seventy  ttmea  ita  perihelion  distance. 

"064.  Pons's  comet  of  1812.  — On  the  20th  of  Jnlj  1812,  a 
r  was  discovered  by  M.  Pons,  whose  orbit  was  raloalated  by 


COMETS. 


507 


Professor  Enck^,  and  was  found  to  be  an  ellipse  of  such  dimensions 
as  to  give  a  period  of  75}  years,  equal  to  that  of  Halley's  comet. 

30l>5.  Gibers'  comet  of  1815.— On  the  6th  of  March  1815,  Dr. 
Gibers  discovered  at  Bremen,  a  comet  whose  orbit,  calculated  by 
Professor  Bessel,  proved  to  be  an  ellipse,  with  a  period  of  74  years. 
The  next  perihelion  passage  of  this  comet  is  predicted  for  the  9th 
of  February  1887. 

3066.  De  Vico*s  comet  of  1846.  — On  the  28th  of  February 
1846y  M.  de  Yico  discovered  a  comet  at  Rome,  whose  orbit,  calcu- 
lated by  MM.  Van  Beinse  and  Pierce,  appears  to  be  an  ellipse,  with 
1  period  of  72-73  years. 

8067.  Bronen's  comet  of  1847.  —  A  comet  was  discovered  by 
H.  BroTsen  at  Altona,  on  the  20th  of  July  1847;  the  orbit  of 
which,  calculated  by  M.  d' Arrest,  appears  to  be  an  ellipse,  with  a 
period  of  75  years. 

3068.  WesiphaVs  comet  of  1852.  —  On  the  27th  of  June,  1852, 
a  comet  was  discovered  by  M.  Westphal  at  Gottingen,  and  was  soon 
afterwards  observed  by  M.  Peters  at  Constantinople.  The  calcu- 
latioa  of  its  orbit  proves  it  to  be  an  ellipse,  with  a  period  of  about 
70  years. 

3069.  Tabular  n/nopsis  of  the  motions  of  these  six  comets.  —  In 
Tible  V.  are  presented  the  data  necessary  to  determine  the  motions 
of  these  six  comets : — 

TABLE  V. 

Synopsis  of  the  Motion  of  the  Elliptic  Comets,  whose  mean  Distances  are 

nearly  equal  to  that  of  Uranus. 


I.  Bsiitr .... 

L  FaM(ISl2).  . 

a.  ott»^(i«is> . 

4.  D>  V*o.  (Wtf) 
fw  9nnn  ( IH|-> 


Mmb 

DivlMC*, 

Earth*t  d. 


ECTPB. 
tllCllJ. 


1798T5 
IT0SV5 

U-a.W)6 
I7  7T!» 
l(i-(i200 


0«74 

OfiSli 
(Hi5<44 
0-9-20 
0-9248 


Perihflion 
DuUnce. 


(1-0 


0-V«66 
0-7771 
1-2129 
0-e6M 
0-4«<79 
1-2610 


Di* 


d"«:a  X 
(l  +  «) 


33-4140 
at  Oi'iO 
34-3ir0 
350710 
31-9700 


hulj  Mothm. 


ilt 

Mean 

Diktaoce. 


46-3 
60-7 
47  9 
48-4 
47-3 
624 


At 

PBriho. 
lioB. 


43SI0 
84305 

Id  lis 

6A&0 
22966 


At 

Aph«« 

lloo. 


12 
13-3 
12-8 
H-7 
18-2 
14-2 


L^ 


I.  H*^rr  .... 

4.  I>p\i.«ilM«l 
ft.  W«rf|>hai  llW2) 


IVrW. 
Venn. 


Lnrgitude 

f.f 
Per  hrlion. 


Loncitude 

of  A«'"eiiil- 

iiij  Niide. 


Iiirlmation. 


Time  of 
Perihelioii  Paaafe. 


74-    0 

71  «'70 
•7  770 


rVM  31  32 

i-i  Ih  4 

1J9  I  > 

^  Si  *(i  ,    '.-, 

TO  12  4f;     2tf^ 


9    59     17    m 

I      2  I  -.1    57 


2-    yt 

a'.     3b 
4S    4*« 


41     .f| 
SI     57 


fi  '  Nov.  15.  ipas. 
;«     S'p'.  Ii.  \y.2. 

l.i  i   Ma:,  j.  I>:6. 


h. 

z: 

7 
2> 
14 


l!»      S    25  '  S.J.'.  9.  HJ47. 
43    12     16  j  346     13    2^  ,  40    5b    32  ,  Ucl.  12,  Ib&L 


in. 

41 

41 

5« 

1 

13    II 
16     6 


DircciioD 

of 
Motion. 


R 

li 

n 

D 

I) 

D 


608  ASTKOKOICT. 

3070.  Diagram  of  thnr  orbit*.  —  In  Jlj.  820,  is  preflentcd  > 
'  plin  of  their  orbits,  brought  upon  &  common  plane,  and  dnwn 
According  to  tbe  scalo  indicated.  This  figure  ehowB,  in  a  murner 
Bofficicntly  exact  for  the  purposes  of  illuatrauon,  the  relatiTe  mtg- 
nitudcB  aod  forms  of  the  ais  orbits,  aa  well  as  tho  directions  of  thnr 
Berentl  axes  with  relation  to  that  of  the  first  point  of  Aries. 


3071.  Plawlary  rhariirlrrg  arc  i\f.arhi  rffared  t'n  thfse  orliltt.  — 
By  comparing  the  elonionta  pivcn  ju  Tabic  V.,  and  the  forms  and 
magnitudes  of  tlic  orbits  sbowti  in  the  iliagram,  with  '.hose  of  llie 
first  group  of  clliplio  compts  jrivon  in  Tiiblc  III.  and  Jrawn  in  /.?. 
812,  it  will  bo  perceived  (liat  tiio  plauet;iry  cliaracteristics  notiei"-! 
in  the  latter  group,  arc  nearly  i.ffaccJ.     Five  of  the  six  comets  com- 


COMETS.  509 

posing  the  secoDcl  group,  Fevolve  in  the  common  direction  of  the 
planets,  and  this  is  the  only  planetary  character  ohservable  among 
them.  The  inclinations,  no  longer  limited  to  those  of  the  planetary 
orbit«iy  range  from  18^  to  74^.  The  eccentricities  are  all  so  extreme, 
that  the  arc  of  the  orbit  near  perihelion  approximates  closely  to  the 
parabolic  form,  and,  in  fine,  the  most  remarkable  body  of  the  group, 
the  comet  of  Halley,  revolves  in  a  direction  contrary  to  the  common 
motion  of  the  planets. 

Bat  it  18  more  than  ill  in  the  elongated  oval  form  of  their  orbits, 
thnt  Ihii  group  of  comets  differs,  not  only  from  the  planets,  but  from 
thf  Jnt  group.  While  their  perihelia  are  at  distances  from  the 
na^  between  those  of  Mars  and  Mercury,  their  aphelia  are  from 
tfoto flre  hundred  millions  of  miles  outside  the  orbit  of  Neptune. 
die  comet  of  Halley,  for  example,  in  perihelion,  is  at  a  dis- 
from  the  sun  less  than  that  of  Venus ;  but  at  its  aphelion,  its 
exceeds  that  of  Neptune  by  a  space  greater  than  Jupiter's 
from  the  sun.  The  mean  angular  motion  of  this  comet  is 
■liflj  the  same  as  that  of  Uranus;  but  its  angular  motion  in  peri- 
y00^  is  three  times  that  of  Mercury ;  while  its  angular  motion  in 
0lidien  is  little  more  than  half  that  of  Neptune, 
fjoe  aoReepooding  variations  of  solar  light  and  heat,  and  of  the 
magnitude  and  motion  of  the  sun  as  seen  from  the  comet, 
dly  inferred. 


.-    ^^. 


BK*  JBuiFTio  Comets,  whose  mean  distances  exceed  the 

UMIT8   OF  the   solar   SYSTEM. 

§tn%  TaMar  tynopsxs  of  twenf^-one  elliptic  comets,  of  great 
and  long  period,  —  Although  the  periodicity  of  this 
comets  has  not  yet  in  any  instance  been  certainly  established 
itions  made  upon  their  successive  returns  to  perihelion, 
Ofcierffttions  made  upon  them  during  a  single  perihelion  passage 
arc  of  their  orbit,  which  exhibits  the  elliptic  form  so 
■i|q[aivoeally,  as  to  supply  computers  and  mathematicians  with  the 
dipa  Bcceasary  to  obtain,  with  more  or  less  approximation,  the  value 
tf'  die  eccentricity,  which,  combined  with  the  perihelion  distance, 
gtftB  the  form  and  magnitude  of  the  comet's  orbit. 

By  calculations  conducted  in  this  manner,  and  applied  to  the 
obeervations  made  on  various  comets  which  have  appeared  since  tho 
latter  part  of  the  seventeenth  century,  the  elliptic  orbits  of  twenty- 
one  of  these  bndies  have  been  cou)putcd,  and  are  given  in  the  order 
of  tlie  dates  of  their  pcribc'lion  pa!«SJigC3  in  the  table  on  p.  510. 

Of  this  group  the  least  eccentric  is  No.  15,  which  passed  its  peri- 
helion in  1^40.  This  comet  was  discovered  at  Berlin  by  M.  Bre- 
miker,  and  its  orbit  was  calculated  by  Gotz,  and  proved  to  be  an 
ellipse,  having  the  elements  given  in  the  table,  subject  to  no  greater 

43* 


Bja*>ptu  of  th*  MotioDa  of  tho  Elliptic  ComeU  wboM  meui  DuUmm 
•iMed  tb*  Uioits  of  the  Solar  Sjitem. 


11 

1- 

13'': 

._• 

i.-m; 

;? 

PrHl... 

IW.U. 

.Sk 

■&■ 

r- 

«"^ 

,^ 

. 

' 

' 

:li 

1 

s 

1 

i 

H 

ill 

'li 

"1 

1 

1 

ll! 

li"; 

■s.-i 

Lrj^l.*. 

^2"'-. 

,.,,„,., 

,..^.„ 

- 

• 

> 

r 

1 

iiii 

111 

SSI 

ill 

Ui 
III 
III 

«f  1 

Hi  1 

ill  1 

uncertainly  llian  g',th  of  tlie  v.ilno  awigncJ  to  the  mean  distanfi*. 
TLe  eceentricify,  and  conser[uen(lj  the  form  of  tbc  orbit,  is  similar 
to  thiit  of  Hallry,  but  tbc  major  axia  is  23  limes,  and  the  peri.-J 
nearly  five  times  greater.  iLf  perihelion  distance  is  eqnal  to  thai 
of  Mars,  and  its  ap\»e\wT\  AW^ihvi^p  TOi\Tt;  vVioti.  three  times  thil  ef 


coMsra  511 

Na  6y  which  passed  its  perihelion  in  1793,  has  an  orbit,  aooord- 
ing  to  the  calcalations  of  B' Arrest,  nearly  similar  both  in  form  and 
magnitu  *9,  as  will  be  seen  by  comparing  the  numbers  ^ven  in  the 
table.  More  uncertainty,  however^  attends  the  estimation  of  these 
elements. 

The  comets  which  approached  nearest  to  the  sun  were  the  great 
comets  of  1680  and  1843,  Nos.  1  and  16  in  the  table,  both  memo- 
rable for  their  extraordinary  magnitude  and  splendour. 

The  elements  of  that  of  1680,  given  in  the  table,  are  those  which 
have  resulted  from  the  calculations  of  Professor  Enck6,  based  on 
all  the  observations  of  the  comet  which  have  been  recorded.  The 
elements  of  the  great  comet  of  1843  have  resulted  from  the  com- 
putations of  Mr.  Hubbard.  Both  are  subject  to  considerable  unccr- 
tunty,  and  must  be  accepted  only  as  the  best  approximations  that 
can  be  obtzuned. 

What  is  not  subject,  however,  to  the  same  uncertainty,  is  the 
extraordinary  proximity  of  these  bodies  to  the  sun  at  their  re- 
spective perihelia.  The  perihelion  distance  of  the  comet  of  1680 
was  about  576,000  miles  — and  that  of  1843,  538,000  miles. 
Now  the  semi-diameter  of  the  sun  being  441,000  miles,  it  follows 
that  the  distance  of  the  centres  of  those  comets  respectively  from 
the  surface  of  the  sun  at  perihelion  must  have  been  only  235,000 
and  97,000 ;  so  that  if  the  semi-diameter  of  the  nebulous  envelope 
of  either  of  them  exceeded  this  distance,  they  must  have  actually 
grazed  the  sun. 

The  velocity  of  the  orbital  motion  of  these  bodies  in  aphelion 
appears  by  the  table  to  be  such,  that  the  comet  of  1680  would 
hare  revolved  round  the  sun  in  a  minute,  and  that  of  1843  in  little 
less  than  two  minutes,  if  they  retained  the  same  angular  motion 
undiminished. 

The  distance  to  which  the  comet  of  1680  recedes  in  its  aphelion 
is  28}  times  greater  than  that  of  Neptune.  The  apparent  diameter 
of  the  sun  seen  from  that  distance  would  be  2",  and  the  intensity 
of  its  liffht  and  heat  would  be  730,000  times  less  than  at  the  earth ; 
while  their  intensity  at  the  perihelion  distance  would  be  26,000 
times  greater,  so  that  the  light  and  heat  received  by  the  comet  in 
its  aphelion  would  be  26,000x730,000=18,980  million  times  less 
than  in  perihelion. 

The  greatest  aphelion  distances  in  the  table  are  those  of  Nos.  5, 
13,  and  17,  the  comets  of  1780,  1830,  and  1844,  amounting  to 
from  100  to  140  times  the  distance  of  Neptune ;  the  eccentricities 
differing  from  unity  by  less  than  tiAjd-  ^hese  orbits,  though 
strietly  the  results  of  calculation,  must  be  regarded  as  subject  to 
considerable  uncertainty. 


ABTBOHOBr. 

3073.  Ptaif/ifu/itrmandiyiatit^inaif- 
ititatfe  o/(A«  orbitt.  — To  codtoj  ui  id™  of 
Uie  form  of  tbo  orbits  of  the  comcis  of  thu 
group,  sad  of  the  propordoD  which  tbeir 
ntagnituile  bears  to  the  dimensions  of  tbe 
Bolur  system,  we  have  dravn,  in  ^ij.  S'il,  la 
ellipse,  which  may  be  coniiideTcd  as  npre- 
seatiDg  the  form  of  the  orbila  of  the  camels 
Nos.  15,  6,  9,  12,  and  1,  of  the  Tabk  VI. 

If  tbe  ellipse  represent  the  orbit  of  &i 
eoniQt  No.  15,  tbe  circle  a  will  represeni  <» 
tbe  Asme  scale  tbo  orbit  of  Neptuoe. 

If  tbo  ellipse  rcpreseat  tbe  orbit  nf  liie 
comet  No.  6,  tbe  circle  b  will  represent  tit 
orbit  of  Neptune, 

K  tbe  elli[>sc  represent  tbe  orbit  of  No,  9, 
tbe  circle  e  will  represent  the  orbit  of  Ntp- 

If  Ibe  ellif«o  represent  tbe  orbit  of  No. 
12,  tbe  circle  d  will  represent  the  orint  of 

If  the  ellipse  represent  the  orbit  of  Na  I, 
the  circle  e  will  represent  the  orbit  of  Stp- 

tunc. 

V.  IIyperbolio  Comets. 

3074.      Taba!ar   tt/nopgii   of    hi/pfrhaUc 

crtmefs.  —  In  tbe  anneied  Table  (VII.)  u* 


lippear,  by  the  rcsnits  of  culculatioos  made  upon  tbe  obaerratioa^ U 
have  pus;^cd  through  the  system  in  hyperbolic  orbits. 

TABLE  VIL 
S^DOpals  of  the  MotiaDB  of  the  Hjrperbalic  Cometa. 


'--'■— 

SH. 

mos! 

'--■ 

- 

'-"^ 

;»- 

\''S. 

\^-6VBO 

;^'^ 

m 

g 

TABLE  Tm. 
of  (he  Oilnta  of  Oometa  aaoertniaeil »:  prMomed  to  b«  panbolie. 


Si  2'"?"' 


IJSJ.'.: 


ASTKOXOKT. 


COMET&  515 


VI.  Parabolic  Comets. 

3075.  Tabular  synopsis  of  the  parabolic  comets. — In  the  annexed 
Table  (VIII.)  are  given  the  elements  of  the  orbits  of  101  comets, 
vhose  paths  in  passing  through  the  system  have  been  either  para- 
bolas or  ellipses  of  eccentricities  so  extreme  as  to  be  undistinguish- 
able  from  parabolas  in  that  part  of  their  orbits  at  which  thej  were 
capable  of  being  observed. 

Vn.  Distribution  of  cometart  orbits  in  space.* 

3076.  Diairibution  of  (he  cometary  orbits  in  space,  —  In  review- 
ing the  vast  mass  of  data  collected  by  the  labours  of  observers, 
ancient  and  modem,  and  which,  so  far  as  we  have  been  enabled  to 
see  grounds  for  classification,  are  marshalled  in  the  series  of  tables 
which  are  given  above,  it  is  natural  to  look  for  some  evidence  of  a 
prevalent  law  in  the  motions  of  these  bodies.  The  absence  of  all 
analogy  to  the  planetary  orbits,  except  in  the  case  of  the  first  group 
of  elliptic  comets  consigned  to  Table  III.,  has  been  already  indi- 
cated 3  but,  although  no  analogy  to  the  planetary  motions  may  exist, 
it  does  not  follow  that  the  cometary  motions  may  not  be  governed 
Vj  some  laws  of  their  own,  the  nature  and  character  of  which  can 
only  be  discovered  by  carefully  conducted  induction. 

3077.  Relative  numbers  of  direct  and  retrograde  comets.  —  It 
lias  been  shown  that  of  the  nineteen  comets  included  in  the  first 
and  second  groups,  which  possess  in  the  most  marked  degree  the 
planetary  character,  one  only  is  retrograde.  Here  is,  then,  the 
mdlcation  of  a  law,  so  far  as  regards  the  direction  of  the  motion  of 
the  comets  of  these  groups. 

To  ascertain  whether  traces  of  the  same  law  are  discoverable  in 
the  other  classes  of  comets,  let  the  other  tables  be  examined  and 
compared. 

Oi  the  twenty-one  comets  included  in  Table  VI.  there  are, 

Direct 10 

Retrograde II 

21 

There  is,  therefore,  among  these  no  indication  of  the  prevalence 
of  any  law  in  relation  to  the  direction  of  the  motion. 
Of  the  seven  hyperbolic  comets  in  Table  VII.  there  are. 

Direct G 

Retrograde 1 


♦  This  BBctwn  contains  the  substance  of  a  paper  by  l\vc  \v\\V.\\viT,  >«V\<:3ti 
Am  b99D  printed  in  the  Proccediaga  of  the  Koyol  A8lroikouik\)\  ^^id^iV5. 


ASTnoyOJIY. 

of  direct  motion  re-tipp«ars;  but  tiic  DambetistM 

gTOUDd  for  any  eala  induc^tjon. 

lalio  oometa  iaoladnd  in  Table  VHI.  there  ue, 


Cirs^tinn  luoscert^iied .. 


endencj  leans  to  retrograde  motion,  bnt  still  not  in  i 
icotiy  decided  to  supply  aafe  ground  for  ■  cooeloiion, 
F  taking  as  the  baaia  of  the  induclJon  tbc  160  panholk 
uke  the  entire  number  of  203  comets  of  whidi  Ilu 
B  ■Boertained,  we  shall  find, 


It  must,  therefore,  be  concluded  that,  notwith standing  the  con- 
udcrablo  number  of  comcta  whose  motions  have  been  obterred, 
no  general  trace  of  anv  law  goveriting  the  direction  of  motian  b 
discoverable. 

3073.  Inclinalton  of  ihe  orhiu.  — Taking  all  the  orl»ta  of  wVA 
the  ioclinnlions  have  been  ascertained,  it  will  be  foand  Iht^  ll 
everj  bundred,  the  iDclioations  are  distributed  as  follows: 

0  lo  :o 10-30 

10  ■■   20 8-80 

20  ■'   30 6-86 

ao  '■   40 11-26 

40  "   50 „ 15-75 

60  "    eo „ .11-70 

60  ■*    70 11-80 

70  "   80 12-73 

80  "    90 8-80 

ibooo 

There  are  here  evident  indicalions  of  a  tendency  of  the  planes  of 
(be  comctary  orbits  to  collect  round  a  plane  whose  inclinatioD  to 
the  plane  of  the  ecliptic  is  45°,  or  if  a  cone  be  imagined  10  t* 
formed  baring  a  semi-angle  of  45°,  and  its  axis  at  right  anglea  U 
the  pjuiie  of  Ihe  ecliptic,  the  planes  of  the  comelarj  orbile  betnji 

tendeacy  to  tsika  \iaa  pofi\\ioa  tA  t;t.T\^«iib  \iUnea  to  the  Burfoee  of 

■sell  a  cone. 


COMETS. 


517 


3079.  Directions  of  the  nodes  and  perthelia, — Taking,  in  like 
manner^  the  loDgitadee  of  the  nodes  and  the  periheliai  we  find 
that  those  of  every  hundred  eomets  are  distribuUKl  in  longitude  as 
fsUows: — 


SO                      00  ••••MM***.*****.*....* • • 

60         00 

IfaiBtwror  NodH. 

HmBlwrer  PwiMkL 

836 

8*86 
11-86 
8-36 
136 
7-00 
990 
8-90 
7-40 
4-90 
8-36 
0-90 

100-00 

0-80 

7-80 

12-26 

11-70 

8-26 

2-90 

6*86 

7-80 

10^0 

12^76 

10-80 

8r40 

90       190  ....M 

190       160 

169       180 

180       no 

no     240 . 

408       270  ».^ 

'       800       830 

fl^W         ^^Kl  •••••«•••••••••••••••••••••«■•«•••••••••••• 

lOOHW 

An  uniform  distribution  would  give  8*83  nodes  to  each  arc  of 
80^.  The  number  in  the  third  sign  between  60^  and  90^  is  nearlv 
12,  and  in  the  seventh  sign  between  180^  and  210^  nearly  10;  bow 
eouiderably  exceeding  the  mean  share. 

The  distribution  of  the  perihelia  is  still  more  unequal.  There  is 
n  evident  tendency  to  crowd  into  the  arcs  between  60^  and  120^, 
and  between  240^  and  800^.  The  number  of  perihelia  due  to  an 
are  of  60^  is  16*66.  Now  the  actual  number  found  between  60^ 
and  120^  is  28-95,  about  50  per  cent,  above  the  mean.  Between 
240^  and  830^  there  are  38*75  perihelia,  where,  as  the  number  due 
to  an  arc  of  90^  is  25,  the  actual  number  being  35  per  cent,  above 
the  mean. 

8080.  Distribution  of 'the  points  of  perihelion,  —  Considering 
how  mnch  the  visibility  of  a  comet  from  the  earth  depends  on  its 
perihelion  distance,  and  that  beyond  a  certain  limit  of  such  distance 
a  comet  cannot  be  expected  to  be  seen  at  all,  it  cannot  be  expected 
that  the  law,  if  any  such  there  be,  which  governs  the  distribution 
of  the  points  of  perihelion  round  the  sun  can  be  discovered  with  any 
degree  of  certainty.  Nevertheless,  it  will  not  be  without  interest  to 
show  the  distribution  of  the  points  of  perihelion  of  the  known  comets 
in  relation  to  their  distances  from  the  sun. 

If  the  centre  of  the  sun  be  imagined  to  be  surrounded  by  spheres 
having  semi-diameters  increasing  successively  by  a  constant  incre- 
nent  of  20  millions  of  miles,  the  number  out  of  every  hundred 
known  comets  whose  perihelia  lie  between  sphere  and  sphere  will 
be  as  follows  :^- 

in.  44 


^^^^^^B 

0 

Oand    40 
0    ••      00 
0-80 
0    "    100 

ASTBOKOUr. 

VoBlMcttlrikfc 



awd 

H-« 

0    ■' 

160 

„ *« 

..„ a« 

. 3« 

(Ki 

10(M» 

0    " 

0    " 

[tie 


is  evident  thnt 
.side  tbe  epbcre,  n 
bribed  to  tho  facb  t, 
«pe  obserratioD :  1 

puribus,  the  comets   . 

the  eitrtb's 

tbia  bo  asaumed,  theo  il 

which  haye  been  c 


I  ion  of  the  perllielik  wind  St 

ru<ii  0  tnillJODS  of  milis,  mnat  le 

imeU        -"ug  ia  such  orbits  will  mMlj 

It  ]  taps,  be  assuined  tliil,  cderu 

jse  lie  witbia  a  sphere  thraoA 

e  nearly  equal  enaocea  of  being  obseiTed.    If 

will  follow  that  the  nambers  of  SDch  oometl 

rved  are  ncarlj  proporliooal  to  their  lotai 

.  numbers,  and  tbcrcforc  that  tbo  numbers  within  this  limit  in 

^preceding  tabic  do  actually  rcpresoot  approximalely  the  distnbntitc 

of  the  poiote  of  perihelia  round  the  sun. 

If  we  compare  then  the  number  of  perihelia  situate  between  ita 
equidistant  spheres  indicated  in.  the  prccediog  table  with  the  cohial 
Bpacea  through  which  thej  are  rcspectirclj  distributed,  we  slull 
obtHin  an  approximate  estimate  of  tho  density  of  their  distHbatioB 
in  relation  to  the  distances  from  the  sun.  I  have  compated  tbefi^ 
lowing  table  with  this  view.  Id  the  second  column  I  hare  ^tm 
the  number  of  comets  per  cent,  wboso  perihelia  are  iocluded  between 
the  equidistant  spheres;  in  the  third  column  the  numbers  expiwi  ■ 
the  cubical  spaces  between  sphere  and  sphere,  the  volume  (S  tha 
sphere  whoso  radius  is  20  millions  of  miles,  being  the  cubical  nnit; 
and  in  tho  fourth  column  the  nunibers  are  the  quotients  of  thoat  hi 
the  sei'ond  divided  by  those  in  the  third,  and  therefore  express  the 
successive  densities  of  the  perihelia  between  sphere  and  sphere. 


OOMETS.  619 

evident  then  that  the  density  of  the  perihelia  increases 
Q  approaching  the  snn.  If  the  numbers  in  the  last  column 
able  be  compared  with  the  inverse  powers  of  the  distance, 
a  found  that  this  increase  of  density  is  more  rapid  than  the 
listance,  but  less  so  than  the  inverse  distance  squared. 

Vni.  Physical  constitution  of  comets. 

Apparent  /arm  —  Head  and  Tail,  —  Comets  in  generali 
«  especially  those  which  are  visible  without  a  telescopei 
he  appearance  of  a  roundish  mass  of  illuminated  vapour  or 
I  matter,  to  which  is  often,  though  not  always,  attached  a 
»re  or  less  extensive,  composed  of  matter  having  a  like  ap- 
The  former  is  called  the  head^  and  the  latter  the  tail 
met 

Nucleus,  —  The  illumination  of  the  liead  is  not  generally 
Sometimes  a  bright  central  spot  is  seen  in  the  nebulous 
rhich  forms  it.  This  is  called  the  nucleus. 
ncleus  sometimes  appears  as  a  bright  stellar  point,  and  some- 
esents  the  appearance  of  a  planetary  disk  seen  through  a 
I  haze.  In  general,  however,  on  examining  the  object  with 
tical  power,  these  appearances  are  changed,  and  the  object 
)  be  a  mere  mass  of  illuminated  vapour  from  its  borders  to 
e. 

Coma.  —  When  a  nucleus  is  apparent,  or  supposed  to  be 
lebulous  haze  which  surrounds  it  and  forms  the  exterior  part 
sad  is  called  the  coma. 

Origin  of  the  name.  —  These  designations  are  taken  from 
ek  word  xofiri  (kom6)  hair,  the  nebulous  matter  composing 
I  and  tail  being  supposed  to  resemble  hair,  and  the  object 
erefore  called  xo^^riyj  (kometes),  a  hairy  star. 

Magnitude  of  the  head.  —  As  the  brightness  of  the  coma 
y  fades  away  towards  the  edges,  it  is  impossible  to  determine 
r  great  degree  of  precision  its  real  dimensions.  These,  how- 
\  obviously  subject  to  enormous  variation,  not  only  in  dif* 
omets  compared  one  with  another,  but  even  in  the  same 
lUring  the  interval  of  a  single  perihelion  passage.  The 
of  those  which  have  been  submitted  to  micrometrical  mea- 
t  was  the  great  comet  of  1811,  Table  VI.  No.  8,  the  dia- 
'  the  bead  of  which  was  found  to  be  not  less  than  1^  millions 
I,  which  would  give  a  volume  greater  than  that  of  the 
the  ratio  of  about  2  to  1.  The  diameter  of  the  head  of 
>  comet  when  departing  from  the  sun,  in  1836,  at  one  time 
d  357,000  miles,  giving  a  volume  more  than  sixty  times 
Tupiter.  These  are,  however,  the  greatest  dimensions  which 
en  observed  in  this  class  of  objects,  the  diameter  rarely 
ig  200,000  miles,  and  being  generally  less  ttiwilQQjSft^- 


ASTBOHOMT 

6.  Magtiilude  of  the  nurlfvt.  —  Attempts  have  bwQ  msje, 
.^  nuclei  wcro  perceivable,  to  estimaie  their  magaitude,  anil 
joters  Jjave  been  asaigDc-d  to  them,  iiiryiDg  from  100  to  5000 

.98.  For  the  reosous,  however,  already  explained,  theae  result! 
-jst  be  regarded  aa  very  doubtful. 

Those  who  deny  tbo  existence  of  solid  matter  wilbio  the  coma, 
muiatain  that  even  the  most  brilliatit  and  coireptcuons  of  these 
bodies,  and  those  which  have  presented  tbo  stroageiit  resemblance 
to  pkaet»,  are  more  or  less  Irausparent.  It  might  be  supposed  tbal 
a  fact  BO  simple  as  this,  in  tbia  age  of  astronomit^  activity,  rauld 
not  remoiQ  aoublful )  but  it  must  bo  considered,  that  the  oosiIh!' 
BaLion  of  circumstaccea  which  aJooe  would  l«st  such  r  quesdon,  ii 
of  rare  occurrence.  It  would  be  nccesaary  that  the  centre  of  ihi 
head  of  the  comet,  although  very  email,  should  pass  criticsllj  over 
a  star,  ia  order  to  ascertain  whether  sucb  star  is  visible  through  it 
With  comctB  having  exteoaive  comw  without  nuclei,  this  haa  sone- 
times  occurred ;  but  we  have  not  had  euch  Batislactory  examples  u 
tbc  more  rue  iostanceB  of  those  which  have  distinct  nuclei. 

Id  the  abeoacc  of  a  more  decisive  test  of  tbo  occullation  of  ■  slit 
by  the  nucleus,  it  has  been  maintained  that  the  existence  of  •  m^ 
nucleus  mny  be  fairly  tuforred  from  the  great  splendour  which  haa 
attccded  tbc  appearuoce  of  some  couicts.  A  mere  ma^s  of  vapou 
could  not,  as  is  cODtemied,  reflect  such  Irilliaot  light.  The  fo^ 
lowiug  are  the  examples  adduced  by  Arago: — 

In  Ihe  ypar  43  before  Christ,  a  comet  apppnrcd  H-hich  vaa  ttaid  to  b* 
Tisibte  to  tbe  Lske^l  ejc  b;  clujligb  t.  It  wna  Iba  comPt  vbigh  tJie  Romuf 
C(uiB[dered  to  b«  the  Boul  of  Cuaar  iraasfecred  to  tbe  heuvens  after  hil 

rere  recorded.     The  Ent  «M 
at  tbe  enti  of  March,  did  not 
prevent  ita  nuclciia,  or  prcn  ita  tail  froni  being  Been.     Tbo  aeconJ  app«r«d 
in  Ibe  month  of  June,  sod  wni  visible  also  for  a  conEiderable  time  befdi* 

In  tbe  jenr  1532,  tbe  people  of  Milnn  were  alarmed  bj  the  appearane* 
of  a  star  nliiuh  «ua  visible  in  Ibe  broad  iln;ligbt.     At  (hut  time  Voiih 
was  not  in  h  poHition  to  he  Tisible,  and  consequmllj  it  ia  inferred  that  thu     ' 
Star  must  huTe  been  a  comet.  | 

The  oomct  of  ISTT  was  dieoovercd  on  tbe  IStfa  of  Korembcr  bj  T^eha 
Brah«,  from  liie  obaervatoi?  oa  the  lEle  of  Hueae,  in  the  Sound,  befort    ] 

Od  tlie  let  of  February,  1T44,  Cliijeaui  obBened  a,  comet  more  brillunt 
than  the  brigbleet  star  in  the  heavens,  which  soon  became  equal  in  spies- 
dour  (o  Jupiter,  and  io  Ihe  beginning  of  March  it  irus  visible  in  the  preaenee 
of  the  Bun.  By  Bolectirg  a  proper  poBJtion  for  obaervalion,  on  the  Ist  of 
March  it  vas  seen  at  one  o'clock  ia  the  aflernoon  wilbont  a  telescope. 

Such  is  the  omount  of  evidence  which  observation  has  supplied 
respecfing  the  eiislcuce  of  a  solid  nucleus.  The  most  that  can  be 
Baid  of  it  is,  that  it  prcsenta  a  plausible  argument,  giving  some  pn> 


COMETS.  521 

Wbflitjy  but  no  positive  certainty,  tbat  comets  bave  Tisited  our 
system  wbieb  bave  solid  nuclei,  but^  meanwbile,  tbis  can  only  be 
maintained  witb  respect  to  few:  most  of  those  whicb  bave  been 
seen,  and  all  to  wbicb  very  accurate  observations  bave  been  directed^ 
bave  afforded  evidence  of  being  mere  masses  of  semi-transparent 
matter. 

3087.  The  taxi.  —  Altbougb  by  far  the  great  majority  of  comets 
are  not  attended  by  tails,  yet  that  appendage,  in  the  popular  mind, 
is  more  inseparable  from  the  idea  of  a  comet  than  any  other  attribute 
of  these  bodies.  This  proceeds  from  its  singular  and  striking  ap- 
pearance, and  from  the  fact  that  most  comets  visible  to  the  naked 
eye  bave  had  tails.  In  the  year  1531,  on  the  occasion  of  one  of  the 
visits  of  Ilalley's  comet  to  the  solar  system,  Pierre  Apian  observed 
that  the  comet  generally  presented  its  tail  in  a  direction  opposite 
to  tbat  of  the  sun.  This  principle  was  hastily  generalized,  and  is 
even  at  present  too  generally  adopted.  It  is  true  that  in  most  cases 
the  tail  extends  itself  from  that  part  of  the  comet  whicb  is  most 
remote  from  the  sun ;  but  its  direction  rarely  corresponds  with  the 
direction  whicb  the  shadow  of  the  comet  would  take.  Sometimes 
it  has  happened  that  the  tail  forms  with  a  line  drawn  to  the  sun  a 
crasiderable  angle,  and  cases  have  occurred  when  it  was  actually  at 
light  angles  to  it. 

Another  character  which  has  been  observed  to  attach  to  the  tails 
of  comets,  wbicb,  however,  is  not  invariable,  is,  that  they  incline 
constantly  toward  the  region  last  quitted  by  the  comet,  as  if  in  its 
progress  through  space  it  were  subject  to  the  action  of  some  resist- 
ing medium,  so  that  the  nebulous  matter  with  which  it  is  invested, 
ioffering  more  resistance  than  the  solid  nucleus,  remains  behind  it 
and  forms  the  tail. 

The  tail  sometimes  appears  to  have  a  curved  form.  Tbat  of  tho 
eomet  of  1744  formed  almost  a  quadrant.  It  is  supposed  that  the 
eonvexity  of  the  curve,  if  it  exists,  is  turned  in  the  direction  from 
which  the  comet  moves.  It  is  proper  to  state,  however,  that  these 
circumstances  regarding  the  tail  have  not  been  clearly  and  satisfac- 
torily ascertained. 

The  tails  of  comets  are  not  of  uniform  breadth  or  diameter ;  they 
appear  to  diverge  from  the  comet,  enlarging  in  breadth  and  dimin- 
ishing in  brightness  as  their  distance  from  the  comet  increases. 
The  middle  of  the  tail  usually  presents  a  dark  stripe,  wbicb  divides 
it  longitudinally  into  two  distinct  parts.  It  was  long  supposed 
that  this  dark  stripe  was  the  shadow  of  the  body  of  the  comet,  and 
this  explanation  might  be  accepted  if  the  tail  was  always  turned 
from  the  sun;  but  we  find  the  dark  stripe  equally  exists  when 
the  tul|  being  turned  sideward,  is  exposed  to  the  effect  of  the  sun's 
light. 

This  appearance  is  nsoally  explained  by  the  BappoeA\iQi^  ^X^XiHIsi^ 

44* 


ASTROKOMY. 


t  hollow,  conical  BtcU  of  vapour,  tbc  external  stufice  of 

fmssesses  a  certain  ihickncaa.     When  we  ticw  it,  we  look 

ugQ  a  considerabk  tbiclinCHS  of  rnpour  at  the  odgca,  sod  tbrongli 

jmparalively  sniiJl  qnantily  at  the  middle.     Tbua  upoD  the  eup- 

-atioQ  of  a  hollow  cone,  the  greittest  brightness  woald  sppear  »t 

)  sides,  and  the  euaCeoce  of  a  dark  space  in  the  middle  would  bs 
jivi-fectly  accounted  for. 

The  tails  of  cometa  ar«  not  alwaon  aiyigle;  some  haYe  appeared  it 
'lifTerent  times  wilb  eeveral  se^  aule.      The  cotnet  of  1744, 

rhiuh  appcBrcd  on  the  Tth  or  f  March,  bad  ds  Imils,  each 

■bout  4°  in  breadth,  and  from  in/-  to  44°  in  length.  Their  Bide* 
were  well  defined  and  tolerably  bright,  and  the  spaces  between  them 
wore  as  dark  aa  the  other  parts  of  the  heavens. 

The  tails  of  comets  have  frequently  appeared,  not  only  of  immetiN 
real  length,  but  eiieodlDg  over  coDsiderahle  spaces  of  the  beavena. 
It  will  be  easily  understood  that  the  apparent  length  depends  eon-  i 
jointly  upon  the  real  length  of  the  tail,  and  the  position  in  which  it 
is  presented  to  the  eye.  If  the  line  of  vision  be  at  right  angles  to 
k,  its  length  will  appear  aa  great  as  It  can  do  at  its  existing  di»-  \ 
lance  ;  if  it  be  oblique  to  the  eye,  it  will  he  foreshortened,  more  or 
less,  according  to  the  angle  of  obliquity.  The  real  length  of  the 
tail  is  easily  calculated  when  the  apparent  length  is  observed  aad 
the  angle  of  obliquity  known. 

In  respect  of  magnitude,  the  tails  are  nnqnestionably  the  mort 
stapendous  objects  which  the  discoveries  of  the  astronomer  hava 
ever  presented  to  human  contemplation. 

The  following  ore  the  resnlta  of  the  observation  and  meuniement 
of  a  few  of  the  mora  remarkable  : — 


T^ 

N> 

«.-.„~ 

OMM  okwrW  Lhi>  K  Td. 

I- 

« 

11 

iBsa 

WW 

G,0O(i.Kn 
«,1>M),000 

nrnKHKW 

ssass 

The  magnitude  of  these  prodigions  appendages  is  even  less 
amazing  ihar  the  brief  period  in  which  they  sometimes  emanate 
from  the  head.  The  tail  of  the  comet  of  1843,  long  enough  to 
Biretch  from  the  aun  to  the  planetoids,  was  formed  m  len  thu 
twenty  days. 

3088.  Miu,  volume,  and  dentUg  of  comda, — The  masMi  of 
oomcte,  like  those  ol  \.\ie  \>\n.DQ\a,  '«fs>M  bo  uoertained  if  the  recip- 


COMETS.  623 

rood  effects  of  their  gravitation,  and  those  of  any  known  bodies  in 
the  system  could  be  observed.  But  although  the  disturbing  action 
of  the  planets  on  these  bodies  is  conspicuous,  and  its  effects  have 
been  calculated  and  observed,  not  the  slightest  effect  of  the  same 
kind  has  ever  been  ascertained  to  be  produced  by  them,  even  upon 
the  smallest  bodies  in  the  system,  and  those  to  which  comets  have 
Approached  moat  nearly. 

In  fine,  notwithstanding  the  enormous  number  of  comets,  observed 
and  unobserved,  which  constantly  traverse  the  solar  system  in -all 
eonoeivable  directions;  notwithstanding  the  permanent  revolution 
of  the  periodic  comets,  whose  presence  and  orbits  have  been  ascer- 
tained ;  notwithstanding  the  frequent  visits  of  comets,  which  so  tho- 
roughly penetrate  the  system  as  almost  to  touch  the  surface  of  the 
sun  at  their  perihelion,  the  motions  of  the  various  bodies  of  the  . 
system,  great  and  small,  planets  major  and  minor,  planetoids  and 
Mtellites,  go  on  precisely  as  if  no  such  bodies  as  the  comets  ap- 
jnxMKshed  their  neighbourhood.  Not  the  smallest  effects  of  the 
Attraction  of  such  visitors  are  discoverable. 

Now  since,  on  the  other  hand,  the  disturbing  effects  of  the  planets 
upon  the  comets  are  strikingly  manifest,  and  since  the  comets  move 
in  elliptic,  parabolic,  or  hyperbolic  orbits,  of  which  the  sun  is  the 
eommon  focus,  it  is  demonstrated  that  these  bodies  are  composed  of 
ponderable  matter,  which  is  subject  to  all  the  consequences  of  the 
law  of  gravitation.  It  cannot,  therefore,  be  doubted  that  the  comets 
do  produce  a  disturbing  action  on  the  planets,  although  its  effects 
are  inappreciable  even  by  the  most  exact  observation.  Since,  then, 
the  disturbances  mutually  produced  are  in  the  proportion  of  the  dis- 
tnrbing  masses,  it  follows  that  the  masses  of  the  comets  must  bo 
smaller  beyond  all  calculation  than  the  masses  even  of  the  smallest 
bodies  among  the  planets  primary  or  secondary. 

The  volumes  of  comets  in  general  exceed  those  of  the  planets  in 
A  proportion  nearly  as  great  as  that  by  which  the  masses  of  the 
planets  exceed  those  of  the  comets.  The  consequence  obviously 
reaolting  from  this,  is  that  the  density  of  comets  is  incalculably 
imalL 

Their  densities  in  general  are  probably  thousands  of  times  less 
than  that  of  the  atmosphere  in  the  stratum  next  the  surface  of  the 
earth. 

3089.  Light  of  comets.  —  That  planets  are  not  self-lnminous,  but 
reoeive  their  light  from  the  sun,  is  proved  by  their  phases,  and  by 
the  shadows  of  their  satellites,  which  are  projected  upon  them,  when 
the  latter  are  interposed  between  them  and  the  sun.  These  tests 
are  inapplicable  to  comets.  They  exhibit  no  phases,  and  are  attended 
hj  no  bodies  to  intercept  the  sun's  light  But,  unless  it  could  be 
nown  that  a  oomet  is  a  solid  mass^  impenetrable  U)  \bft  vjto  tvj^^ 


I 


nf 


ASTBONDMr. 


tbe  nim -existence  of  pbaaes  is  not  a  proof  Ihat  the  bodj  does  sot 
receive  its  ligtit  from  the  sun. 

A  mere  miss  of  cloud  or  vapour,  thougb  not  self-luiniiions,  bet 
rendered  visible  by  borrowed  light,  would  sliU  exhibit  do  effwt  of 
this  kind  :  ite  ioiperfect  opacitj  vonld  nllotr  tbe  solar  light  te  afled 
iiB  constituent  psrta  throughout  iu  entire  depth — so  that,  like  a  tliin 
fleecy  cloud,  it  would  oppcar  not  BUperSciitlJy  illuminated,  buE  r«- 
eeiving  and  reflecting  light  Uirough  all  ita  ditoensions.  With  r^prct 
Id  .comets,  therefore,  the  doubt  which  has  existed  is,  whether  th« 
light  which  proceeds  from  them,  and  by  which  tbej  bec«;me  riiibl<, 
is  B  light  of  their  own,  or  is  the  light  of  tbe  Eun  Bbining  upon  then, 
and  reflected  to  onr  eyes  like  light  front  a  cloud.  Among  scTeral 
tests  which  have  been  proposed  to  decide  this  question,  one  i 
gcsted  by  Arogo  merits  attention. 

It  has  been  already  shown  (1131  et  le^S),  tbat  the  appunt 
brightness  of  a  visible  object  is  the  some  at  alt  diatanoea,  snppcaiDi 
ita  real  brightoeas  to  remain  unchanged.  Now  if  comets  shone  wiia 
tbcir  proper  light,  sod  not  by  light  received  froni  the  sna,  their 
apparent  brightness  would  not  decrease  as  they  would  recede  from 
the  sun,  and  they  would  cease  to  be  visible,  not  because  of  tb« 
&intncss  of  their  light,  but  because  of  tbe  smalluess  of  thor  ap- 
parent magnitude.  Now  the  contrary  is  found  to  be  tbe  case.  Ai 
the  comet  retires  from  tbe  sun  its  apparent  brlghtacss  npidlj 
decreases,  and  it  ceases  to  be  visible  from  the  mere  fointness  of  its 
light,  while  it  subtends  a  considerable  visual  angle. 

30S10.  Enlargement  of  magnitude  on  dr^partinrj  from  the  n%.— 
It  will  doubtless  excite  surprise,  that  tbe  dimensions  of  a  coout 
should  be  enlarged  as  it  recedes  from  the  source  of  heat.  It  ku 
been  often  obi>erved  in  astronomical  inquiries,  that  tbe  effects,  whicb 
&t  first  view  seem  most  improbable,  are  nevertheless  those  which 
frequently  prove  to  be  true;  and  so  it  is  in  this  case.  It  was  long 
believed  that  comets  enlarged  as  they  approached  the  sun ;  and  this 
supposed  eflfeet  was  naturally  and  probably  oscribeJ  to  tbe  heat  of  th< 
BUQ  expanding  their  dimensions.  But  more  recent  and  exact  tshmt- 
vations  have  shown  tbe  very  reverse  to  bo  the  facia.  Coioei* 
increase  their  apparent  volume  as  they  recede  from  the  sun;  m' 
this  is  a  law  to  which  there  appears  to  be  no  well-ascertained  c 
oeption.  This  singular  and  unexpected  phenomenon  has  been 
Sttempted  to  be  accounted  for  in  several  waya.  Vah  ascribed  it  to 
the  pressure  of  the  solar  atmosphere  acting  upon  the  comet;  (bit 
atmosphere  being  more  dense  near  the  sun,  compresses  tbe  comet 
and  dirniui.iiort  lis  diT.n-n.si.m^  ;  and,  at  a  gre:it.r  disl;ine.?,  being 
relieved  from  this  coercion,  the  body  swells  to  its  natural  bnlk.  A 
yery  ingenious  train  ai  reaaown^  was  produced  in  support  of  this 
theory.  The  density  of  l\\e  ui\u  vUo<a\V«,x%  viA  ^lan.  ^Uaticit j  U 
tie  comet  being  assumed  W\»  b^u^  ^a  wii^  ^iT^^iaiMs^-i'wi'oai. 


COMETS.  625 

poaedy  die  Tariations  of  the  comet's  bulk  are  dedaced  by  striot 
leaaoniDg,  and  show  a  surprising  coincidence  with  the  observed 
change  in  the  dimensions.  But  this  hypothesis  is  tainted  by  a  fatal 
error.  It  proceeds  upon  the  supposition  that  the  comet,  on  the  one 
hand,  is  formed  of  an  elastic  gas  or  vapour ;  and,  on  the  other,  that 
it  ia  impervious  to  the  solar  atmosphere  through  which  it  moves. 
To  establish  the  theory,  it  would  be  necessary  to  suppose  that  the 
elastic  fluid  composing  the  comet  should  be  surrounded  by  a  nappe 
or  envelope  as  elastic  as  the  fluid  composing  the  comet,  and  yet 
wholly  impenetrable  by  the  solar  atmosphere. 

After  several  ingenious  hypotheses  *  having  been  proposed  and 
successively  rejected  for  explaining  this  phenomenon,  it  seems  now 
to  ascribe  it  to  the  action  of  the  varying  temperature  to 
which  the  vapour  which  composes  the  nebulous  envelope  is  exposed. 
As  the  comet  approaches  the  sun,  this  vapour  is  converted  by  in- 
tense heat  into  a  pure,  transparent,  and  therefore  invisible  elastic 
fluid.  As  it  recedes  from  the  sun,  the  temperature  decreasing,  it  is 
partially  and  gradually  condensed,  and  assumes  the  form  of  a  semi- 
transparent  visible  cloud,  as  steam  does  escaping  from  the  valve  of  a 
steam  boiler.  It  becomes  more  and  more  voluminous  as  the  distance 
from  the  source  of  heat,  and  therefore  the  extent  of  condensation^  is 
augmented. 

3091.  Pro/eswr  Struve*8  dratnnffs  of  EnckS's  comet  —  Pro- 
ienor  Stmve  made  a  series  of  observations  on  the  comet  of  Encke, 
at  the  period  of  its  re-appearance  in  1828,  and  by  the  aid  of  the 
great  Dorpat  telescope,  made  the  drawings  given  in  PI.  XIY .,  Jigs. 
land  2. 

Fig.  1  represents  the  comet  as  it  appeared  on  the  7th  November, 
the  diameters  a  b  and  c  d  measuring  each  18'.  The  brightest  part 
of  the  oomet  extended  from  a  to  x,  and  was  consequently  eccentrio 
to  it,  the  distance  of  the  centre  of  brightness  from  the  centre  of 
magnitude  being  »  k.  Between  the  7th  and  the  30th  November, 
the  magnitude  of  the  comet  decreased  from  that  represented  in  fig,  1 
to  that  represented  in  fig.  2 ;  but  the  apparent  brightness  was  so 
much  increased,  that  at  the  latter  date  it  was  visible  to  the  naked 
eye  as  a  star  of  the  6th  magnitude.  The  apparent  diameter  was 
then  reduced  to  9'. 

On  November  7th  a  star  of  the  11th  magnitude  was  seen  through 
the  oomet,  so  near  the  centre  x  of  brightness  that  it  was  for  a  mo- 
ment mistaken  for  a  nucleus.  The  brightness  of  the  star  was  not  in 
the  least  perceptible  degree  dimmed  by  the  mass  of  cometary  matter 
through  which  its  light  passed. 

It  was  evident  that  the  increase  of  the  brightness  of  the  comet 

*  For  seTeral  of  these,  see  Sir  J.  Herschel's  memoir,  Prooeedlngs  of  As* 
traiemSeal  £fooietj,  voL  vi  p.  104. 


nS  ASTR0!i01(T. 

on  the  SOlU  November,  must  be  ascribed  to  Ibc  conlnetioti,  u4 
eon*C(|Uuut  cimdeDsalion,  of  Ibc  uebuloos  [Dattt>r  cacuposing  it  in 
rcwrliiig  from  tlie  sun,  for  iu  distance  from   ibe  eartb  on   ibe  Tlh 
November,  wlien  it  aubtended  an  aoglo  of  IS',  waa  0-515  {the  i 
earth's  nicao  ilieinaee  from  the  sun  being  =1);  while  iu  dintanct  | 
DO  tbe  30tb,  wben  it  subtended  an  angle  of  9',  was  only  0-477.    Iu 
cubical  dimeustons  luual,  tberefore,  bave  been  diminiahed,  and  tbt 
densitir  of  the  matter  composing  it  augmented  in  more  than  an  a^U  { 
fold  proportion. 

3092.  Jii:marl-ahle  phi/tical  phenomena  tnani/eslni  bg  IJaHrf'i 

fomfl.  —  Tbe  erpectation  so  generally  cDtertaioed,  that,  on  the  m- 

oaeion  of  its  return  to  perihelion  in  1836,  this  cornel  wonid  tfiard 

observers  occasion  for  obtaining  new  data,  for  the  foundation  d 

ftome  aaiisfactorj  riews  To^pectLng  the  physical  constitntion  of  lb 

_      class  of  wbich  it  is  so  striking  an  example,  was  not  dissppoinled. 

L     It  no  sooner  re-appeared  tban  phenomena  began  to  be  manifbite^ 

I     preceding  and  accompanying  the  gradual  formation  of  the  till,  lit 

'      observation  of  wbicb  Las  been  most  justly  regarded  a^  fomuag* 

memorable  epoch  in  osU-onomioal  biatory. 

'  Happily,  these  strange  nnd  important  appearances  were  ob^tfTed 
with  the  greatest  zeal,  and  dolinealed  with  ibe  most  elaborate  ui 
scrupulous  fidelity  by  several  eminent  astronomers  in  both  heini- 
spheres.  MM.  Bessel,  at  Konigsberg,  Scbvrabc,  at  Dcssaa,  i»i 
Struvc,  at  I'ultowa,  and  Sir  J.  Herscbel  and  Mr.  Maclear,  it  ite 
Cape  of  Good  Hope,  have  severally  published  their  obsercaBMt, 
accompanied  by  numerous  drawings,  exhibiting  the  successive  ttti* 
formatiorjs  presented  under  (he  physical  iuflucoee  of  varying  tempa- 
ataro,  in  its  approach  to  and  departure  from  the  sun. 

The  comet  Srst  became  visible  as  a  small  round  nebula,  withoat 
s  tail,  and  having  a  bright  point  more  intensely  luminous  ihanlbt  , 
rest  ecconirically  placed  witbia  it.  On  the  li  October,  the  tul 
began  to  be  formed,  and,  increasing  rapidly,  acquired  a  length  cf  ' 
about  5°  on  the  5rh;  on  the  20tb  it  attained  its  grestest  length, 
which  was  20°.  It  began  after  that  day  to  decrease,  and  its  dimi- 
nution was  so  rapid,  that  on  the  29tb  it  was  reduced  to  3°,  and  on 
the  5th  November,  to  Sj",  The  comet  was  observed  on  the  dij 
of  its  perihelion  by  M.  Struve,  at  the  Observatory  of  Fultowa,  when 
no  tail  whatever  was  apparent. 

The  circumstances  which  accompanied  tho  increase  of  the  tail 
from  2d  October,  until  its  disappearance,  were  estrcmely  remarka- 
ble, and  were  observed  with  scrupulous  precision,  simultaneously  bj 
Bessel,  at  Konigsberg,  by  Struve,  at  Pultowa,  and  by  Schwabe,  at 
B«ssau,  all  of  whom  made  drawings  from  time  to  time,  delineatiog 
tbe  successive  changes  which  it  underwent. 
On  the  2od,  the  comuieikceiii^'ax.  ol  x^  ^fn^i^WLX':^.  of  the  tail  look 
pt&oo  by  the  appeataTtce  ot  a,  ntoVwA  tjtRji'sa,  <A.  -o^Sw^isso^  -mi^ia^ 


ri 


COMST&  527 

fitKn  that  part  of  the  comet  which  was  presented  towards  the  snn. 
This  ejection  was,  however,  neither  uniform  nor  continnoos.  Like 
the  fiery  matter  issuing  from  the  crater  of  a  volcano;  it  was  thrown 
oat  at  intervals.  After  the  ejection,  which  was  conspicuous,  accord- 
ing to  Besse],  on  the  2nd,  it  ceased,  and  no  efflux  was  ohserved  for 
aeveral  days.  About  the  8th,  however,  it  recommenced  more  vio- 
lently than  before,  and  assumed  a  new  form.  At  this  time  Schwabe 
noticed  an  appearance  which  he  denominates  a  '^  second  tail,"  pre- 
sented in  a  direction  opposed  to  that  of  the  original  tail,  and,  there- 
fore, towards  the  sun.  Thb  appearance  seems,  however,  to  be 
regarded  by  Bcsscl  merely  as  the  renewed  ejection  of  nebulous 
matter  which  was  afterwards  turned  back  from  the  sun,  as  smoke 
would  be  by  a  current  of  air  blowing  from  the  sun  in  the  direction 
of  the  original  tail. 

From  the  8th  to  the  22nd,  the  form,  position,  and  brightness  of 
the  nebulous  emanations  underwent  various  and  irregular  changes^ 
the  last  alternately  increasing  and  decreasing. 

At  one  time  two,  at  another  three,  nebulous  emanations  were 
ohserved  to  issue  in  diverging  directions.  These  directions  were 
continually  varying,  as  well  as  their  comparative  brightness.  Some- 
times they  would  assume  a  swallow-tailed  form,  resembling  the 
flame  issuing  from  a  fan  gas-burner.  The  principal  jet  or  tail  was 
also  observed  to  oscillate  on  the  one  side  and  the  other  of  a  line 
drawn  from  the  sun  through  the  centre  of  the  head  of  the  comet, 
exactly  as  a  compass  needle  oscillates  between  the  one  and  the 
other  side  of  the  magnetic  meridian.  This  oscillation  was  so  rapid, 
that  the  direction  of  the  jets  was  visibly  changed  from  hour  to 
hour.  The  brightness  of  the  matter  composing  them,  being  most 
intense  at  the  point  at  which  it  seemed  to  be  ejected  at  the  nucleus, 
fiuled  away  as  it  expanded  into  the  coma,  dhrving  backwards,  in 
the  direction  of  the  principal  tail,  like  steam  or  smoke  before  the 
wind. 

3093.  Struue's  dratoings  of  the  comet  approaching  the  sun  in 
1835. — These  curious  phenomena  will,  however,  be  more  clearly 
conoeived  by  the  aid  of  the  admirable  drawings  of  M.  Struve,  which 
we  have  reproduced  with  all  practicable  fidelity,  in  Plates  XV., 
XVI.,  and  XVII.  These  drawings  were  executed  by  M.  Kruger, 
an  eminent  artist,  from  the  immediate  observation  of  the  appear- 
ances of  the  comet  with  the  great  Fraanhoffer  telescope,  at  the 
Paltowa  Observatory.  The  sketches  of  the  artist  were  corrected  by 
the  astronomer,  and  only  adopted  definitively  after  repeated  compa- 
risons with  the  object.  The  original  drawings  are  preserved  in  the 
library  of  the  observatory. 

3094.  Its  appearance  29^A  September,  —  Plate  XY.jJrg.  1,  re- 
presents the  appearance  of  the  comet  on  the  29th  September.  The 
tail  was  difficult  to  be  recognised,  appearing  to  be  composed  of  ver^ 


ASTROKOUT. 

•  nebnloos  inattpr.     The  nucleus  paxsed  almost  centricaUyorw 

r  of  the  lOtli  magnitude,  without  in  ibu  eliglitest  degree  sflect- 

<  its  ■pporent  bTigbtneHs.     The  elar  was  ilistiDctly  seen  throagh 

I  denieet  jMirt  of  the  comet.     Aaothor  traaeit  of  a  alar  took  plaeo 

■idi  %  like  remit. 

Annexed  U  tLe  scdc,  accordiog  to  wLich  this  drawing  has  been 


(     hiiiiiiiii 1 ' 1 1 i 

8095.  Ajyietrrii„ce  on  October  3,  —This  U  represented  in/y.  2, 
OB  the  Mne  aenle. 

The  coraet  ch  inged  imt  only  its  mngnitude  and  form,  but  alao  its 
piMitioQ  wnoB  Sfp'pmber  'JO.  On  thai  day  the  diroctioti  of  the  tail 
WU  that  of  the  fiarallLl  of  decliDatioD  through  the  head.  Od  Oo- 
tobsr  3,  it  was  iiicliiicd  from  that  pnrullcl  towarda  the  north  at  a 
BBttll  angle,  and,  insicad  of  being  stnight,  waa  curved.  The  dia- 
BMler  of  the  head  wns  inereaaed  in  the  ratio  of  2  to  3,  and  tbe 
kngth  of  the  tuil  iu  llie  ratio  of  neaily  1  to  3. 

3096.  ApptaTuiuT^  ™  t/rtoAcr  8.  — Pkte  XVI.  /y.  1.  This 
drawiog  is  made  on  the  subjoined  scale  of  aeconda. 


|ii' II     I    1     I     '    I     I     I 

Od  the  5tb,  Rth,  and  7th,  the  comet  underwent  sercnl  changea; 
the  nucleus  bccarae  more  conspicuous.  On  the  6tb,  a  fan-fornwd 
flame  issued  from  it,  which  disappeared  on  the  7th,  and  re-appeand 
on  the  8th  with  iucftased  splendour,  as  represented  ia  the  Ggai«. 
The  nucleus  appeared  like  a  bumiDg  coal,  of  oblong  form,  nod  yel- 
lowish colour.  The  extent  of  the  flame-like  elongation  was  •boat 
30".  The  feeble  nebula  surrounding  the  nuclei  extended  much  he* 
Tond  the  limits  of  the  drawing,  but,  being  overpowered  by  the  mooo- 
light,  could  not  be  measured. 

3097.  Ap^icarance  <m  Oc(o6er  9.— Plato  XVI. /y.  2,  same  scale, 
represents  the  nucleus  and  flame-like  emanation,  which  entirely 
changed  tbeir  form  and  magnitude  since  the  preceding  night  The 
tail  (not  included  in  the  drawing)  measured  Tei;  nearly  2°.  The 
flame  consisted  of  two  parts,  one  reeemhling  that  seen  on  the  8th, 
and  the  other  issuing  like  the  jet  from  a  blow-pipe  in  a  direction  at 
right  angles  to  it.  The  figure  represents  the  nucleus  and  flame  as 
they  appeared  at  21''  sid.  time,  with  a  magnifying  power  of  254. 

3098.  Appfaran':e  on  O^tofitr  10.  — Plate  XVI. J^.  3,  on  the 
same  scale.  The  (ail,  which  still  measured  nearly  2°,  was  now 
much    brighter,  being  visible  to  the  naked  eye,  notwithslandiiig 


lAI.I  I.V  S   i-iiMKT 


C0MET8.  629 

troDg  moonlight.  The  coma  was  evidently  broader  than  the  tail, 
lie  flaming  nucleus  is  represented  in  the  drawine  as  it  appeared 
inder  a  ma^ifying  power  of  86,  with  a  field  of  18'  diameter,  the 
Dtire  of  which  was  filled  with  this  coma.  The  diameter  of  the 
atter  must,  therefore,  have  been  more  than  18'.  The  drawing  was 
■ken  at  21  A.  s.  t. 

3099.  Appearance  on  October  12.  —  Plate  XVI.  fy.  4,  on  the 
ame  scale.  The  comet  appeared  at  0  h, — 25  m.  s.  t.,  for  a  short 
Dterval,  in  uncommon  splendour,  the  nucleus  and  flame,  however, 
lone  being  visible,  as  represented  in  the  drawing.  The  greatest 
ixtent  of  the  flame  measured  64''*7.  Its  appearance  was  most  beau- 
iful,  resembling  a  jet  streaming  out  from  the  nucleus  like  flame 
rem  a  blow-pipe,  or  the  flame  from  the  discharge  of  a  mortar^  at- 
ended  with  the  white  smoke  driven  before  the  wind. 

3100.  Appearance  on  October  14.  —  Plate  XVI.  Jiff.  6,  on  the 
same  scale.  The  principal  flame  was  now  greatly  enlarged,  extend- 
ing to  the  apparent  length  of  184''.  Its  deflection  and  curved  form 
were  most  remarkable. 

3101.  Appearance  on  October  29.  — A  cloudy  sky  prevented  all 
cbservation  for  12  days.  On  the  27th,  the  comet  appeared  to  the 
naked  eye  as  bright  as  a  star  of  the  third  magnitude,  the  tail  being 
distinctly  visible.  The  coma  surrounding  the  nucleus  appeared  as 
a  aniform  nebula.  The  tail  was  curved,  and  of  great  length ;  but, 
owing  to  the  low  altitude  at  which  the  observation  was  taken,  it 
coald  not  be  measured.  On  the  29th,  however,  the  comet  was  pre- 
w&ted  under  much  more  favourable  conditions,  and  the  drawings. 
Hate  XV.  fg.  3,  and  Plate  XVII.  Jt</.  1,  were  made.  The  former 
^presents  the  entire  comet,  including  the  whole  visible  extent  of 
m  tail,  and  is  drawn  to  the  annexed  scale  of  minutes.     The  lattci 

9f  w  w  9»  w 

11  1 1 1  1  n  1  M  I I I 

represents  the  head  of  the  comet  only,  and  is  drawn  to  the  annexed 
Kale  of  seconds. 

Wf  Off       20ff       tat       Wf       Wf      VX»f     I20tf 

[1'Ml       It        I       t       f       I       t        T       I       I      I       [ 

At  20*-  30"'  8.  t.,  the  head  presented  the  appearance  represented  in 
Hate  XVII.  fff.  1.  The  chief  coma  was  almost  exactly  circular,  and 
had  a  diameter  of  165".  With  a  power  of  198,  the  nucleus  ap- 
peared as  in  the  figure,  the  diameter  being  about  1"'25  to  1-50. 
The  flame  issuing  from  the  nucleus,  curved  back  like  smoke  before 
the  wind,  was  very  conspicuous.  The  appearance  of  the  formation 
of  the  tail  as  it  issues  from  the  nucleus  was  rcmaikaVA^  ^e^^^o^^^ 

ni.  45 


580  ASTRONOXT. 

3102.  Appearance  on  November  5.  —  Plate  XVII.  fig.  2.  This 
dimwing  represents  the  nucleus  and  flame  issuing  from  it  on  the 
annexed  scale  of  seconds. 


w     V  w*  4ar  V  tor 

iMtt|       f      1       I       I       1       I       t       1       i       I       I      I 

The  proper  nucleus  was  found  to  measure  about  2^-3.  Two 
flames  were  seen  issuing  from  it  in  nearly  opposite  directions,  aod 
both  curved  towards  the  same  side.  The  brighter  flame,  directed 
Viwanls  the  north,  was  marked  by  strongly  defined  edges.  The 
other,  directed  towards  the  south,  was  more  feeble  and  ill-defined. 

3103.  Sir  J.  UencheVs  deductions  from  these  phenomena, — Sir 
J.  Herschel,  who  also  observed  this  comet  himself  at  the  Cape  of 
Good  Hope,  makes  from  all  these  observations  the  following  ifi* 
ferences. 

1.  That  the  matter  of  the  comet  vaporised  by  the  sun's  beit 
escapes  in  jets,  throwing  the  comet  into  irregular  motion  by  its 
reaction,  and  thus  changing  its  own  direction  of  ejection.  ] 

2.  That  this  ejection  takes  place  principally  from  the  part  pre-     J 
senteJ  to  the  sun. 

3.  That  thus  ejected  it  encounters  a  resistance  from  some  ud-      | 
known  force  by  which  it  is  repulsed  in  the  opposite  direction,  and 

so  forms  the  tail. 

4.  That  this  acts  unequally  on  the  cometary  matter,  which  i5nr»t 
all  vaporized,  and  of  that  which  is,  a  considerable  portion  is  retamed 
so  as  to  form  the  head  and  coma. 

5.  That  this  force  cannot  be  solar  gravitation,  being  contrary  to 
that  in  its  direction,  and  very  much  greater  in  its  intensity,  as  is 
manifest  by  the  enormous  velocity  with  which  the  matter  of  the 
tail  is  driven  from  the  sun. 

G.  That  the  matter  thus  repelled  to  a  distance  so  great  from  a 
body  whose  mass  is  so  small  must  to  a  great  extent  escape  from  the 
ffcble  influence  of  the  gravitation  of  the  mass  composing  the  head 
and  coma,  and,  unless  there  be  some  more  active  agency  in  ope- 
ration, a  large  portion  of  such   vaporised  matter   must   be  lost  in 
bpace,  never  to  reunite  with  the  comet.     This  would  lead  to  the 
consequence,  that  at  every  passage  through  its  perihelion  the  comet 
would  lose  more  and  more  of  its  vaporisable  constituents,  on  which 
the  production  of  the  coma  and  tail  depends,  so  that,  at  each  suc- 
cessive return,  the  dimensions  of  these  appendages  would  be  less 
and  less,  as  they  have  in  fact  been  found  to  be. 

«il04.  Aj^prtt ranee  of  the  comet  after  prrihclio?}.  —  On  receding 
from  the  sun  after  its  perihelion,  the  comet  was  observed  under  very 
/i'ivourablc  circumstviticcd  ?il  \\ve  ^\i^^  V^'  "^vc  ^.  W^i^^chel  and  Mr. 


COMETS.  581 

an  aspect  altogether  differcDt  from  that  under  which  it  was  seen 
before  its  perihelien.  It  had  evidently,  as  Sir  J.  Hersohel  thinks, 
undergone  some  great  physical  cbangc/which  had  operated  an  entire 
transformation  upon  it. 

"  Nothing  could  bo  more  surprising  than  the  total  change  which 
had  taken  place  in  it  since  October.  ...  A  new  and  unexpected 
phenomenon  had  developed  itself,  quite  unique  in  the  history  of 
comets.  Within  the  well-defined  head,  somewhat  eccentrically 
placed,  was  a  vivid  nucleus  resembling  a  miniature  comet,  with  a 
bead  and  tail  of  its  own,  perfectly  distinct  from  and  considerably 
exceeding  in  intensity  the  nebulous  disk  or  envelope  which  I  have 
above  called  the  '  head.'  A  minute  bright  point,  like  a  small  star, 
was  distinctly  perceived  within  it,  but  which  was  never  quite  so  well 
defined  as  to  give  the  positive  assurance  of  the  existence  of  a  solid 
sphere,  much  less  could  any  phase  be  discovered."* 

3105.  Observations  and  drawings  of  Messrs.  Maclear  and  Smith. 
The  phenomena  and  changes  which  the  comet  presented  from  its 
reappearance  on  the  24th  of  January,  until  its  final  disappearance, 
have  been  described  with  great  clearness  by  Mr.  Maclear,  and  illus- 
trated by  a  beautiful  series  of  drawings  by  that  astronomer  and  his 
assistant,  Mr.  Smith,  in  a  memoir  which  appeared  in  the  tenth 
volume  of  the  Transactions  of  the  Royal  Astronomical  Society,  from 
which  we  reproduce  the  series  of  illustrations  given  on  Plates  XVIII. 
and  XIX. 

3106.  Appearance  on  January/  24.  —  The  comet  appeared  as  in 
fig,  1,  visible  to  the  naked  eye  as  a  star  of  the  second  magnitude. 
The  bead  was  nearly  circular,  and  presented  a  pretty  well-defined 
planetary  d\sc,  encompassed  by  a  coma  or  halo  of  delicate  gossamer- 
like brightness.  The  diameter  of  the  head,  without  the  halo  or 
eoma,  measured  131",  and  with  the  latter  40*2''. 

3107.  Appearance  on  Januari/  25.  —  Fi(j.  2.  Circular  form 
broken,  and  magnitude  increased.  '  Three  stars  seen  through  the 
eoma  and  one  through  the  head. 

3108.  Appearance  on  January  2G.  —  Fig.  3.  Magnitude  again 
increased,  but  coma  diminislicd. 

3100.  Appearance  on  January  27.  —  Fig.  4.  Comet  began  to 
asanme  the  parabolic  form,  and  increase  of  magnitude  continued. 

3110.  Appearance  on  January  28.  —  Fig.  5.  The  coma  or  halo 
quite  invisible,  but  the  nucleus  appeared  like  a  faint  small  star. 
The  magnitude  of  the  comet  continued  to  increase.  The  observer 
£incied  he  saw  the  faint  outline  of  a  tail. 

3111.  Appearance  on  January  30.  —  Fig.  6.  The  form  of  the 
comet  now  became  decidedly  parabolic.  The  breadth  across  the 
head  was  702",  being  greater  than  on  the  24th  in  the  ratio  of  41)  to 

*  Capo  Observations,  p  897. 


u  10,  which  correspondE  to  tin  inorGue  of  volnme  in  tho 

1  to  3,  BuppoaiDg  the  form  to  remain  mjohaDged ;  hot  it 

nted  tliat  the  eitcQsion  in  length  gave  a  gnporfieial  iDcrFiue 

liiiiO  of  35  to  ],  ntiich  would  corrospoiid  to  a  much  grratcr 

entation  of  volume. 

12.   Appearance  on  February  1.  —  F^.  7.      Further  increase 
litode,  the  form  remaiDiog  the  same. 

.   Appearance  o»  /Virutirj  7.  — Plite  XIX.  Ji'j.  8.     The 
fas  on  this  night  rendered  f  '-'  hj  the  eSiict  nf  mooolighL 
Appcai-ance  on  F-'brunri         —  Fiij.  9.      Further  increwe 
le.      A  star  visible  through  the  body  of  ibe  comet. 
u.  AppmratH-e   on    Fcbraari/   16   and  'j:!.  —  F,<jt.   10,   11. 
.  inugnitude  neat  ou  increuing,  while  the  illumiDation  became 
^^■0  and  more  fainl.,  and  ibii;  uootinucd  until  the  comet's  final  di«- 
aDDearance ;  the  outline,  aft«r  a  short  time,  hccame  so  faiut  aa  to  be 
n  the  surrouDding  darkness,  leaving  a  bkud  oubuloufi  bloU-li 
a  bright  centre  enveloping  the  niiuleua. 
1 16.   Nitmler  of  cojiuin.  —  Acconiing  to  Mr.  Hind,  the  number 
f  oomets  which  have  appeared  since  the  birth  of  Chnst  In  each  suc- 
BBBive  oentOTT  is  u  G:>11qws  :  I.,  22  ;  II.,  23 ;  IIL,  44 ;  IV.,  27 : 
v.,  16;  Vl.,25j  VII.,22;  Vltl.,  10;   IX.,  42;   X.,96;    XI., 
36;     XII.,  2fi;    XIII.,  2(i;    XIV.,  2!);    XV.,  27;    XVI.,  31 : 
XVII.,  25;  XVIII.,  64;  XIX.  (first  half),  80.     Total,  607. 

3117.  Diiradon  of  Ike  appearance  of  comets.  —  Since  comets  are 
visible  only  near  their  perilielia,  when  their  velocity  is  greatest, 
the  duration  of  their  viaibiliiy  at  any  single  perihelion  passage  is 
generally  short.  The  longest  appearance  on  record  in  that  of  tbc 
great  comet  of  1811  (No.  8,  Table  VI),  which  continued  to  le 
Tisiblc  for  510  days.  The  comet  of  1825  (No.  II.,  Table  VI.)  mt» 
visible  for  twelve  nioolhs,  and  others  which  appeared  since  have 
been  seen  for  eight  months.  In  general,  however,  these  bodies  dii 
not  continue  to  be  seen  for  more  than  two  or  three  months. 

3118,  NenT  apj>roa(k  of  ct/meh  to  tlie  earlh. — Considering  the 
Tsst  numbers  of  comt^ts  which  have  paesi-d  through  the  system, 
such  an  incident  as  the  eollii-ioD  of  one  of  them  with  a  planet  miebt 
seem  no  very  improbable  contingency.  Lexcll'a  comet  was  supposed 
to  have  paiiscd  among  the  £atellil«s  of  Jupiter;  and,  if  that  was  the 
case,  it  is  certain  that  the  motions  of  these  bodies  were  not  in  the 
least  affected  by  it.  The  nearest  approach  to  the  earth  ever  mad« 
bj  a  comet  was  that  of  the  comet  of  1684  (No.  55,  Table  VIIL), 
which  came  within  216  semi -diameters  of  the  earth,  a  distance  not 
BO  much  as  four  times  that  of  the  moon.  We  are  not  aware  of  any 
nearer  approach  than  this  being  cerlaioly  ascertained.  I 


•■      •       1 


T  ..  '      ■ 


.     .  hi-     I 


tMlT  lH:r.\imMl  KItoUTHR  sr.VIX  ItVlii 


THEORY  OF  VARIABLE  ORBITS.  M8 


CHAP.   XIX, 
THEORY  OF   VARIABLE  ORBITS. 

3119.  Conditions  tinder  which  elliptic  orbits  are  described,"'^ 
If  any  number  of  bodies  P,  p',  p'',  &c.,  moving  with  any  velocities 
in  any  directions  whatever,  be  exposed  to  the  influence  of  the  at- 
traction of  a  central  body  s,  in  a  fixed  position,  such  attraction 
varying  in  its  intensity  inversely  as  the  square  of  the  distance  of  the 
attracted  body  from  s ;  and  if  at  the  same  time  the  several  bodies 
p,  p',  p^',  &c.,  exert  no  attraction  upon  each  other  or  upon  the  central 
body  8 ;  these  bodies  P,  p',  p",  4c.,  will  each  of  them  revolve  in  an 
ellipse  of  which  the  centre  of  the  attracting  body  8  is  the  focus.  Each 
of  these  elliptic  orbits  will  be  invariable  in  form,  magnitude,  and  po- 
sition, and  so  long  as  such  a  system  would  be  exposed  to  the  influence 
of  no  other  force  than  the  central  attraction  of  s,  each  of  the  bodies 
p,  p',  p'',  &c.,  would  continue  to  revolve  round  s  in  the  same  inva- 
riable orbit. 

The  general  proposition  here  enunciated  was  demonstrated 
by  Newton  in  the  first  book  of  his  celebrated  work  entitled  the 

fttlNCIPIA. 

3120.  Forces  other  than  the  central  attraction  would  destroy  the 
dUptic  form.  —  If,  however,  the  bodies  composing  such  a  system 
were  exposed  to  the  influence  of  any  other  attraction,  whether  pro- 
ceeding from  each  other  or  from  any  cause  exterior  to  and  inde- 
pendent of  the  system,  the  motions  of  p,  p^,  p^',  &c.,  would  no  longer 
take  place  in  such  elliptic  orbits.  Their  paths  would,  in  that  case, 
depend  on  the  directions,  intensities,  and  law  of  variation  of  those 
other  attractions,  whether  internal  or  external,  to  the' operation  of 
which  they  are  exposed.  If  such  forces  have  intensities  which  bear 
any  considerable  proportion  to  the  intensity  of  the  central  attraction 
exercised  by  8,  the  elliptic  form  impressed  on  the  orbits  by  the  latter 
would  be  altogether  effaced,  and  the  bodies  p,  p',  p^',  &c.,  would  be 
thrown  into  new  and  wholly  different  paths,  the  problem  to  deter- 
mine which  would  be  one  of  the  greatest  physical  complexity  and 
mathematical  difficulty. 

3121.  But  when  these  forces  are  feeble  compared  with  the  central 
attractiony  the  elliptic  form  is  only  slightly  affected.  —  But  if  the 
focees,  whether  internal  or  external,  to  the  operation  of  which  the 
system  is  exposed,  have  intensities  incomparably  more  feeble  than 
the  central  attraction  exercised  by  s  upon  P,  P^,  p'',  &c.,  then,  as 
may  bo  readily  conceived,  the  influence  of  s  in  imparting  the  elliptic 
form  to  the  paths  of  P,  p'^  p",  &c.,  around  it,  will  still  in  iVv^  xnvvw 

45* 


THEORY  OF  VAKIAfiLE  ORBITS.  ^33 


CHAP.  XIX. 

THEORY  OF   VARIABLE  ORBITS. 

3119.  Conditions  under  which  elHptic  orbits  are  described. -^^ 
If  any  Dumber  of  bodies  P,  p',  p",  &c.,  moving  with  any  velocities 
in  any  directions  whatever,  be  exposed  to  the  influence  of  the  at- 
traction of  a  central  body  s,  in  a  fixed  position,  such  attraction 
varying  in  its  intensity  inversely  as  the  square  of  the  distance  of  the 
attracted  body  from  8 ;  and  if  at  the  same  time  the  several  bodies 
p,  p^,  F^',  &c.,  exert  no  attraction  upon  each  other  or  upon  the  central 
body  s ;  these  bodies  P,  p',  p'',  &c.,  will  each  of  them  revolve  in  an 
ellipse  of  which  the  centre  of  the  attracting  body  8  is  the  focus.  Each 
of  these  elliptic  orbits  will  be  invariable  in  form,  magnitude,  and  po- 
sition, and  so  long  as  such  a  system  would  be  exposed  to  the  influence 
of  no  other  force  than  the  central  attraction  of  s,  each  of  the  bodies 
p,  p',  F^',  &c.,  would  continue  to  revolve  round  s  in  the  same  inva- 
riable orbit. 

The  general  proposition  here  enunciated  was  demonstrated 
by  Newton  in  the  first  book  of  his  celebrated  work  entitled  the 

lilNCIPIA. 

3120.  Forces  other  than  the  central  attraction  would  deztroy  the 
dliptic  form,  —  If,  however,  the  bodies  composing  such  a  system 
were  exposed  to  the  influence  of  any  other  attraction,  whether  pro- 
eeediog  from  each  other  or  from  any  cause  exterior  to  and  inde- 
pendent of  the  system,  the  motions  of  p,  p^,  p^',  &c.,  would  no  longer 
take  place  in  such  elliptic  orbits.  Their  paths  would,  in  that  case, 
depend  on  the  directions,  intensities,  and  law  of  variation  of  those 
other  attractions,  whether  internal  or  external,  to  the*  operation  of 
which  they  are  exposed.  If  such  forces  have  intensities  which  bear 
any  i^on8iderable  proportion  to  the  intensity  of  the  central  attraction 
exercised  by  8,  the  elliptic  form  impressed  on  the  orbits  by  the  latter 
would  be  altogether  efflEiced,  and  the  bodies  p,  p',  p'',  &c.,  would  be 
thrown  into  new  and  wholly  different  paths,  the  problem  to  deter- 
ttioe  which  would  be  one  of  the  greatest  physical  complexity  and 
mathematical  difficulty. 

3121.  But  when  Oiese  forces  are  feeble  compared  with  the  central 
aUraction^  the  elliptic  form  is  only  sUyhtly  affected.  —  But  if  the 
foreeSy  whether  internal  or  external,  to  the  operation  of  which  the 
STBtem  is  exposed,  have  intensities  incomparably  more  feeble  than 
the  central  attraction  exercised  by  s  upon  p,  p^,  p'',  &c.,  then,  as 
may  be  readily  conceived,  the  influence  of  s  in  imparting  the  elliptio 
form  to  the  paths  of  P,  f^^  p",  &c.,  around  it,  will  still  in  iVv^  Tuiwv 

45* 


534  ASTRONOMT. 

prevail.  These  paths  will  not.,  in  strictness,  be  ellipses,  bat,  owing 
to  the  comparatively  small  effect  of  the  disturbing  forces,  they  will 
deviate  from  the  elliptic  form,  which  in  the  absence  of  such  forces 
they  would  rigorously  assume,  in  a  degree  so  slight  as  to  be  only 
perceptible  when  the  most  exact  methods  of  observation  and  mea- 
surement are  brought  to  bear  upon  them,  and  in  many  cases  not 
even  then  until  the  effects  of  such  feeble  forces  have  been  allowed 
to  accumulate  during  a  long  succession  of  revolutions. 

3122.  This  is  the  case  in  the  system  of  the  Universe,  —  Now  it 
happens  that  the  Great  Architect  of  the  Universe  has  so  constructed 
it,  that  in  all  cases  whatever,  without  a  single  known  exception,  the 
forces  which  arc  independent  of  the  central  attraction  8,  whether 
they  be  those  which  arise  between  the  bodies  composing  the  systems, 
or  whether  they  proceed  from  causes  exterior  to  and  independent  of 
them,  are  under  the  conditions  last  mentioned.  In  no  case  do  their 
intensities  exceed  very  bukUI  fractions,  such  as  an  hundredth,  and 
more  generally  not  a  thousandth,  of  the  central  attraction.  Hcdcc 
it  is  that  the  ellipticity  of  the  orbits  is  so  preserved,  their  niagoi- 
tudes  so  maintained,  and  their  positions  so  little  variable,  that  in  all 
cases  the  most  exact  means  of  observation,  and  in  general  long 
periods  of  time,  arc  nccossjiry  to  di.«fcover  and  measure  the  changes 
produced  upon  tbcm. 

812o.  FI'iicc  jyrocird  tp-en(  /aciJifies  of  rnrr.'iff^fjfion  and  nilrd- 
hitimi. — neiicc  arise  consequences  of  vast  importance  in  the  dovolo^>- 
ment  of  the  laws  of  nature  and  the  pronrross  of  physical  knowlcvl^^e. 
The  problem  proscuted  by  a  sy.stcni  subject  only  to  such  feeble 
inti'rfercDccs  with  the  influence  of  the  central  attrarti<»n,  is  incompa- 
rably more  simple  and  easy  of  solution  than  would  be  that  of  a 
system  in  which  int<^rferinrr  attraetiuns  of  much  greater  relative 
intensity  might  prevail.  ]\Iethods  of  investigation  and  calculati"n, 
as  well  as  modes  of  observation,  are  applicable  in  the  one  case,  which 
would  be  altogether  inadmissible  in  tiie  other ;  and  results  are  ob- 
tained and  buvs  (leveb)ped  which  would,  under  the  more  complioateJ 
ccmditions  of  the  other  problem,  be  utterly  unattaiuable. 

»)ll2-i.  Prrtnrhnfion^  and  d/'sturhho  fnrccin. — The  central  attrac- 
tion,  therefore,  being  in  all  cases  regarded  as  the  chief  presiiliiiL: 
physical  power  by  which  the  S3'stem  is  held  together,  and  by  wliioli 
its  nioiions  in  the  main  are  regulated,  the  orbits  of  the  revolvin): 
b(H]ies  r,  i»',  i>",  t^v.,  are  first  calculated  as  if  they  depended  P"lc-y 
ni)on  the  central  attraction  of  s.  This  gives  a  iirst,  but  very  cl>>'', 
approximation  to  them.  Tlie  forces  by  which  they  are  affecto<l. 
independent  of  the  central  attraction  of  s,  are  then  severally  taken 
into  account,  and  the  deviations,  minute  as  they  always  are,  from 
the  elliptic  paths  first  determined,  arc  exactly  calculated.  Thon' 
deviations  an*  called  DTSTHRnANCKs  or  VKR'rrRBATioNS;  and  tbc 


THEORY  OF  VARIABLE  ORBITS.  585 

forecs  which  prodace  them  are  called  disturbino  or  perturbing 

FORCES. 

3125.  Method  of  variable  elements, — The  instantaneous  ellipse, 
— Let  a  body  P  be  supposed  to  revolve  in  a  certain  orbit,  subject  to 
the  central  attraction  F  of  a  certain  mass  S;  and  at  the  same  time  to 
a  disturbing  force  D  much  more  feeble  than  F  in  its  intensity. 
There  are  two  ways  in  which  the  problem  to  determine  the  exact 
path  of  P  may  be  approached.  1st  The  body  p  may  be  regarded 
as  under  the  influence  of  two  forces  F  and  D,  of  given  intensities  and 
directions ;  and  i^  actual  path  may  be  investigated  by  the  prin- 
ciples of  mathematical  and  physical  analysis.  This  path  would,  in 
every  case  presented  in  nature,  be  a  very  complicated  curve  of  no 
regular  form,  although  in  its  general  shape  and  outline  it  would 
differ  very  little  from  an  ellipse  having  its  focus  at  s.  2ndly.  In- 
stead of  attempting  to  determine  the  exact  geometrical  character  of 
thid  complicated  curve,  the  body  p  may  be  regarded  as  revolving 
round  s  in  an  ellipse,  the  form,  position,  and  magnitude  of  which 
are  subject  to  a  slow  and  continuous  variation.  To  comprehend 
this  method  of  considering  the  motion  of  P,  let  the  disturbing  force 
D  be  imagined  to  be  suspended  at  any  proposed  point  of  p's  path. 
From  the  moment  of  such  suspension,  p  would  move  in  an  exact 
and  invariable  ellipse,  having  s  as  its  focus.  The  form,  position, 
and  magnitude  of  this  ellipse,  or,  what  is  the  same,  its  elements^ 
that  18,  its  major  axis,  eccentricity,  longitude  of  perihelion,  inclina- 
tiony  and  longitude  of  node,  would  be  exactly  deducible  from  p's  dis- 
tance fi'om  8  at  the  moment  of  suspension  of  the  disturbing  force, 
its  velocity,  and  the  direction  of  \is  motion.  The  problem  of  its 
determination  in  such  case  would  have  nothing  indeterminate. 
One,  and  but  one,  ellipse,  could,  under  such  conditions,  be  described. 

If  the  disturbing  force  D  be  imagined  to  be  suspended  at  another 
moment  and  at  a  different  point  in  the  path  of  p,  another  and  a  diffe- 
rent ellipse  would  bo  in  the  same  manner  described  by  P  after  such 
aospcnsion.  If  the  interval  between  the  two  moments  of  such  sup- 
posed suspension  be  not  considerable,  as,  for  example,  when  they 
occur  at  different  parts  of  a  single  revolution  of  p  round  s,  the  two 
ellipfies  will  not  in  general  have  any  appreciable  difference  in  any 
of  Uicir  elements,  from  which  it  follows,  that  when  a  single  or  even 
several  revolutions  of  P  round  s  are  only  considered,  the  path  of  p 
may  in  general  be  regarded  as  an  ellipse  of  fixed  position  and  inva- 
riaole  form  and  magnitude,  such  as  P  would  describe  independently 
of  the  influence  of  b.  But  if  the  interval  between  the  two  moments 
of  sapposed  suspension  be  very  great,  as,  for  example,  when  it 
extends  to  a  long  series  of  revolutions  of  p  round  s,  then  the  dis- 
turbing effects  of  D,  having  accumulated  from  revolution  to  revo- 
lotioDi  will  become  very  sensible  and  measurable,  and  the  two 
ellipses  may  differ  one  from  the  other  in  any  or  all  of  their  elements^ 


ASTItONOMT.  ^^^P 

n  est«i)t  more  or  Usa  con»ideraliIe  sccording  to  the  iliMMli; 
F  «nii  ilircctioD  of  llie  diaturbing  force  d. 

The  ellifwe  in  wbicb  p  would  tlins  move,  if  at  »ny  point  of  it* 
Htb  the  BCtion  of  tlie  disturbing  force  were  thus  suspended,  u  oiled 

lie  "INSTANTANEOCB  ELLIPSE." 

According  to  tbis  second  molhod  of  viewing  the  effects  of  distarb- 
^Bg  forces,  therefore,  the  body  P,  which  is  subject  to  their  action,  is 
regarded  as  moving  in  an  elliptic  orbit  of  which  b  is  the  focw;  bat 
tbis  orbit  is  supposed  from  momcDt  to  moment  to  change  its  pca- 
tion,  form,  and  magnitude  in  a  cerUun  minute  degree.  The  pertnr- 
Wion  bring  tbus,  aa  it  were,  transferTed  from  the  body  f  IoUm 

fcrbit  which  it  describes,  the  body  being  supposed  to  move  aa  *  bwj 
would  »lide  on  a  fine  wire,  while  the  wire  itself,  being  flexible,  wmU 
twiid  into  various  fonns,  the  bead  still  moving  along  it,  the  mcthid 
bB»  betu  denominated  aa  that  of  "variable  elements." 
This  is  the  method  of  oonsidering  the  effects  of  disturbing  fimet 
irhicb  was  adopted  by  Newton,  under  the  title  of  moreable  with, 
U)d  is  still  generally  adopted  as  the  most  simple,  clear,  and  col- 
Tcnient  nicaus  of  investigating  and  cxphining  the  phenotaeDi  of 
f      perturbations. 

&V2G.  FcehJntas  of  the  disturbing  forees  in  the  catti  prrtenkd 
in  ihe  Ktlar  ii/iletn  acplaine/l.  —  In  the  cases  which  ore  presenled  in 
the  actual  system  of  tbc  world,  the  extremely  feeble  intensilies  of 
the  disturbing  forces,  compnrcd  with  those  of  the  central  altraetiinu, 
arise  in  some  cuhcs  fmra  the  vastness  of  the  masses  of  the  eealnl 
compared  with  those  of  the  disturbing  bodies;  in  olhers,  from  tU 
emnllncHS  of  the  distance  of  the  central  compared  vritb  that  of  lh« 
disturbing  from  the  body  which  is  attracted  and  disturbed;  and,  19 
some  cases,  from  the  combination  of  both  these  causes. 

Thus,  when  a  planet  attracted  by  the  sun  is  disturbed  by  ib> 
'  attraction  of  anolher  planet,  the  enormous  preponderance  of  tbe 
mass  of  the  sun,  wiiicb  is  more  tban  a  thousand  times  greater  than 
I  the  larger,  and  hundreds  of  thousands  of  times  greater  tban  tbe 
imaller  planets,  gives  to  the  effects  of  its  attrvc^on  a  predomi- 
nance  which  could  only  be  compensated  by  a  greater  degree  ot 
proximity  of  tlie  disturbing  to  the  disturbed  planet  than  is  con- 
iistent  with  tbe  wise  conditions  under  which  the  eolar  system 
ia  placed.  The  differences  between  the  mean  distances  of  ths 
planets,  taken  in  succession  from  Mercuir  outwards,  arc  so  great, 
and  the  eccentricities  of  their  several  orbita  so  small,  that  in  no 
possible  position,  not  even  when  they  are  in  heliocentiio  ctm- 
jnnction  (2986),  with  one  in  aphelion,  and  the  other  in  perihelion, 
can  they  approach  each  other  so  as  to  give  to  the  disturbing 
force  exerted  by  any  one  upon  any  other  an  intensity  amount- 
log  to  more  tiian  a  \eT3  th\ii\).xr.  tttWAan.  li^  '^it  taxAro).  ittnction. 
This  will  be  Tenierci  i^iv^  a.^^wtA  \i.wwS»3.>  «sA.  ■«*  *isE^ 


THEORY  OF  VARIABLE  ORBITS. 


637 


assnme  it  provisioDallj  for  the  present  in  onr  exposition  of  tbo 
general  effects  of  the  disturbing  forces  which  prevail  among  the 
b<xiies  of  the  system ;  premising,  however,  that  other  conditions 
besides  the  consideration  of  relative  masses  and  proximity  will  be 
necessary  for  the  exact  estimation  of  the  effects  of  the  disturbing 
forces. 

3127.  Order  of  eorposUion.  —  In  the  present  chapter  we  shall 
then  explain  generally,  without  reference  to  any  particular  disturb- 
ing or  disturbed  body,  the  effects  produced  by  disturbing  forces  upon 
the  elements  of  the  orbit  of  the  disturbed  body ;  and  in  the  succeed- 
ing chapters  we  shall  show  the  application  of  the  general  principles 
thus  established  to  the  most  important  cases  of  perturbation  pre- 
sented in  the  solar  system. 

3128.  Resolution  of  the  dhturhiny  force  into  rectangular  compo- 
nents, —  From  whatever  cause  the  disturbing  force  may  arise,  it  can 
always  be  resolved  into  three  components,  each  of  which  is  at  right 
angles  to  the  other  two;  and  its  effects  may  be  investigated  by 
ascertaining  the  separate  effects  of  each  of  these  components,  and 
then  combining  the  results  thus  obtained. 

The  resolution  of  any  force  into  three  rectangular  components 
parallel  to  three  lines  or  axis,  arbitrarily  chosen,  is  a  process  of 
great  utility  in  mathematical  physics,  and  one  which  is  based  upon 
the  gcnend  principles  of  the  composition  and  resolution  of  force, 
formerly  so  fully  explained  and  illustrated  (144)  et  teq. 

To  render  this  more  clearly  intelligible,  let 
Vjfig,  822,  be  the  position  of  the  disturbed 
body  at  any  proposed  time,  and  let  the  direc- 
tion of  the  disturbing  force  D  be  p  R,  its  inten- 
sity being  such  that,  if  no  other  force  acted 
on  P,  it  would  cause  that  body  to  move  over 
PR  in  the  unit  of  time.  Let  pz,  PX,  and 
PT  be  the  three  axes  at  right  angles  to  each 
other,  taken  at  pleasure  in  any  directions 
along  which  the  disturbing  force  D  is  to  be 
resolved.  Suppose  three  lines,  rr',  rr", 
and  rr'",  drawn  from  R  parallel  to  these 
three  axes,  P  z,  p  t,  and  p  x,  so  as  to  form 
the  rectangular,  die-shaped  solid,  called  a 
parallelepiped,  represented  in  the  figure. 
Now,  by  the  principles  of  elementary  geometry,  it  appears  that  R  R' 
P  /  ifl  a  rectangle,  of  which  p  r  is  the  diagonal.  It  follows,  there- 
fure  (154),  that  the  disturbing  force  D,  represented  by  P  R,  is  equiva- 
lent to  two  forces  represented  by  p  r'  and  p  r^.  But  p  r"'  /  r"  being 
also  a  rectanffle,  the  component  p  r^  is  equivalent  to  two  components 
represented  by  p  r"  and  p  r"',  directed  along  the  axes  p  x  and  p  t 


Fig.  822. 


ASTRONOMY. 

Thus  it  appeara  that  ibe  disturliiog  force  d,  ivprcsentcd  f>7  PK, 
i'ji  resmlved  iulo  tljree  componCDto,  represented  by  pb'  dirwtf^ 
]  mlong  P  Z,  P  /'  direot"^  nloog  p  X,  and  P  r"'  directed  »}ong  p  T  w* 
I  Bpev lively.  If  the  angles  nt  which  the  direction  P  R  of  ihc  disturb. 
'  ing  forvo  ia  iadined  to  the  three  axes  PX.  pr,  and  PZ  be  knuvn,  il 
is  eoay  to  obtaia  arithmetical  esprcsdioDs  for  these  three  comjraacati 
of  it. 

I,tt  the  angles  Rpx,  kpy,  and  Bpz.  at  nbicb  PB  is  incIiiicJw 
tlic  ttics  P  X,  P  Y,  and  r  z  respectively,  be  ezprv^ed  by  o,  3,  siri  y; 
and  lot  tlie  three  componontB  p/*,  Pr"',  aud  pr'  lie  eipnriBal  bj 
3C,  V,  and  Z  respectively.  Since  the  angles  p/'b,  Pr^B,  inJ 
p  b'  B  are  each  GO",  il  will  follow  that 


X  =  COS.  B  >; 

D. 

Y  =  C08.  3  X   D, 

sinoe  by  th<i 

figure 

we  bare 

PB*  = 

p  b"  +  B  a",         B  b"  = 

shall  have 

pe'  = 

p  a"  +  B'  a""  + 

d'  =  x'  +  y'  +  z'. 
Each  of  the  components  is,  therefore,  found  by  multiplying  the  di^ 
tnrbing  force  by  the  cosine  of  the  angle  which  its  direction  fonni 
with  the  axis  upon  which  the  component  is  taken,  and  the  Buai  of 
the  itqunres  of  the  three  components  ii  erjual  to  the  square  of  the 
disturbing  force. 

Such  is  the  principle,  in  its  most  general  expression,  by  whidi 
the  resolution  of  the  disturbing  forea  is  effected ;  and  if  the  efli*» 
of  each  of  the  three  components  upon  the  orbit  of  p  be  Geparatd} 
Rscerlained,  and  the  like  process  be  applied  to  every  disturbing  fora 
by  which  p  is  affected,  the  actual  changes  produced  in  the  orbtl  mil 
be  determined. 

3129.  Resolution  of  th)  dittiirlin.j  foret  with  reiiilion  to  Qit 
radivi  vector  and  ihe  plane  of  ihe  orbii.  —  But  for  the  purposes  et 
elementary  Giposilion,  it  is  found  convenient  to  give  to  the  ales  P  s, 
PT,  and  FZ,  iu  llie  directions  of  which  the  components  have  as- 
sumed a  position  having  immediate  relation  to  the  pl.inc  of  p'l 
orbit,  and  to  the  position  of  P  in  ita  orbit.  Since  the  directions  of 
these  ftiea  are  altogether  arbitrary,  being  restrained  by  no  other  coa- 
ditioDS  than  that  of  being  mutually  perpendicular,  it  is  atwavs  pof- 
sible  to  take  one  of  them,  PZ  for  example,  perpendicular  to  the 
plane  of  p's  orbit,  and  in  that  ease  the  piano  of  the  other  twoy  Pi 
and  PY,  will  coincide  with  that  of  p'h  orbit. 

Jiut  when  this  is  done,  the  directions  of  PX  and  py  in  that  plu* 
«re  still  arbitrary;  and  it  has  been  found  convenient  to  aHigu  Id 
ODb  of  them  t\)t:  d\tecl\cAt  «\\\vn  lA  xk^  n.duui  vecliir  from  p  to  tBa 
central  body  R,  or  of  Vtc  \ttTi^'ot  Ho  v"s  ot\\\  ivwra  ■^■too^  »'• 


THEORT  OP  VARIABLE  ORBITS.  589 

t  the  moment  the  disturhiDg  force  is  supposed  to  act,  such 
being  in  effect  the  direction  of  p's  motion  at  that  moment, 
le  of  the  axes,  P  Y,  for  example,  be  taken  in  the  direction  of 
las  vector,  the  other  will  necessarily  be  that  of  a  line  drawn 
I  p  in  the  plane  of  the  orbit  perpendicular  to  the  radius 

16  of  the  axes,  p  x,  for  example,  be  taken  in  the  direction 
tangent,  the  other  will  necessarily  be  that  of  the  normal 
(rbit,  at  the  point  at  which  the  disturbing  force  is  supposed 

>.  Orthogonal  component.  —  In  referring  to  these  several 
s  of  resolving  the  disturbing  force,  jt  will  conduce  to  brevity 
>amess  to  give  the  several  components  distinct  designations 
ve  of  the  directions  which  they  have  in  relation  to  the  plane 
orbit,  and  to  the  position  of  the  disturbed  body  in  its  orbit 
is  purpose  we  shall  adopt  the  designations  which  have  been 
proposed  for  them  by  elementary  writers, 
component  which  is  perpendicular  to  the  plane  of  the  orbit 
listurbed  body  will  then  be  distinguished  as  the  orthogonal 
«ENT  of  the  disturbing  force. 

..  Radial  and  transversal  components.  —  If  the  other  two 
lents  be  taken  in  the  directions  of  the  radius  vector,  and  of  a 
the  plane  of  the  orbit  at  right  angles  to  it,  we  shall  call  the 
the  radial  and  the  latter  the  transversal  component. 
I.  Tangential  and  normal  components.  —  If  the  other  two 
ents  be  taken  in  the  directions  of  the  tangent  and  normal 
)rbit,  we  shall  call  the  former  the  tangential  and  the  latter 

IMAL  component. 

I.  Orthogonal  component  affects  the  inclination  and  th/i 
— It  is  evident  that  of  these  components  the  orthogonal  alone 
'C  any  disturbing  effect  upon  the  plane  of  p's  orbit.  The  other 
lents  being  all  in  that  plane,  can  have  no  tendency  to  move 
turbed  body  p  into  any  other  plane.  The  orthogonal  com- 
howevcr,  being  at  right  angles  to  the  plane  in  which  p  is 
J  must  have  a  direct  tendency  to  carry  p  out  of  that  plane, 
one  side  or  the  other^  according  to  the  direction  in  which  it 

component  therefore,  and  this  alone,  affects  the  inclination 
orbit,  and  the  longitude  of  its  node.  The  kind  of  effect  it 
SB  on  these  elements  will  be  explained  hereafter. 
L  Radial  and  transversal  components  affect  the  central  at' 
%  and  angular  motion.  —  To  explain  in  general  the  effect 
sd  on  p's  motion  by  the  radial  and  transversal  components  of 
itnrbing  force,  let  Pc,  fg.  823,  be  the  radial,  and  Pa  the 
nal  component,  the  diagonal  p  r  being  therefore  the  part  of 
torbing  force  which  acts  in  the  plane  of  p's  orbit. 


aSTROKOMT. 


s  evMent  tliat  ihe  Tsdial  componeot  P  c,  as  bera  tepnMDtali 

will  have  the  effect  <jf  augmeDting  (lie  attraction  bj'  vhiob  t  ■ 
drawn  towards  s,  and  that  tbe  traDsver^l  component  p  a,  IxiDgil 
right  angles  to  the  ladiua  vector,  will  have  a  teiidt'ooy  to  increi* 
tho  angular  velocity  of  r  round  s,  sinc-e  this  angular  velocii;  it 
mcasurod  by  the  motion  of  p,  at  right  angles  to  p  s,  the  radim  1 1 
being  euppoEcd  to  be  given. 

These  components,  however,  may  be  otherwise  directed  io  tel»- 
tion  to  the  radius  vector.  If,  for  example,  the  element  of  the  dis- 
tucbing  force  which  acts  in  the  plane  of  v's  orbit  Lave  the  direcUoa 
F  /f  its  radial  component  will  he  r  c*,  and  its  transversal  pa'.  Tbe 
former,  acting  direutly  against  s's  attraction  oQ  F,  would  have  a  ten- 
dency to  diminish  that  attraction  ;  and  the  latter,  being  contiwy  U 
the  direction  of  r's  motion,  would  have  a  tendency  to  dimini^  iu 
angular  velocity.  The  two  components  therefore,  in  this  cue,  would 
produce  cficcls  on  i>  directly  the  reverse  of  those  produced  in  tlie 
former  case. 

If  the  element  of  the  disturbing  force  have  the  direction  pr", 
the  radial  component  P  c  will  tend  to  augment  the  central  attrM- 
tion,  and  the  transversal  p  a'  to  diminish  the  angular  velodij. 

If,  in  fine,  the  disturbing  clement  have  the  direction  Pr™, 
the  radial  component  p  c'  will  tend  Io  diminish  tbc  central  aUn> 
tion,  nod  the  transversal  P  n  to  augment  the  angular  velocity. 

3135.  Tangaitial  and  normcU  componcnU  affect  Ae  liruar 
txhrify  and  curvature.  —  The  effects  of  the  tangential  uid  do- 
mal  components  are  subject  to  the  same  varieties.  It  may  ba 
shown,  that  if  a  rectangle  v  v  r  c,  fig.  824,  be  drawn,  of  wliich 
the  disturbing  element  p  r  is  the  diagonal,  the  element  F  r  mij 
be  replaced  by  the  two  sub-componenta,  Pc  in  the  " 
tie  tangent,  and  r  c  in  ftie  iwet^w^  til  'ii*  tksctmI, 

These  nre  Hobject  to  \.\ia  6»m»  -^kiuAi  «S. 
reaco  to  the  ^tectioa  ot  flw  (»n.\mii.  »S*Jtwas»^  «&. -^ifc  «»»*« 


THEORY  OF  VARIABLE  ORBITS. 


541 


Fig.  824. 

of  the  moUon  of  p,  as  have  been  explained  in  relation  to  the 
ndial  and  transyersal  sub-components,  and  which  will  be  easilj 
comprehended  by  the^^.  824. 

8136.  Pbdtive  and  negative  components,  —  It  will  conduce  at 
once  to  brevity  and  clearness  to  distinguish  each  of  the  com- 
pooents  of  the  disturbing  force  according  to  its  direction,  with 
reference  to  the  motion  of  the  disturbed  body,  the  direction  of 
the  central  attraction,  and  the  plane  of  the  disturbed  orbit  We 
•hall  therefore  consider  the  transversal  or  tangential  component 
as  positive  or  +  when  it  acts  in  the  direction  of  p's  motion, 
and  therefore  tends  to  accelerate  it;  and  negative  or  —  when 
it  sots  in  the  contrary  direction,  and  therefore  tends  to  retard  it. 
We  shall  in  like  manner  consider  the  radial  or  normal  compo- 
nent as  positive  or  +  when  it  acts  towards  the  concave  side  of 
V^B  orbit,  and  therefore  tends  to  augment  the  central  attraction, 
and  negative  or  —  when  it  has  the  contrary  direction,  and  tends 
to  diminish  the  central  attraction.  In  fine,  we  shall  consider  the 
orthogonal  component  positive  or  +  when  it  is  directed  towards 
the  plane  which  b  adopted  as  the  plane  of  reference,  and  ncga- 
tive  or  —  when  it  is  directed  from  that  plane. 

3137.  In  dtglitly  elliptic  orhitSy  the  normal  and  radial  com* 
ponentSf  and  the  tangential  and  transversaly  coincide,  —  It  is 
evident  that  when  the  elliptic  orbit  is  but  slightly  eccentric,  and 
therefore  very  nearly  circular,  the  radial  and  normal  components 
are  very  nearly  identical  in  their  direction ;  and,  in  like  man- 
ner, the  transversal  and  tangential  components  are  nearly  coinci- 
dent. As  this  is  the  case  with  all  the  orbits  to  be  considered 
m  this  chapter,  we  shall,  without  again  recurring  to  this  point, 
consider  these  components  as  practically  identical. 

We  shall  then  explain,  in  the  first  instance,  without  special 
reference  to  any  particular  disturbing  body,  the  effects  which  are 
prodaced  npon   the  orbit  of  p,   Ist,  by  the  ndial  ^mYstk^^V\ 

m.  46 


nHH'  ASTItO:40MY. 

W  ftndly,  by  tho  traDsTcninl  oomponcnt ;    and   3rdly,  bj  tlie  ottbty 
gosaJ  oompoceDt  of  any  ilistarblog  forc«  whatever. 


3tS8.  Eqitallf  (fncrifti'on  of  areaj  not  ditliirhed  6y  it. — TTii 
aqnable  description  of  areas  round  tbe  centre  being  independent  rf 
tlie  law  of  central  attraction,  find  ioTolving  no  other  eonditiaa, 
except  tbat  tlie  rcToking  body  should  be  sSecCed  by  no  fonrea  eicEpt 
Euch  ae  have  directions  passing  Llirongb  tbe  fixed  centre  (*2599),  h 
will  not  be  affected  by  tbe  radial  component,  the  direction  of  vhid 
Deoessarily  passes  through  that  point 

3139.  In  rffTl  on  Mr  mean  dalatice  and  period.  — If  xeipRV 
tiie  eeotral  nwss,  a  the  mean  distance,  and  P  the  period  proper  to 
the  instantatieoua  cUipw,  we  shall  have,  according  to  wtat  bia  hea 

proved  (2634),  u  =^  -;.     Now  tLe  radial  component  either  ng- 

inonts  or  dimiainlies  Ihe  cenlral  attraction,  according  as  it  is  pa>iiite 
or  negalive.  This  is  equivalent  to  a  inomenlary  iDcreaw  or  dimi- 
nutian  of  tbe  central  na£g  M,  nhich  would  be  attended  by  ■  ctr 

responding  iocreafio  or  diminution  of  ~  ;  tlat  is,  of  the  ratio  of  fla 

cube  of  Ibc  mean  distance  to  tbo  sqnaro  of  tbe  periodic  time  ia  llw 
instiintaneouB  ellipse. 

8140.  S/  ike  radial  cnnijxmml  vary  arrording  to  ant/  conJitiaU 
tehii-Jt  depend  tolelj/  on  the  distanfe,  it  tcxH  not  change  the  form  V 
magnitude  of  the  inglanlanroui  ellipae.  —  It  has  been  established  tt 
a  principle  of  high  generality  by  matbcmBticians,  that  if  tbe  nn- 
alioD  of  the  central  force  depend  only  on  the  distance  of  tbe  rcioUiig 
body  from  the  centre  uf  attraction,  tbe  orbital  Tciotity  of  the  boiii, 
or  the  space  it  moves  ibrougb  in  the  unil  of  lime,  will  al!.o  depcud 
solely  on  the  distance.  Now,  from  this,  combined  with  the  genoil 
principle  of  equable  areas,  it  may  be  inferred  that,  under  such  coB' 
ditions,  tbe  apsides  of  the  instantaneous  ellipse  will  be  alwayii  at  tU 
Banie  distances  from  the  centre  of  attraction.  For  tbe  apsides  mwt 
be  always  a,t  those  particular  distances,  and  no  other,  at  which  the 
Telocity  (which  by  the  supposition  depends  on  the  di.'ttance)  mol 
tiplied  by  the  distance  is  equal  to  twice  the  area  which  the  revolciog 
body  describes  in  tbe  unit  of  time,  that  being  necessarily  the  caw  by 
the  common  principles  of  elementary  geometry  when  the  direciioa 
of  the  moiion  is  at  right  angles  to  the  radius  vector.  This  will 
therefore  always  give  the  same  values  for  tbe  radii  vectores  which 
are  at  right  angles  to  the  tangent,  or  what  is  the  same,  to  the  dia- 
taoces  of  tbe  apsWea  of  >.\\e  \os\KQVaTO;o\is  A\\^*fe  ftata  the  focus. 
Uut  it  ia  clear  that,  it  \\ie  fc^AiiCc  it'  A"  >A  SiiH  v^K^^t^  Vtvs&.'^ 


THBOBT  OF  VARIABLE  ORBITS. 


548 


foens  be  always  the  same^  tbe  major  axis  2  a^  and  tbe  eccentricity 

-,  will  also  be  always  the  same ;  for  we  shall  have 
a 


2,a  =  d'^d", 


^c  =  d''  —  d\         t  =  %. ^. 

^  d'*  +  d' 


Hg.  825 


Althoagh  the  instantaneous  ellipse  be  thus  invariable  in  its  form 
and  magnitude,  under  the  conditions  here  assumed,  it  does  not,  how- 
eyer,  follow  that  it  Js  equally  invariable  in  its  position.  It  may, 
and  does^  as  will  presently  appear,  in  certain  cases,  revolve  round 

the  centre  of  attraction,  its  major  axis  con- 
tinually shifting  its  direction,  so  that  the 
real  path  of  the  disturbed  body  will  be  such 
as  is  represented  in  jig.  825. 

8141.  Effect  of  a  gradually  increasing 
or  decreasing  radial  component.  —  If  the 
radial  component,  whether  it  be  positive  or 
negative,  were  by  its  continual  increase  or 
decrease  to  cause  the  effective  central  at- 
traction continually  to  increase,  the  revolving 
body  P  would  be  brought  every  revolution  nearer  and  nearer  to  the 
central  body  s ;  and  if  it  caused  the  effective  central  attraction  con- 
tinually to  decrease,  the  contrary  effect  would  be  produced.  In  ope 
eue,  tbe  angular  motion  of  the  revolving  body  would  be  continually 
accelerated ;  and,  in  the  other  case,  continually  retarded. 

3142.  Effects  on  the  period  and  mean  motion  more  sensible  than 
Ao$e  on  the  mean  distance,  —  If  the  mean  distance  by  means  of 
foeh  radial  disturbances  as  here  described  should  bo  varied  in  an 
extremely  small  proportion,  such,  for  example,  as  that  of  one  part 
ID  a  million  in  each  revolution,  such  a  change  would  become  sen- 
nUe,  even  to  the  most  delicate  instruments  of  observation,  only  after 
the  lapse  of  centuries.  The  continual  change  effected  on  the  period, 
and  thereby  on  the  mean  motion,  would,  however,  tell  in  a  sensible 
Banner  on  the  mean  place  of  the  body  in  a  comparatively  short 
time. 

3148.  Its  effect  on  the  position  of  the  apsides,  —  The  effect  of 
the  radial  component  on  the  direction  of  the  major  axis  of  the 
cMtf  will  vary  with  the  part  of  the  orbit  at  which  the  dis- 
torbed  body  is  found  at  the  moment  the  disturbing  force  acts 
upon  it. 

3144.  It  diminishes  or  increases  the  angle  under  th^  radius  vector 
and  tangent,  according  as  it  is  positive  or  nrgative. ' —  It  must  be 
considered  that,  in  general,  the  radial  component,  when  +,  has  a 
tendency  to  diminish  the  angle  nvf^^fg.  818,  formed  by  the  direc- 
tion Pi»  of  V^s  motion  and  the  radius  vector  sp;  and,  when  — ,  to 
it     This  will  be  nearly  self-evident  on  inspecting  lli*^ 


1- 


ASTKOSOUr. 

fuj.  826.     If  f;>  represent  the  &tc  of  t&o  orbit  wUAt 

is  goiug  to  describe  a.t  the  momcDt  tbat  the  force  B  Mil 
upon  it;  i»d  if  B  be  enppoeed  to  be  +.  uid  ttunAn 
to  have  a  tcudtinc;  to  iucrcasc  tho  energy  of  tb»  fcrae 
directed  to  o ;  it  is  eyideat  that  in  the  noil  of  tim*  tltt 
force  wbicli  previously  deflected  p  to  p,  will  no*  ddliict 
it  still  more  to  p'  ory*;  so  that  tte  arc  of  tb«  neworiiit 
Pj/  or  pj>"  will  be  more  inclioMl  b)  PC,  that  ia,  it  viU 
muko  n  loss  angle  with  it 

If,  on  the  contniry,  R  be  ncgativo,  it  will  lend  to 
diminish  the  intessitj  of  the  central  force,  and  tfatre- 
f  i(.  B20.     fnru  to  lessen  the  abli<]ni(j,  or  increase  the  ugkaFO 

undor  the  laagcQt  and  the  nulius  vectrir. 
S145.  7(  Tiiutt  or  iJrprtaei  llii  ttnpfy  foctu  of  Ou  tHiplic  oriii 
^have  or  helotc  the  axis,  ai^rnrdtnij  to  ikt  posillim  of  the  diaaiiti 
boity  in  it»  rllijitic  orhit.  — Let  R./j-  827,  be  the  pUce  of  tl«  wo- 
tral  body,  a*  the  eoipty  focus  of  the  instantaocoiu  ellipse,  and  P,  f, 
I  p",  p"'  the  dislnrbed  body  at  different  parts  of  the  ellipse.  It  mtj 
be  assumed  that,  in  an  ellipse  of  smull  eceentriciiy,  ibc  radial  ^la- 
ponent  will  produce  no  eonsible  effect  on  the  orbital  Telocity  of  r, 
and  therefore  nooc  (as  will  more  fully  appcu  hereafter)  on  tb 
magnitude  of  tbo  major  axis  of  the  ellipse. 


P    e„ 


Now,  let  us  suppose  that  P,  moving  in  the  direction  of  the  arrow, 
receives  the  action  of  a  positive  radial  component.  This  would 
deflect  the  direction  of  p's  motion,  and  therefore  of  the  tangent  rt, 
towards  tbe  radius  -vectoT  e  s,  "Bvit  ii\\i<k,  «CGording  to  the  geome- 
trical properties  of  l^e  eUV^ac,^\\&  »,a^  i%^  N&Ni^'OiAvK^'^-msAt 


THBOBT  OF  VARIABLE  ORBITS.  M5 

of  sps'y  it  follows  that  the  decrease  of  <  p  s  will  oanse  a  decrease 
of  twice  the  magoitude  in  the  angle  s  p  s'  ^  and,  since  the  direction 
of  8  P  is  fixed,  that  of  p  s'  must  he  deflected  towards  P  s,  so  that  p  s' 
vill  change  its  position  to  Ps.  But,  since  the  major  axis  of  the 
lUipse  is  not  affected  hy  the  disturbing  force,  and  since,  by  the  pro- 
perties of  the  ellipse,  p  s+P  s'  is  equal  to  the  major  axis,  it  follows 
Jiat  the  disturbing  force  will  not  change  the  length  of  P  s'.  To 
somprehend,  therefore,  the  effect  of  the  disturbance,  we  have  only 
te>  imagine  the  line  P  s  to  turn  on  p,  as  a  centre  towards  P  8,  and  to 
take  the  position  ps.  In  effect,  the  empty  focus  will  be  transferred, 
by  the  nidial  component,  from  s'  to  s. 

Now,  as  the  disturbed  body  approaches  nearer  to  m  n,  the  line 
through  s'  at  right  angles  to  the  major  axis,  the  line  p  s',  drawn 
from  it  to  the  empty  focus,  approaches  more  and  more  to  the  direc- 
tioD  of  the  perpendicular  ms";  and  the  point  to  which  the  empty 
focus  would  be  transferred  by  the  disturbing  force,  is  less  and  less 
removed  from  the  axis ;  and  when  the  disturbed  body  is  at  m,  that 
focus  is  displaced  by  the  disturbance  to  another  point  upon  the  axis 
nearer  to  perihelion  p  than  s'. 

After  passing  m,  the  disturbed  body,  at  p',  for  example,  being 
aeted  upon  as  before  by  a  positive  radial  component,  the  effect  wiU 
be  to  deflect  ps'  towards  Ps';  but  in  this  case,  the  angle  Pa's 
being  obtuse,  the  new  position  /  of  the  empty  focus  will  lie  above 
the  axis. 

If  we  take  the  disturbed  body  at  p",  the  empty  focus  will  be 
transferred  to  «",  a  point  still  above  the  axis.  As  the  disturbed 
body  approaches  n,  the  point  to  which  the  empty  focus  is  transferred 
comes  nearer  and  nearer  to  the  axis,  and  lies  upon  it  when  the  dis- 
turbed body  is  at  n. 

Thus,  it  appears,  that  while  the  disturbed  body  moves  from  m, 
through  aphelion  a  to  n,  the  point  to  which  the  empty  focus  would 
be  transferred  by  a  positive  radial  component  would  move  from  the 
axis  to  a  certain  distance  above  it,  and  would  again  return  to  the 
axis  when  the  disturbed  body  would  arrive  at  n. 

After  passing  n,  let  us  suppose  the  disturbed  body  at  any  point 
j^\  For  the  same  reasons  the  line  p"'  s'  will  be  deflected  from 
l^'  8,  and  the  empty  focus  will  be  transferred  to  ^",  a  point  below 
the  axis. 

Thus  it  appears,  in  general,  that  while  the  disturbed  body  moves 
from  m  through  a  to  n,  the  empty  focus  is  transferred  to  points 
more  or  less  above  the  axb,  and  while  it  moves  from  n,  through  p 
to  m,  it  is  transferred  to  points  more  or  less  below  it. 

8146.  Effects  of  a  positive  radial  component  on  the  apsides.  —  It 
18  evident,  therefore,  that  a  positive  radial  component  will  change 
the  direction  of  the  apsides,  or  of  the  major  axis  of  the  instantar 
ellipse.     The  new  direction  given  at  each  pomt  to  the  major 

46* 


ASTRONOMY. 

liat  of  the  line  drawn  from  8,  throngh  Uie  d 
<  euijiLf  focus,  it  will  be  efident,  from  what  has  jost  been  ci- 
L-d,  tbaC  vhile  the  disturbed  body  moves  from  m  ihrougb  a  to 
•e  DOW  direction  of  the  aiie  s  /,  b  «",  &c.,  wiil  be  such,  tbAt  tlii 
4  perihelion  will  Ho  hthm  p,  i~^  the  new  aphelion  abort  a. 
ose  points  would,  therefore,  he  reiuut  od  from  their  origiasl  pUces, 
EL  direction  contrary  to  the  motion  of  p.  The  motion  iraparteil  la 
;m  would  then  bo  reyremVe. 

While  the  disturbed  body  movea  from  n  through  p  to  m,ll 

rection  of  the  axis  si,  &i"',  fix.,  must  be  sueh  that  the  new  pflt- 

lion  will  lie  above  p,  and  the  new  aphelion  hfhw  a.     These  paiali 

unld,  therefore,  be  removed  from  t^eir  original   places,  in  tbe  di- 

Kstion  of  the  motion  of  P.     The  motion  imparled  to  Ibem  toqH 

_ien  be  pm'jret$ice. 

Thus,  it  appears,  that,  with  a  positive  radial  component,  the  «i! 

the  orbit,  or  the  line  of  apsides,  has  a  progressive  motion  while 

le  revolving  body  passes  over  the  bto  nj>m,  and  a  regressive  m 

bile  !t  passes  over  the  arc  man, 

3147.   Efffelt  of  a  nrgalive  radial  component  on  Uie  Jiosilim  nj 

ifkt  axU. — If  the  radial  component  be  negative,  it  is  evident  thtl 

the  effects  will  be  precisely  the  opposite  of  those  here  stated ;  ibil 

il  to  say,  the  motion  of  tbe  axis  ivill  be  rcgrcgsivc  while  P  uiorM 


THBOBT  OF  VABIABIiS  ORBITS. 


647 


diroQgh  the  arc  np  m,  and  progreflsiye  while  it  moves  throngh  the 
&M  man. 

8148.  Diagram  indicating  these  effects, — In  Jig.  828  we  have 
indicated  by  the  feathered  arrows  the  direction  of  p's  motion,  and 
bj  the  arrows  with  a  cross  npon  their  shafts  the  direction  of  the 
motkm  of  the  apsides  when  the  radial  component  is  positive.  Its 
motiony  when  negative,  will  be  indicated  by  supposing  it  to  take 
place  in  directions  contrary  to  those  in  which  the  latter  arrows 
point 

8149.  This  motion  of  the  apsides  hears  a  very  minute  proportion 
lo  that  of  the  disturbed  body. — It  must  not,  however,  be  supposed 
that  these  alternate  progressive  and  regressive  motions  of  the  apsides 
bear  any  considerable  proportion  to  p's  motion ;  they  are,  on  the 
contrary,  incomparably  smaller;  so  that,  although  while  P  moves 
from  q'  to  Pf  p  is  moving  in  the  same  direction,  it  is  moving  with 
to  small  a  velocity  that  p  arrives  at  j?,  and  passes  it  almost  as  soon 
at  if  p  were  not  moving  at  all :  and  the  same  observation  will  apply 
lo  the  regressive  motion. 

3150.  Diagram  illustrating  the  motion  of  the  apsides, — The 
ioecessive  positions  assumed  by  the  orbit  subject  to  the  disturb- 


Fig.  829. 


548  ASTRONOMY. 

ing  action  of  &  positive  radial  mmpoDeDt,  while  P  pusn  from 
J>  to  jf",  ure  represented  in  Jii/.  8i9,  wbcre  Pit^,p",!'"',  repre- 
KDt  tho  tiuecuEsive  pnaitioDS  of  tbe  point  of  perilielioB,  ind 
a,  a',  a",  a'",  tLo  nuccessivo  poeilioDS  of  tbe  point  of  aphelion.  If 
the  orbit  be  imagiocd  to  revolve  in  the  other  direction  ftnm 
jf"  %  a'"  to  p  s  a,  tbe  motion  will  t>e  that  which  it  would  recuTt 
from  the  disturbing  action  of  the  positive  radial  component  vbile 
p  moves  through  the  aro  Q  a  ti,fii/.  S'29. 

3151.  Thi*  motion  of  the  apsidct  mereanet  ai  the  eccmirKitj 
of  the  orhit  dimt'niike*,  other  thing*  being  the  tame-  —  It  ii  Ml 
difficult  to  perceive  that  this  eSect  of  tbe  ntdial  compoceni  :a 
imparting  a  motion  of  revolution  progrcesive  or  rcgrcisiTe  Id  the 
line  of  apsides  is  greiiter,  ceteris  partl/tu,  when  the  orbit  of  tbe 
dt^turbod  body  is  less  eccentric- 

This  will  be  evident  bjr  the  mere  icspcctioD  of  fgs.  830  tad 
S31.  In  fg.  830,  the  orbit  of  the  dieturbtd  body,  of  wbici 
;>  II  is  a  part,  has  but  small  eccentricity;  uod  the  action  of  tbt 
disturbing  force  at  ji  deflecU  the   body  into  the  arc  represeattJ 


THEORY  OF  VARIABLE  ORBITS.  549 

bj  the  dotted  line.  To  find  the  new  position  of  perihelion,  it 
is  only  necessary  to  take  c  as  a  centre,  ^  c  as  a  radius,  and  to 
describe  a  circle.  The  middle  point  />'  of  the  dotted  arc  of  the 
new  orbit  included  within  this  circle,  will  be  the  position  of  the 
new  perihelion.  If  we  take  the  case  of  a  much  more  eccentric 
orbit,  represented  in  fig,  831,  it  will  be  evident  that  the  arc 
of  the  orbit  included  within  the  circle  for  the  same  degree  of 
deflexion,  will  be  less  than  in  fig.  830;  and  consequently  its 
middle  point,  which  is  the  new  perihelion,  will  be  proportionally 
nearer  toj9. 

3152.  Effect  of  the  radial  component  on  the  eccentricity.  — 
By  what  has  been  explained  (3145),  as  to  the  change  of  posi- 
tion of  the  empty  focus,  the  effect  of  the  radial  component  in 
ill  cases  on  the  eccentricity  will  be  easily  understood.  The  mag- 
nitude of  the  major  axis  not  being  affected,  the  variation  of  the 
eccentricity  will  be  proportional  to  that  of  the  distance  of  the 
empty  focus  from  s.  But,  since  the  distances  of  p  from  the  two 
fbd  are  not  affected  by  the  disturbing  force,  the  distance  between 
the  foci  will  be  increased  or  diminished,  according  as  the  angle 
8  P  s',  fig.  827,  is  increased  or  diminished  by  the  disturbing  force. 
Bat,  from  what  has  been  explained  it  is  clear  that,  while  P 
moves  from  perihelion  p  to  aphelion  a,  the  angle  s  P  s'  is  dimin- 
ished ;  and  while  it  moves  from  aphelion  a  to  perihelion  p,  that 
angle  is  increased  by  the  disturbing  force. 

It  follows,  therefore,  that  a  positive  radial  component  will  dimin- 
ish the  eccentricity  while  P  moves  from  perihelion  to  aphelion, 
and  will  increase  it  while  it  moves  from  aphelion  to  perihelion; 
and  it  is  evident  that  a  negative  radial  component  will  produce 
the  contrary  effect. 

The  effect  produced  on  the  eccentricity  may  also  be  under- 
stood by  the  following  considerations :  —  While  the  revolving  body 
^9  fiO'  ^^^i  passes  from  perihelion  to  aphelion,  its  distance  P  s 
from  the  central  body  s  continually  increases;  and  while  it  passes 
from  aphelion  to  perihelion,  on  the  other  hand,  its  distance  p's 
from  the  central  body  continually  diminishes.  Now,  it  is  evident 
that  the  more  eccentric  the  elliptic  orbit  is,  the  more  rapid  will 
be  the  increase  of  the  radius  vector  in  the  one  case,  and  its 
decrease  in  the  other.  Any  influence,  therefore,  which  will  have 
a  tendency  to  diminish  that  rate  of  increase  or  decrease  of  the 
ndius  vector  will  have  the  effect  of  diminishing  the  eccentricity 
of  the  orbit;  and,  on  the  other  hand,  any  influence  which  would 
have  the  contrary  effect  of  augmenting  this  rate  of  increase  or 
decrease,  would  have  the  effect  of  augmenting  the  eccentricity. 

Now,  it  is  evident  that  a  positive  radial  component,  having 
nceesBarily  the  effect  of  increasing  the  energy  of  the  central  attrao- 
tioo,  will  necessarily  diminish  the  rate  at  which  p  departs  from 


"to  in 


ASTRONOMY. 


'fe  in  going  from  perihelion  to  aptelion,  and  will  < 
■cwording  to  wliat  bas  Wen  jusl  explained,  Lave  : 
dimiuisliing  tlic  cvcvulrivity  of  tbc  orbit ;  bat  tbe  f 
ndiiil  cotuponent,  coDttuuing  to  net  wLilc  P  passes  from  ft&- 
belion  to  DpbclioD,  will  augment  tbc  nttc  at  trbicb  Ibe  ruliiu 
Tcctor  decreases,  and  will  tberefore  increase  the  ecc«ntricitj. 


II. — ErPECTS  OF    THE    TRANSVERSAL    OOMPO.SEST    OF    lEB 
DISTURBI.VO   roBCE. 

S163.  //  aeceUralcs  or  relardi  the  orhilal  motion.  —  In  cobill 
of  very  Bmoll  eccentricity,  such  as  alone  are  here  cooHderBd,  ibt 
radius  vector  is  never  inclined  to  tbe  t&ngent  drawn  in  the  dicMtia 
of  f'b  molinn,  at  an  angle  oiueh  less  or  much  greater  iLan  90*. 
Prom  aphelion  to  perihelion  this  angle  is  always  a  Uulo  JM 
than  00°,  being  least  at  the  extremity  of  the  minor  aiisj  ui 
from  perihelion  to  aphelion  it  ia  always  a  little  gTEatei  thu 
80°,  beine  greatest  at  the  extremity  of  the  minor  axis. 

Now,  the  transvcrFiil  component  being  always  at  right  ingls 
to  the  radius  vector,  it  follows  that,  when  it  is  positive,  it  fmsa 
s  very  acute,  and  when  negative  a  very  oblnsc  angle  with  llu 
direction  of  p's  motion.  In  tbe  former  case,  therefore,  very  nearfj 
its  whole  effect  is  expended  in  augmenting,  and  in  the  Utter  ia 
diminishing,  p's  orbilul  velocity. 

In  the  iiihlantaaeoua  ellipse,  the  orbital  velocity  of  r  cmisUnilj 
increases  from  aphelion  to  perihelion,  and  constantly  decreisa 
from  perihelion  to  aphelion.  Between  the  extreme  limits  of  tbt 
velocity,  tliere  is  tberefore  a  certain  velocity  which  correepoDdi 
to  each  [articular  distance  of  p  from  either  apse, 

315-1.  /(  increases  or  decreases  the  major  axit,  according  at 
i(  IS  pfiitU-e  or  nrgathe.  —  It  is  demonstrated  upon  pbysinl 
principles,  combined  with  tbe  geometrical  properties  of  the  ellipse, 
that  if  V  express  the  orbital  velocity  of  P,  z  tbc  radius  vector 
corresponding  to  any  point  in  the  orbit,  and  a  tbe  semiaxis  major 
of  the  ellipse,  we  shall  have 


Now,  if  tbe  transversal  component  be  posi^ve,  it  will  increase  T, 

and  will  conse()QeDtIy  diminish  -,  and  tberefore  increase  a;  tod, 

on  the  contnry,  if  it  be  negative,  it  will  for  like  reasons  dimin- 
ish a.  It  fo'l^wy,  tberefore,  that  a  positive  transversal  componeal 
will  augment,  aod  a  negative  diminish,  the  mean  distance  of  P 
in  the  iostantaneiiua  ellipse. 

Jt  follows,  bv  comVmmgftiwTesiAv-m'^i  'Ccw.  Vnv&Qnio  law,  tiist 
a  positive  tranE«erao\  covtt^viiivA  «\\\  Svovcm^  ■&»  vdku&  ■s&'^as 


THBOBT  OF  VARIABLE  ORBITS. 


551 


notion  of  P,  and  that  a  negative  transversal  component  will  in- 
erease  it, — an  effect  quite  the  opposite  of  what  might  be  at  first  view 
expected. 

8155.  It  produces  progression  of  the  apsides  from  perihelion  to 
aphelion^  and  regression  from  aphelion  to  perihejion,  when  positive; 
and  the  contrary  when  negative. — The  principle  here  annoanced, 
which  18  of  coDsidcrable  importance,  may  be  dcmoastrated  and  illus- 
trated in  several  ways. 

1.  It  has  just  been  shown,  that  a  positive  transversal  component 
augments  the  orbital  velocity,  and  that  in  the  instantaneous  ellipse 
the  orbital  velocity  proper  to  each  point  continually  increases  from 
aphelion  to  perihelion,  and  continually  decreases  from  perihelion 
to  aphelion.  By  augmenting  the  velocity,  therefore,  the  positive 
transversal  component  imparts  to  p  in  all  cases  a  velocity  proper  to 
a  point  nearer  to  perihelion,  and  therefore  in  effect  brings  perihelion 
nearer  to  p  than  it  would  have  been  if  the  disturbing  force  did  not 
act.  It  follows,  therefore,  that  when  p  is  moving  from  aphelion  to 
perihelion,  the  point  of  perihelion,  being  made  to  approach  it,  will 
nave  a  motion  contrary  to  that  of  p,  and  therefore  regressive ;  and 
when  P  is  moving  from  perihelion  to  aphelion,  the  point  of  perihe- 
lion, still  approaching  p,  must  follow  it,  and  therefore  have  a  motion 
in  the  same  direction,  or  progressive. 

It  is  evident  that  a  negative  transversal  component  must  produce 
the  contrary  effects,  and  would  therefore  impart  a  progressive  motion 
to  the  apsides  when  P  moves  from  aphelion  to  perihelion,  and  a  re- 
gressive motion  when  it  moves  from  perihelion  to  aphelion. 

It  will  be  apparent,  that  at  the  very  points  of  perihelion  and 
aphelion  where  the  effects  of  a  transversal  component  on  the  posi- 
tion of  the  axis,  whether  positive  or  negative,  change  from  progres- 
sion to  regression,  or  vice  versdy  the  actual  effect  upon  the  direction 
of  the  line  of  apsides  will  be  nothing. 

2.  The   same   principle   may  be    demonstrated  as  follows :  ^ 

By  what  has  been  already  shown 
(3154),  a  positive  transversal  com- 
ponent increases  the  major  axis 
of  the  instantaneous  ellipse.  Let 
/)  P  a  p',  fg.  832,  represent   that 

19  ellipse,  the  body  being  supposed  to 
move  in  the  direction  pv^  ap. 

Let  s  be  the  central  body,  and 
s'  the  other  focus  of  the  ellipse. 
By  the  properties  of  that  cur\'e  we 
shall  have 


Fig.  832. 


8P  +  »'p=^a. 


ha  '       lity  of  p  be  augmented  \>j  the  eflcct  of  &  po«fiT« 
ial  0        DDeot,  tbo  major  his  2ti,  and  consei^aeiiily  a^r, 
iisunoo  "■     li8  empty  fDCos  of  the  orbit  from  1",  masl  4li0  be 
unted.  i  dutuibing  force  will  therefore  transfer  that  faeat 

ae  such  I'uiJt  83  y  upoQ  tho  cootiaiutioD  of  the  line  PS*,  ao^    1 
•liogljr,  tbe  new  dirvctioo  of  the  major  axia  will  be  ^s/in- 
of/tsu,  and  it  will  tliercfure  rcTolvo  round  switb  a  regmnra 

bed  body  bo  at  ;  from  peribclioQ  to  apbcHim, 

will  in  like  __»..»  ~e  transferred  to  s",  mi  thi 
tba  oxtB  being  y  ss",  it  vUl  have  »  progceadn 
3. 

evident  that  &  negative  trsnaveml  componenl  snri 
contrary  effects. 

f^cl  on  t/if  efttnlricity.  —  It  ia  easy  to  sbow  tlal  I 

iiHiu  tcuD&VtTWil  componeat  will  augment  tbe  eccentricity  vki 
the  distance  of  P  from  a  i>  lesi,  uJ 
^        A  ^  will  diminisb  it  when  grealer,  tbi 

the  mean  distance,  and  that  a  ne^ 
tiro  transversal  compancnt  ril 
have  tbe  contrary  effect. 

It  is  a  properly  of  tbe  ellipe, 

"  tliut  for  a  given  position  of  F  wiili 

relation  to  the  tninsverac  aiL',  ia 

distances   P  a  and   V  s',  J\-j.  Sj3, 

from  the  two  foci  are  more  or  las 

unequal  according  as  the  ellipse  b 

*  more  or  less  oecentric.     Thi*  pn>- 

Fig.  633.  perty  will    indeed    appear    n«r!y 

eelf-evident,    if    different    etlipMi 

having  tbe  Eame  mnjor  asis  be  compared. 

If  tben  op  bo  tbe  major  axis,  and  b  h  the  minor  axis,  tbe  pointi 
h  being  at  a  distance  from  s  equal  to  half  the  transverse  axis,  l«t  x 
positive  trsDHversal  component  be  supposed  to  act  upon  P  anyvbeffi 
between  bb  and  perihelion.  Saoh  a  force,  according  to  what  hu 
been  proved  above,  will  increase  the  distunee  s'  from  p;  and  fiuee 
tbia  distance  ia  greater  than  PS,  such  a  change  will  render  the  dis- 
tances pe  and  vs'  more  unequal,  and  will  ihcrcfure  increase  the 

But  if  a  positive  transversal  component  act  anywhere  between  hh 
and  aphelion,  as  at  l^,  then  by  augmenting  the  distance  P'  ^,  which 
is  less  than  p'  s,  it  will  render  the  distances  P*  s  and  p'  s*  less  ui^ 
equal,  and  will  therefore  diminish  tbe  eccentricity. 

It  is  evident  thcit  &  negilivo  transversal  component  aclJDg  at  tlx 
flnmc  points  wiU  proAutc  a  noii^jBi^  t^isA. 

It  may  therefore  \>c  Wlwi'iij'vti.  g,uiiarA,'iiai.'iit«KKs«bs*\^. 


THEOBT  or  YABIABLE  OBBITS. 


668 


be  iDCieMed  by  a  podtiiTe  transvonal  oompoDcnt  between  the  mean 
distance  and  perihelion^  and  by  a  neeatiye  one  between  the  mean 
diatance  and  aphelion ;  and  that  it  will  be  diminished  by  a  positive 
tnnsrenal  e<Hnponent  between  mean  distance  and  apheHon^  and  by 
a  BMiti've  one  between  mean  distance  and  perihelion. 

Tbns  it  appears  that  if  a  positive  transversal  component  of  the 
disturbing  force  were  to  act  constantly  on  a  planet  during  the  entire 
xevolntion,  it  would  cause  the  eccentricity  of  the  instantaneous  ellipse 
eontannally  to  increase  from  perihelion  to  the  end  of  the  lesser  axis, 
where  it  would  attain  its  major  limit  From  that  point  it  would 
decrease  until  the  planet  arrives  at  aphelion,  where  it  would  attain 
its  minor  limit  •  From  that  it  would  again  increase  until  the  planet 
would  come  to  the  other  extremity  of  the  minor  axis,  where  it  would 
again  attain  its  major  limit,  after  which  it  would  again  decrease 
vntil  the  planet  would  arrive  at  perihelion,  where  it  would  attain 
again  its  minor  limit 

It  has  been  erroneously  stated,  in  some  astronomical  works,  that 
tbe  points  at  which  the  eccentricity  would  attain  its  major  limit  by 
thia  cause,  would  be  the  extremities  of  a  perpendicular  to  the  major 
passing  through  the  empty  focus  of  the  orbit."^ 


8157.  Its  effects  on  the  major  axis  at  the  apsides. — Let  pPQ, 
fg.  834,  be  the  undisturbed  orbit,  p  being  perihelion  and  Q 
aphelion.     Now,  if  we  suppose  the  revolving  body  at  perihelion  p 


xri: 


^JBee  Henobel'B  Outlines  of  Astronomy, —  ed.  \%4.^,  ^.^%\. 

47 


ABTROSOMY. 

the  action  of  the  poejtive  tntnaverul  Mmponent,  mcfi 
„crcnsiDg  its  Telocity  will  throw  it  iolo  sn  arc  such  as  pp", 
would  ioclode  p  P  within  il,  and  the  revolving  body  will  eon- 
cntly  move  in  the  orbit  pv'a'  instead  of  the  orbit  ^pq,  ia 
h  it  would  bare  revolved  had  it  been  nndiaiurbed.     The  wrbil, 
•fnCf  which  would  result  Irom  the  perturbing  action  of  tin 
e  transversal  force  at  P,  would  bo  one  in  which  the  line  of  ' 
■  would  have  the  same  direction,  hut  in  which  the  point  of 
n  q'  would  he  more  remote  from  o  than  the  point  of  apbelin 
io  "n,listnrbed  orbit.      The  effect  therefore  is,  that,  without 
direction  of  the  line  of  npaidea,  the  trassvene  i: 
jy  the  disturbing  force. 
-  ■=■  ua  now  consider  the  effect  of  a  positive  transveraal  eomponf 
□pen  the  revolving  body  at  apbeljon.     Let  q,  Jig,  835,  te 
jelion,  and  p  the  perihelion,  of  the  undisturbed  orbit  c«f  t 
living  round  the  central  body  c.     A  positive  transversal  f 

acting  at  Q,  accelerating  the  veloci^  u 
before,  will  cause  the  body  to  monin 
an  orbit  Q  I'j/  having  the  nine  poill 
0  for  its  remote  focns,  and  includiiij 
the  undiaturbed  orbit  within  it. 

It  is  evident  that  in  this  case,  whili 
the  afhelioD  distance  CQ  is  the  same 
for  both  orhiU,  the  perihelion  diiunee 
Cp'  of  the  disturbed  orbit  is  (^ 
than  tlie  peribelion  distance  c;)  of  Uit 
undisturbed  orbit;  and  coasei^Qsnllji 
the  Iraasverse  axis  of  the  disturbed 
orbit  is  greater  than  that  of  the  u 

lence  it  may  be  inferred,  in  gei»- 
ral,  that  a  positive  transrereal  fan* 
aoticgupon  the  revolving  body,  whether 
at  perihelion  or  aphelion,  will  have  tbt 
effect  of  augmenting  the  transvew 
axis  of  the  orbit,  but  that  whec  ' 
at  perihelion  it  increases,  and  wbeail 
acta  at  aphelion  it  diminishes,  the  ec 
centrici  tj- 
negative  transversal  component  will  ha« 
mlrary  effect,  diminishing  in  all  cases  the  transverse  aiil 
of  the  orbit  by  decreaping  the  eccentricity  near  perihelion,  aod 
increasing  it  near  aphelinn. 


THEOBT  OF  VARIABLE  ORBITS.  566 


m  —  EFraOTS  OF    THE    ORTHOGONAL  COMPONENT  07    THE 

DISTURRINQ  FORCE. 

8158.  It  changes  the  plane  of  the  orbit — -plane  of  reference,—^ 
It  has  been  already  explained,  that  the  effect  of  this  component 
ia  to  produce  a  change  in  the  position  of  the  plane  of  p's  orbit 
Ib  Older,  therefore,  to  express  such  change  of  position,  it  ii 
neeeasary  that  some  fixed  phiDe  be  selected  with  relation  to  whicb 
the  position  of  the  plane  of  p's  orbit  may  be  expressed.  Socb 
m  plane  may  be  chosen  arbitrarily,  and  we  shall  denominate  it 
generally  the  piane  of  reference. 

The  position  of  the  plane  of  p's  orbit  then  will  depend  on  ita 
fine  of  intersection,  and  its  inclination  to  the  plane  of  reference. 

8159.  Nodes  of  disturbed  orbit  on  plane  of  reference,  —  Let 
aba'  and  AC  a',  fig,  836,  represent  respectively  the  plane  of  re- 
ftnnee  and  that  of  p's  orbit,  seen  in  the  same  manner  as  we 
an  aceoatomed  to  view  the  equator  and  ediptic;  A  being  the 


Fig.  836. 

aaeending  node  corresponding  to  the  vernal  equinoctial  point, 
and  a'  the  descending  node  corresponding  to  the  autumnal  equi- 
noctial point,  and  c  being  that  point  of  the  semicircle  which 
eomaponds  to  the  solstitial  point,  and  which  is,  therefore,  the 
point  most  remote  from  the  plane  of  reference.  We  shall  call 
A  0  the  first  quadrantf  counting  from  the  ascending  node ;  c  a' 
the  second  quadrant;  and  the  corresponding  quadrants  of  the 
other  half  of  the  orbit  the  third  and  fourdi,  quadrants, 

8160.  Effect  of  orthogonal  component  varies  fcith  distance 
Jrom  node.  — Now  let  us  suppose  the  body  subject  to  pertur- 
Dntion  to  be  at  some  point  such  as  p  in  the  first  quadrant,  and 
to  noeive  there  the  action  of  a  positive  orthogonai  component, 
the  direction  of  p's  motion  being  indicated  by  the  arrow.  Since 
this  potttive  component  has  a  tendency  to  draw  p  towards  the 
plane  of  reference,  it  is  evident  that  the  motion  which  p  will 
leoeivei  by  its  action,  must  cause  it  to  proceed  in  a  direction 
hetween  P  c  and  a  line  drawn  from  P  perpendicular  to  the  plane 
of  reference,  that  is,  in  such  a  direction  as  P  ti  inclined  to  P  0 
and  below  it. 

If  the  body  subject  to  perturbation  be  in  the  second  qnadrant, 
M  at  F^i  it  will  for  a  like  reason,  after  the  disturbing  aotion^ 


ASTBONOHT. 


'if. 


rm 

W    ■BATS   in  a  direction  Tg,  slightly  incliiteil  to  t^A'  and  belu*  iL 

I    If  tho    orthogonal  component  be   negative,    it  wilt   be  appirent 

*    IhK  nt  V  tho  bodjr  would,  nfWr  the  action  of  the  disturbing  fmt, 

move   in  that  direction   pn',  slightly  inclined  to  pc  nod  litm 

and  in   like   manner,  at  p'  it  would   move  in    the  diiediat 

',  slightly  inclined  to  P*  a'  and  &  little  above  it. 

^ow  GBch  of  these  diatnrbances  will  change  both  the  nodei  ud 

inclination. 

3161.  XbtlfM  proffreu  or  regren  accort?inff  at  tJie  roinponfX 
it  negative  or  pontine.  —  If  n  p  be  continued  baokttards.  it  liU 
intersect  the  plane  of  reference  at  a  point    r  beyond  ita  forma 

I  nods  A.  It  is  CTiJcnt,  therefore,  that  in  this  cue  the  uoetxt 
Ing  node  wnuld  regress  upon  the  plane  of  referenco.  If  tba  in 
y  9  be  in  like  niauuer  continued  to  meet  the  plane  of  reJuCM 
tt  q,  tliis  point  q  will  he  in  like  manner  behind  a'.  Tboi  tia 
new  position  of  the  dcKending  node  will  be  behind  ita  foBBC 
jtoBitloD,  and,  ooDBcqucntly,  in  this  case  also  the  node  repcnn 
It  appcats,  therefore,  tliat  wherever,  in  the  semi-circle  ACA',t 
I  positive  orthogonal  coraponent  acts,  its  etTect  will  be  to  impart  to  ^ 
node  a  regressive  motion. 

The  fiamo  reosoning  will  equally  apply  to  tho  cases  in  which  rii 
in  the  third  and  fourth  quadrant;  and  therefore  generally  it  majlie 
inferred,  that  in  sU  parts  of  p'a  orhit  a  positive  orthogonal  com- 
ponent will  produce  a  regression  of  tlie  noJca. 

By  like  reasoning  it  will  be  perceived,  that  when  P  is  subject  to 
&  negative  orthogonal  component,  and  therefore  in  the  first  quadnuit 
moves  in  the  ora  p  n',  and  in  the  second  in  the  arc  p  q',  tho  nodn 
will  receive  a  progressive  motion,  the  new  nodes  r"  and  ^  being  io 
advance  of  tho  original  nodes  A  and  a';  and  the  same  reasoning  ■ill 
apply  to  the  third  and  fourth  quadrants.  It  will  follow  geneiatly 
that  a  negative  orthogonal  component  will  everywhere  impart  a  {so- 
gressive  motioa  Io  the  nodes. 

3162.  EffKi -upon  the  indination.  —  It  will  be  evident  opoo  the 
mere  inspection  of  the  dingram,  thnt  the  obliquity  p  r  B  is  less  and 
the  obliquity  p/b  greater,  than  the  original  obliquity  pa  B,  when 
P  is  in  tbe  first  quadrant;  and  that,  on  the  contrary,  the  obliqoiij 
P'^B  is  greater,  and  p'j'b  is  less,  than  the  original  obliquity  p'a's 
in  the  second  quadrant.  It  follows,  therefore,  that  a  positive  ortho- 
gonal component  acting  in  the  first  quadrant  decreases,  and  in  the 
second  increases,  the  obliquity;  and  that  a  negative  orthogonal  eom- 
ponent  in  the  first  quadrant  increases,  and  in  the  second  quadrant 
decreases  the  obliquity.  It  will  follow,  in  like  manner,  that  th« 
effects  of  these  componenla  respectively  in  the  third  quadrwit  are 
similar  to  their  effects  in  the  first,  and  that  their  effecto  in  the  fonrth 
gnadrant  are  s'lmiW  \a  t,\\e\T  e&ei:\»\'a\\it^  «;»«&&. 

It  may  then  be  BtateA  ^enevtiVj ,  'CaW.  «i  v*'^'^^*  'W^'o^w^  "MSf 


^aiORT  or  VAKUBLE  OBBITS. 


557 

B  the  oUmjiu^  wbeo  the  disturbed  body  ia  in  tlw  Gnt 
■od  thiid  qiudniita,  ud  incnuM  it  when  io  the  second  snd  fuurtb ; 
ud  thftt  ft  negBlne  orthognud  oompouent  is  atteodod  with  the 
oppouta  efiects. 

VT.  QXHKKAL  BnMHAAY  OP  TBI  BFIXOTB  Of  A  DISTUKBINQ  fOBd. 

8168.   Ti^»dar  $yopnt  of  Ae  tffteU  of  the  teaeral  cotnponmtt  of 
the  dtUnrbing  force. — 


Atr»M,Mim... 

Apl-Jto- 

It  will  be  coDTeuicnt,  tbeo,  to  collect  and  arrange  in  juxlapo- 
wtjaa,  fat  the  purpose  of  refereoce,  the  vsrioiis  effects  produced  bj 
the  three  componentB  of  the  diaturbtog  force,  as  explained  in  the 
ptMeding  paragraphs.  We  bave  accordinglj  done  tbia  in  the  above 
tabolar  stal«mcnt.  The  sense  in  vhich  the  Kjnibols  +  and  —  are 
applied  to  each  of  the  compoDenta  has  been  already  explained.  As 
^>pUed  to  the  cemi-aiis  a,  the  eccentricity  e,  and  the  inclination  t, 
•f  is  wed  here  to  signify  increase,  and  —  dimiiiatm,  aod.  Q  ^]a& 
«  ia  whicb  they  uo  not  ftffeoted  bv  ibe  daXv^foxa  ^mw. 
47* 


ABIROXuUT 


As  applied  to  the  motiooB  of  the  perihelion  (li)  a.nil  the  node  (.),  + 
indicates  progres-'iive  and  —  regresa^re  motion.  The  sign  0  u 
placed  where  there  is  no  motion  imparted  to  these  points  bj  tfat 
diBlurbing  farce. 


I  TBOBLEU  OF  THKEE  BODIES. 

81ft4.  AUrarli'on  irulrpcndml  of  the  mow  of  the  altraded la!}. 
—  To  obtain  clou  nnd  diBtiact  ideas  of  the  eSects  of  the  distartniig 
■ction  of  masses  brought  into  proximity  with  bodies  moTiog  in  m- 
hits  roond  a  centre  of  attraction,  it  is  most  necessary,  in  the  b>t 

[    Stance,  to  comprehend  clearly  the  Ittw  and  oondilions  which  dtia- 

W  taiine  such  attractions. 

*  The  nttrnction  eierted  by  one  body  npon  another  depends  eoldj 
upon  ibe  mfisa  of  the  ntlriirtinfj  body,  and  its  distance  from  the  »1- 
tracted  body,  and  is  allogelhir  inilfpenJitit  of  the  maf*  nf  the  lailrT.  i 
It  id  the  more  necessary  to  indicate  this,  inasmuch  aa  stndeata  m  1 
apt  to  confound  the  effects  of  attraction  with  those  of  foives  Ova-  \ 
initled  by  impact,  pressure,  or  other  incchanical  agency.  There  i*. 
however,  an  essential  difference  between  these  effects  and  thnae  of 
attraction.  AVhen  a  force  is  transmitted  by  mechanical  agency,  Um 
motion  which  it  imparts  to  the  body  upon  which  it  acts  is  so  mm^li 
the  less  as  the  mass  of  (hat  body  is  greater ;  but  this  is  not  ai  ill 
the  cSLse  with  attraction.  If  a  body  whose  mass  is  m  acta  upoo  an- 
other P  at  the  distance  D,  it  will  impart  to  r,  being  free,  a  ocrtain 
motion  towards  M.  Now,  if  anollier  body  equal  in  njasa  to  p  bs 
placed  in  ju:^ljip>)sitiuu  with  f,  M  will  imj^rt  Uiilua  ei^uul  mMiuo 
in  the  same  direction ;  and  if  three,  four,  or  more  such  bodies  be  in 
like  manner  placed  at  the  same  distance  d  near  each  other,  the; 
will  be  all  equally  attracted  by  M,  and  will  move  towards  M  Uuioo^ 
equal  spaces,  the  atiriction  which  k  excites  on  any  one  of  them 
not  at  lUl  interfering  with  or  diminishing  its  action  upon  the  otherv 
If  we  suppose  these  several  mosses  to  cohere  and  te  fonn  a  sicgle 
mass,  this  single  mass  will  move  towards  h  with  the  same  velocilj. 
It  follows,  therefore,  that  inasmuch  as  M  exercises  separate  and  in- 
dependent attractions  upoii  every  particle  composing  the  mass  F, 
that  mass  will  be  moved  towards  m  by  the  atbaction  of  M  at  the 
same  rate,  whether  it  be  great  or  snuil/. 

Thus,  for  example,  it  appears  (Table  IV.  page  462)  that  the  »t- 
traction  which  the  sun  exerts  npon  the  earth  at  the  distance  of 
oinety-fiTO  miUiona  ot  miVta  "k  sacV  ^  Tia^ld  cause  the  eartb,  if  it    i 
were  at  rest  and  tree,  to  mo^t  \ftwo.i4s.  'Csit  ■saa.  'iii>»i^  ^^^^itf 


PROBLEM  OF  THREE  BODIES.  659 

•n  ineh  in  one  second  of  time.  Now,  if  the  mass  of  the  earth 
were  10  or  100  times  greater  or  less  than  it  is,  the  sun's  attraction 
exerted  at  the  same  distance  would  produce  precisely  the  same  effect 
upon  it. 

3165.  Hence  the  denomination  ^^  accelerating  force,** — ^This  spe- 
cies of  force,  the  effect  of  which  is  exclnsivelj  a  certain  Telocity 
imparted  to  the  body  affected,  is  distinguished  in  physics  from  that 
other  sort  of  force  which  varies  in  its  effects  with  the  mass  of  the 
body  moved,  by  the  term  accelerating  force;  while  the  force  which 
varies  in  its  effect  with  the  mass  of  the  body  moved,  is  called  moving 
force,  or  momentum. 

31G6.  Accelerating  force  of  gravitation. — The  accelerating  force 
of  gravitation  is  therefore  measured  by  and  proportional  to  the  space 
through  which  a  body  is  drawn  in  the  unit  of  time  by  the  attraction 
of  a  given  mass  at  a  given  distance. 

Let  the  unit  of  accelerating  force  be  the  space  through  which  a 
body  would  be  drawn  in  the  unit  of  time  by  the  unit  of  mass  placed 
at  tne  unit  of  distance  from  it.  The  accelerating  force  exerted  at 
the  unit  of  distance  by  any  other  mass  M,  will  therefore  be  expressed 
by  the  number  of  units  in  M ;  and  since  the  attraction  decreases  in 
the  same  proportion  as  the  square  of  the  distance  increases,  the  ac- 
celerating force  exerted  by  M  at  the  distance  D  bciog  expressed  by 
A,  we  shall  have 

M 

—  a  formula,  which,  properly  understood,  expresses  the  law  of 
gravitation  in  its  highest  generality. 

3167.  Problem  of  two  bodies.  —  When  a  lesser  body  p  revolves 
in  an  elliptic  orbit  round  a  greater  mass  s,  the  place  of  s  being  the 
focus  of  the  ellipse,  it  has  been  hitherto  assumed  that  s  is  fixed, 
and  not  at  all  affected  by  p's  attraction,  the  ouly  attraction  assumed 
hypothetically  to  be  in  operation  being  that  of  s  upon  p.  Now  if 
p  be  the  distance  between  them,  and  A  the  space  through  which  p 
would  be  drawn  by  s  in  the  unit  of  time,  we  should  have,  according 
to  what  has  been  just  explained, 

_  s 

D* 

Bat,  by  the  universal  reciprocity  of  the  principle  of  gravitation,  p 
acts  upon  s  as  well  as  s  upon  p ;  and  if  the  accelerating  force  of  P 
OQ  8  be  expressed  by  a',  we  shall  have 

A'-- 

It  romains;  therefore,  to  consider  in  what  manner  this  effect  of  p's 


ASTBCUtOUY. 


iriU  modify  the  conclusioiu  ftt  wblcb  we  hkve  uriTcd 

^jppoHliion  tbnt  the  attraction  aloae  of  s  wos  ia  operatioa. 

..JeDt  that  b;  p's  attraction  s  is  dnwa  towards  P,  while  bj 

...iracllon  !■  is  drawQ  towirda  a. 

.f  B  alone  nere  supposed  to  aot,  iha  distance  o  woalil  in  the  unit 

time  ba  decreased,  supposing  the  bodies  free  to  move  towarda 

cb  other,  by  the  space  A.     But  now  that  the  action  of  p  is  adaut> 

.d,  the  disbuice  D  between  P  and  s  will  be  diniinished  bj  the  sum 

if  the  epices  through  which  B  and  p  may  be  respectively  moved  in 

I  unit  of  time,  each  by  the  attraction  of  the  other;  ao  that  wa 

luld  have  the  actual  force  of  mutual  attraction  between  the  two 

,       B  +  P 

A  + a'=  — r-. 

'''  appears,  llicicfore,  that  ihe  mutual  attraction  of  tbe  two  bodies 

;atet  than  when  S  nione  acted  in  the  proportion  of  S  to  6  +  P; 

,  consequently,  that  the  rolative  motion  of  P  round  3  will  t»« 

aely  the  same  aa  if  the  mass  of  e  were  increased  by  tbe  addi- 

to  it  of  the  mass  of  P  and  F  were  deprived  of  its  reciprocal 

'action.     Since,  then,  this  increased  attraction,  like  the  original 

siLinction  of  s,  is  one  which  increases  as  the  square  of  the  di^uiK-e 

decreases,  it  ia  aubject  to  the  aame  law  as  that  which  det«rmjaea  the 

elliptic  form  of  tbe  orbits ;  and  it  consequently  follows,  that,  subject 

to  this  reciprocal  attraction  of  the  two  bodies,  F  will  still  describe 

an  elliptic  orbit  round  s  as  a  focna;  but  the  central  attraction  being 

angmented  in  the  ratio  of  B  +  P  to  8,  the  ratio  of  the  cube  of  tbe 

mean  distance  to  the  square  of  the  periodic  time,  according  to  what 

has  been  established  (2634),  will  undergo  a  corresponding  jaoreue; 

■0  that  if  a  were  the  mean  distance,  and  ji  the  period  of  p  moving 

round  a,  subject  to  s'e  attraction  only,  and  exerting  no  attrac^oa 

of  iu  own,  and  a'  were  the  mean  distance  and  p'  the  period  when  F 

exerts  the  reciprocal  attraction  upon  6,  ws  sh&U  have 

Thna  it  appears  that  the  admission  of  p'b  reciprocal  attnction 
on  s  would  augment  the  distance  with  the  same  period,  or  diminish 
the  period  with  the  same  distance;  in  short,  at  the  same  distuce 
the  mean  motion  of  the  revolving  body  would  be  accelerated,  or  with 
the  same  mean  motion  its  distance  would  be  increased. 

To  this  extent,  and  in  this  sense  only,  a  pertarbAtion  would  be 
produced  by  tho  reciprocal  attraction  of  P  upon  b. 

316^.  Problem  of  three  bodies.  —  It  is,  therefore,  only  when  i 
third  body  intervenes  that  a  perturbing  force  is  produced  which  hu 
«ij  tendency  to  impair  tbe  elliptic  chancier  of  the  orbit;  and  tlw 


PROBLEM  OF  THRSB  BODIES.  661 

investigation  of  the  effects  of  sach  a  combioatioD  has  acquired  great 
celebrity  in  the  history  of  science,  from  the  difficulties  which  it 
presented,  and  the  importance  of  the  results  which  followed  its  solu- 
tion.     This  question  is  generally  denominated  the  problem  of 

THREE   BODIES. 

The  three  bodies  involved  in  the  problem  are,  1st,  the  central 
body  8 ;  2ndly,  the  revolving  body  p,  which,  if  undisturbed,  would 
describe  an  elliptic  orbit  round  s  as  a  focus ;  3rdly,  the  disturbing 
body  M. 

3169.  Simplified  by  the  comparative  feebleness  of  the  forces  «b- 
erted  by  the  third  body.  —  In  all  the  cases  presented  in  the  great 
phenomena  of  the  universe,  the  mass  of  s  is  incomparably  greater 
than  that  of  P,  -and  the  attraction  exerted  by  M  is  incomparably 
more  feeble  than  the  central  attraction  of  s  on  p,  either  because 
of  the  comparative  smallness  of  m's  mass,  or  because  of  its 
great  distance  from  the  attracted  body^  or  from  both  these  causes 
combined. 

3170.  Attracting  force  of  third  body  not  whoUy  disturbing. — 
But  whatever  be  the  force  exerted  by  m,  it  is  most  necessary  to 
bear  in  mind  two  things  respecting  it :  IsV,  that  its  attraction  does 
not  necessarily  produce  a  disturbing  action  at  all  upon  p's  orbit ; 
and  2ndly,  that  when  it  does,  the  disturbing  action  is  not  identical 
with  m's  attraction  upon  P,  either  in  intensity  or  direction.  It  is 
never  equal  to  it  in  intensity,  and  very  rarely  identical  with  it  in 
direction,  often  having  a  direction  immediately  opposed  to  that  of 
m's  attraction. 

8171.  Attracting  force  whicJi  would  produce  no  disturbing  effect, 
—  Such  a  force  must  be  one  which  would  cause  s  and  p  to  be  moved 
in  parallel  lines  in  the  same  direction  through  equal  spaces  in  the 
same  time.  It  is  quite  evident  that  such  a  force,  while  it  would 
transport  s  and  p  with  this  common  motion  in  a  common  direction, 
could  not  in  the  least  degree  derange  their  relative  position  or 
motion.  If  p,  previously  to  the  action  of  such  a  force,  revolved 
round  8,  for  example,  in  a  circle  with  a  uniform  velocity,  it  would 
continue  to  revolve  round  it  in  the  same  circle  with  the  same  velo- 
city when  subject  to  the  force  here  supposed ;  for  the  effect  would 
be  merely  that  the  two  bodies  with  their  circular  orbit  would  be 
transported  in  space  as  bodies  would  bo  which  might  be  supposed  to 
have  any  motion  upon  the  deck  of  a  ship  in  full  sail. 

3172.  This  would  be  the  vase  if  the  third  body  were  enormously 
distant  compared  with  the  second.  —  But  in  order  to  impart  such  a 
force  to  8  and  P,  the  body  M  must  be  at  such  a  distance  from  them 
that  the  distance  between  s  and  p  should  subtend  at  M  a  visual  angle 
•o  small  as  to  be  insensible;  since  otherwise  the  lines  of  m's  at- 
Iractiony  being  sensibly  convergent,  would  not  be  parallel.  If  the 
distanoei  however^  of  m  be  enormously  great  compared  with  the  dis- 


^D  E  and  F,  then  the  direction  of  h's  attnotion  on  s  kcd 

I  Btneibly  poralltl ;  ind  for  the  tarae  reasoD,  ihe  vsrialion 

1  intensil;  of  m'h  attraction  will  bo  likeirise  inconaideraUf, 

.d  it  Tsriee  inTcrselj'  ai  the  squnre  of  tbc  distance,  and  inoce,  bj 

EUppositioD,  Ibe  distaocu  of  p  from  s  is  quite  imignifieant  cobv 

£d  with  the  distaoce  of  H  troni  either  of  tbcm. 

3173.  Krample  of  a  forte  tappttscd  to  act  on  the  »6lar  ^tlein, 

•  Thus,  if  wc  suppose  tbat  tbe  solar  systAin  is  subject  to  tbc  iV 

ition  of  eomc  masa  or  collcotion  of  masses  among  the  Gzed  slan 

I  distance  bo  prodigious  that,  compared  witb  it,  tbe  whole  dimeo- 

its  of  tbe  BjBtem  would  ahriok  into  a  point,  such  an  attroc^oD 

uld   have   the   character  here  dcBcribed,  and   the  whole   boIu 

'Btcm  would  bo  moved  by  it  with  a  common  motion  in  a  girra 

irectioD,  all  tbe  bodies  composing  it  describing  parallel  lines  with 

■IS  game  velocity,  and  consequently  preserving,  so  far  as  Lbej  an 

ictcd  by  this  common  motion,  tbeir  relative  positions. 

^174.   Cane  in  tcAtcA  the  dUtanre  of  third  botly  it  not  compara- 

'^  great.  —  Let  us  now,  however,  s  ippoee  tbat  the  third  bodj, 

8  placed  at  sucb  a  diitancc  &oni  p  t  ad  B  tbat  it  acts  upon  Ibenii 

only  in  different  dirccUons,  bnt  wv.h  forces  of  different  inten- 

■iticB,  and  consequently  impurts    to  them   motions  which,  being 

neither  equal  nor  parallel,  must  necessarily  derange  their  relatire 

posilJonB,  and  which  consequently  give  rise  to  the  disturbing  force. 

The  qaestion  then  remains  to  be  solved,  to  determine  the  inteaeilj 

and  direction  of  the  disturbing  force,  being  given  the  intensities  and 

directions  of  this  attractions  exerted  by  the  mass  of  M  upon  p  and  s. 

Let  the  distance  ps  =  r,  ms^P,  and  MP=^z.     If  m  8  and 

8P,Jig.  837,  express  respectively  the  masses  of  the  three  bodies,  m 

ahall  have 


Id's  attraction  upon  s  =  ^ 

d's  attraction  upon  p  ^  --, 

Fig.  83r.  s's  attraction  upon  p  =  -j, 

Now  let  us  imagine  two  forces  each  equal  to  m'b  attnction  on  a, 

tbat  is,  to  -jj,  to  act  upon  p  in  opposite  direetiona;  one  in  tbedi- 

reclioD  Vm  parallel  to  h  r,  and  tbe  other  in  the  direction  immedi- 
ately opposed  to  this.  These  two  forces  being  equal,  and  immfr 
diatcly  opposed,  will  of  course  produce  no  effect  whatever  upon  P, 
Md  therefore  their  introduction  is  allowable  without  involving  *o; 
change  in  tbe  mechanioal  conditiona  of  the  system.     But  tbe  fbrct 


PROBLEM  OF  THREE  BODIES.  568 

wbich  now  acts  upon  P,  parallel  to  b  m,  and  opposite  to  p  m,  would 
impel  P  through  a  space  parallel  to  B  M  in  the  unit  of  time^  exactly 
equal  to  that  through  which  m's  attraction  upon  s  impels  s.  These 
two  forces,  therefore,  would  carry  p  and  s  in  parallel  directions 
through  equal  spaces  in  the  unit  of  time,  and  would  therefore  pro- 
duce DO  duturhing  effect  (3170).  All  the  disturbance,  therefore, 
which  can  be  produced  upon  p  by  the  forces  in  operation  must  arise 
from  the  combined  action  of  the  two  forces  acting  upon  p :  1st  m's 
Attraction  in  the  direction  P  M ;  and  2ndly,  a  force  equal  and  con- 
trary to  m's  attraction  on  s,  acting  in  the  direction  P  m  parallel  to 
M  B.  If,  therefore,  we  take  the  line  P  m  in  the  same  proportion  to 
p  M  as  the  attraction  of  M  upon  s  has  to  the  attraction  of  M  upon  p, 
and  complete  the  parallelogram  p  m  x  M,  the  diagonal  P  x  will  ex- 
press, in  intensity  and  direction,  the  resultant  of  the  forces  expressed 
by  the  sides  pm  and  pm;  in  other  words,  the  diagonal  Px  will 
ezpreas  in  quantity  and  direction  the  resultant  of  the  only  two  forces 
which  can  produce  a  disturbing  effect  upon  p.  Since  m's  attraction 
on  By  represented  by  M  x,  is  to  m's  attraction  on  P,  represented  by 
II P^  as  the  square  of  M  P  is  to  the  square  of  M  s,  it  follows  that 

8  m'  :  p  m'  : :  p  M  :  M  X ; 
or^  if  we  use  the  symbols  already  indicated,  we  shall  haTo 

Z'* :  2" ::  2f :  Mx; 
nd  eoDBequently 

MX  =  p5 (1.) 

We  shall  obtain  an  expression  for  s  x,  the  distance  of  the  point  x 
from  the  central  body  8,  by  subtracting  m  x  from  s  M ;  consequently, 

^^  —  ^—pi  —  —pr-f 

Bat  flinoe 

r^  — 2»  =  (/—z)  X  (/«  +  /z  4-  ««), 

we  flhall  haye 

sx  =  (/-z)x(l  +  ^4-^,) (2.; 

By  either  of  these  formulae  (1)  or  (2),  the  direction  of  the  dis- 
iorbing  force  can  always  be  determined.  It  is  only  necessary  to 
take,  upon  the  line  joining  the  disturbing  and  central  bodies,  a 
§fmo6  MX  or  8X|  determined  by  one  or  the  other  formulsQ  (1) 
or  (2). 

8176.  2b  determine  ike  ratio  of  the  duturbing  to  the  cciOtal 
yftfiK  ^^Far  ibigparpo§e  let 


ASTRONOMT. 
d's  Bttraction  on 


a"=  s's  attniofioQ  on  M. 
D  =  the  diRturbipg  force  Px. 
F  =  b's  attraction  on  p. 
:  shall  then,  according  to  what  has  been  explaineil  i 


By  multiplying  all  these  together  we  ehall  obtiun 

DM.* 


■(3.) 


By  this  formnla  the  ratio  of  the  disturbing  force  D  to  the  ceotnl 
.traction  ¥  can  always  be  calculated  when  the  masses  of  the  Hi- 
bing  QDil  central  bodies,  and  their  distances  from  each  other  lad 
disturbed  body,  are  known ;  for  in  euch  cases  the  line  Fz  B*n 
I  calculated  by  the  oommon  principles  of  trigonometry;  lodtt)^ 

Bequcntly  — ,  or  the  ratio  of  tbc  disturbing  to  tho  central  altrsetion, 

will  be  found. 

3176.  IToio  tlie  direction  of  the  disturbing  force  variet  wiA  A< 
relative  iliitancei  0/  the  disturbed  and  the  disturbing  from  the  «■- 
tral  body.  —  By  tlio  formula  (1),  it  b  evident  that  M  x  will  be  lea 
or  greater  than  r'  according  aa  :  ib  lesa  or  greater  than  /;  and  ihil 
if  s  be  equul  to  r',  M.c  irill  be  equal  to  M  s.  It  appears,  therefore, 
that  when  the  distance  of  »i  from  V  ia  less  than  its  distance  from  8, 
the  direction  of  the  disturbing  force  will  lie  between  M  and  b;  tliii 
when  it  is  greater  than  p'a  distance  from  s,  the  central  body  E  wilt 
lie  between  the  direction  of  tho  disturbing  force  and  M ;  and  tlial 
when  M  is  equally  distant  from  S  atfd  P,  the  disturbing  force  will  U 
directed  to  B. 

Thia  appears  also  from  the  consideration  of  the  formula  (2):  f* 
if  z^r',  83:  =  0,  which  indicates  that  the  disturbing  foroo  is  ia 
that  ease  directed  to  s;  and  according  as  r*  ia  greater  or  less  thaa 
e,  r" — r,  and  therefore  ex  ia  positive  or  negative;  showing  that  in 
the  former  case  it  b  to  be  tnken  from  b  towards  M,  and  in  the  litlci 
cose  in  the  opposite  direction. 

To  trace  tije  varying  direction  of  the  disturbing  force  during  the 
synodic  revolution  of  v  round  s,  wc  must  consider  successively  the 
OHflea  in  which  the  disturbing  body  or  its  projection  on  the  plane  of 
p's  orbit  lies  oniside  and  inside  that  orbit;  the  former  case  reprfr 
Muting  tho  disturbing  action  of  a  superior  upon  an  inferior,  and 
tbe  luttcr  that  of  an  inferior  upon  a  superior  planet.     We  aiH" 


PBOBLBH  or  THBSB  BODIKS.  6w 

ttereftire  mnader,  in  the  fint  instaoee,  the  efieotfl  only  of  that 
component  of  the  distnrbiDg  force  which  is  in  the  pUne  of  the  dio- 
taiTfaed  orbit,  utd  aftenrarda  that  of  the  tnlhogODBl  oomponent 

S177.  FlKBT  Gasx.  The  component  of  Ae  dx»hirbing  forte 
M  de  plaiie  of  the  orbit  when  A*  dulvrbinff  body  u  outiidi  Ae 
mint  of  0*t  dittwbed  bodg.  ~-L«t  8,  fig.  888,  be  the  oentnl 


' 

\ 

'"     '"'-.^■'^ 

r 

^ 

^'* 

r.  ^   P./^ 

' 

\ 

X.  _„ 

\ 

/  /7 '■ 

'''>^ 

\k'l^. 

?^''" 

/ 

1* 

Md  II  Um  diMnrbing  body ;  and  let  p„  p^  P.,  fto.  bs  th< 
tnbed  body  in  a  enooeuion  vX  its  aynodio  positiooa. 

It  ii  erideot  from  the  formalie  (I)  and  (2),  that  aa  p  n 
from  o,  taking  MieDeasiveljr  the  fynodie  pontiont  ¥,)  ^n  "^i 


ASTROS  OUT. 

reforc  Mx,  constantly  increiBCs;  aad  consequealjy  (In 

..mit  the  direction  of  the  dislurbing  furoe   meeln  ihu  I'm 

.jnslaDlIj  approacbea  a.     The   angle  B  p,  x„  obtuse  »t  linr, 

.uiaes  less  and   less   bo  at  p,  aud  P„  until   nt  a  certain   [xnnt 

it  is  reduced   to  90°.     There    tbo  direction  P|  x,  of  the  tli»- 

bing  force  ia  therefore   that  of  the  tangent   to  p'a  orbit;  ud 

I  direction  being  opposed  to  p'h  motion,  it  is  negative. 

After  passing  this  point  p„  the  angle  formed    bj  the  digtnrb- 

ig  force  with  the  direction  pm  becomes  lera  ihan  90°.     When 

■  lie  distance    PM   becomes  equal   to  8  M,  as   at  P„  the  direetinn 

the  disturbing  force,  iic«ording  to  what  has  been  shoWQ  (3I7t>)i 

MOB  through  B,  and  accordingly  x,  ooincidea  with  8. 

Aftcr  P  passes    ihia  position,  the  direction  of  the   disturbing 

■cc  passes  above  s  as  at  P|  x,,  the  angle  M  Px  increasing.     Al 

ocrtain  point  p,  this  angle  again  becomes  90° ;  and  the  direc- 

>a  Pg  X,  of  the  disturbing  force    being  at  right  angles  to   8  F, 

comes   tangential.      The   point   x  ooatiauca   to   lewde  from  b 

til  p  oniveB  at  c. 

While  P  psses  from  o  to  o  through  the  other  half  of  iU 
■jnodio  revoluljon,  the  direction  of  the  disturbing  force  under- 
goes  like  changes,  but  in  a  contrary  order,  being  tangential  at 
T,'  and  rj,  and  radiul  at  r.', — pfiinls  which  severally  correjjwnd 
to  Pe,  Pg,  and  P,  in  the  other  half-synodic  revolution. 

3178-  To  determine  the  si<fn  of  each  of  the  components  of  the 
dUturbiag  force,  in  each  euccrssive  point  of  the  orbit.  —  Com- 
mencing at  0,  m's  attraction  on  P  will  b 

on  B  will  be  — rj-  The  former  being  greater  than  the  Utter,  the  dis- 
turbing force  D,  exerted  on  r,  will  be 

M  M  /I  1  I 

eod  this  force  being  directed  from  P  to  M  will  be  opposed  (a 
the  central  attraction,  and  will  therefore  be  negative. 

While  r  passes  over  the  arc  o  P„  this  negative  radial  win- 
poncnt  gradually  diminishes,  and  the  tangential  component,  wbich 
at  o  is  nothing,  gradually  increases,  being  also  negative.  When 
f  arrives  at  r,,  the  negative  radial  eomponent  vanishes,  and  ibe 
whole  disturbing  action  consists  of  a  negative  tangential  force. 

After  passing  r,  the  radial  compoucnt  changes  its  sign  and 
becomes  positive,  the  tangential  component  continuing  to  be  negt- 
tive  and  to  diminish,  prom  p,  to  P„  as  for  example  at  P^  tbe 
negative  tangential  component  gradually  diniinishee,  and  vaoiebes 
altogether  at  p,,  while    tie  positive   radial   componeat  i 


PROBLEM  OS  THREE  BODIES.  667 

tod  at  P4,  constitates  the  whole  disturbing  forcC;  being  then 
directed  to  8. 

After  passing  Vi,  as  for  example  at  p,,  the  tangential  component 
changes  its  sign,  and  becomes  positive,  so  that  both  components 
of  the  disturbing  force  are  positive,  the  radial  component  now' de- 
creasing. 

When  p  arrives  at  v^,  the  radial  component  \:anishes,  the  whole 
disturbing  force  becoming  tangential. 

After  passing  p^  the  radial  component  again  changes  its  sign,  and 
becomes  negative,  as  at  P7,  and  increases  continually  to  c,  the  posi- 
tive tangential  component  at  the  same  time  continually  decreasing, 
and  becoming  =  0  at  c.  At  this  point  c,  therefore,  the  disturbing 
force  is  wholly  radial,  and  is  negative,  being  therefore  in  antagonism 
not  only  with  the  central  attraction  of  s,  but  with  the  immediate 
attraction  of  M,  which  is  its  cause. 

It  may  be  naturally  asked,  how  it  can  happen  that  the  attracting 
force  of  M  produces  a  disturbing  force  in  immediate  opposition  to  its 
own  direction  ?     This,  however,  is  easily  explained,     m's  attraction 

on  s  being  -7=,  and  m's  attraction  on  p  at  c  hQiuz  -—. r;,  the  for- 

mer  being  greater  than  the  latter,  we  shall  have   the  disturbing 

force 

M  M 

which  is  negative :  in  fact,  s  is  attracted  towards  m  with  a  greater 
accelerating  force  than  p,  and,  consequently,  s  and  p  are  caused  to 
separate  from  each  other  by  a  space  equal  to  the  difference  of  the 
two  attractions,  which  is  equivalent  to  a  repulsion  acting  from  s 
upon  P,  or,  what  is  the  same,  a  negative  disturbing  force. 

The  tangential  component  vanishing  at  c  changes  its  sign ;  the 
radial  component,  however,  continuing  negative.  From  0  to  Pe',  for 
example  at  p,',  therefore,  both  components  are  negative,  and  the 
radial  component  gradually  diminishes  until  p  arrives  at  Pf',  when  it 
vanishes;  the  whole  disturbing  action  being  a  negative  tangential 
force. 

After  passing  Pj',  as  for  example  at  Pg',  the  radial  component 
changing  its  sign  becomes  positive,  the  tangential  component  con- 
tinuing negative  and  decreasing  gradually  until  it  vanishes  when  p 
arrives  at  p/,  at  which  point  the  whole  disturbing  action  is  a  positive 
radial  force. 

After  passing  p/,  as  for  example  at  P3',  the  tangential  component 
again  changes  its  sign  and  becomes  positive ;  both  components  are, 
therefore,  positive  to  P2',  whore  the  radial  component  becomes  no- 
thing, and  the  whole  disturbing  action  consists  of  a  positive  tangen- 

tul  mmA. 


ASTSOKOHT.  ^^H 

pasuDg  P]',  as  for  example  at  f,',  the  ndial  componntt 

V— ngpB  ita  sign  and  becomes  negative;  the  tangeotial  compo- 
.  coDtinuiug,  hoiTcver,  poaitive,  uutU  P  arririag  at  o  compleicg 

S179.  Diagram  iVtalrating  ihete.  chamjet  of  direction*.  —  In 
be  diagram  ne  Lave  indicated  in  aQ  obvious  vaj  these  sncceMive 
ohanges  of  the  directions  of  the  components  of  the  disturbing  force, 
ibe  radial  compoacnt  being  expressed  by  r,  and  the  tangenlial  bj  I, 
ad  their  qaatity  or  value  being  expressed  bj  the  Bjrmbols  +,  — , 
Q,  vhich  follow  them.     The  diagram,  thoagh  appearing  at  fiiii 

n  complicated,  is  really  aimple  andeaailj  understood ;  and  the  indi- 

fttiona  given  will  be  found  by  tho  student  to  bo  extremely  ooave- 
jieot  and  uaefiil. 


PKOBLEM  OF  THREB  BODIES.  569 

8180.  Second  Case,  in  tcMch  the  disturbing  "body  is  within  the 
disturbed  orbit, — Let  us  now  suppose  that  M  is  within  p's  orbit,  as 
in  Jiff,  839,  and  that  its  distance  from  the  central  body  s  is  greater 
than  half  the  radius  of  p's  orbit.  Taking,  as  before,  the  disturbed 
body  p  in  a  succession  of  positions  P,,  Pg,  Ps,  P4,  &c.,  the  direction  of 
the  disturbing  forces  p,  a-,,  P2  X2,  Ps  oct,  &c,,  &c.,  is  found  in  the 
sune  manner  exactly  as  before. 

Now  it  will  be  easy  to  perceive,  by  following  the  lines  upon  the 
diagram,  how  the  direction  of  the  disturbing  force  varies  with  rela- 
tion to  M  and  8.  At  a  point  such  as  Pi  it  falls  at  or,,  between  M  and 
8;  at  P2,  where  M  P2=  M  s,  it  is  directed  to  s,  as  has  been  already 
proved.  At  this  point,  therefore,  the  disturbing  force  is  wholly 
ndial.  When  P  has  advanced  to  the  position  P4,  at  which  the 
direction  of  the  disturbing  force  is  at  right  angles  to  the  radius  vector 
8  P4,  it  is  wholly  tangential,  the  radial  force  vanishing. 

At  c,  where  m's  attraction  is  at  right  angles  to  the  tangent,  the 
tangential  force  vanishing,  the  disturbing  force  is  wholly  radial. 
In  the  semicircle  described  by  P  in  passing  from  c  to  o,  there  are 
two  points,  P4'  and  pg',  corresponding  to  the  points  P4  and  Pj,  at  the 
former  of  which  the  radial,  and  the  latter  the  tangential^  component 
vanishes. 

3181.  Clianges  of  sign  of  the  components  in  this  case.  —  It  will 
now  be  easy  to  trace  the  successive  changes  of  direction  of  each  of 
the  components  of  the  disturbing  force  to  which  p  is  subject  in  the 
SQCcessivc  positions  which  it  assumes  throughout  its  synodic  period. 

At  o^  m's  attraction  upon  p  is      '      g,  and  m's  attraction  on  s  is 

^;  and  since  both  these  attractions  are  directed  towards  M,  the 

relative  effect  upon  p  and  s  will  be  their  sum ;  and  therefore  P  and 
8  will  be  attracted  towards  each  other  by  a  disturbing  force,  the 
value  of  which  will  be, 

M        ,  M  /      1  Iv 

»=^;=^  +  7«  =  *' ^  ((7=0^  +  ?*)• 

In  this  case  it  is  obvious  that  the  disturbing  force  will  be  wholly 
ndial  and  positive,  the  tangential  force  being  nothing,  inasmuch  as 
the  direction  of  the  disturbing  force  is  at  right  angles  to  the  tangent. 
"When  the  body  leaving  o  moves  towards  P2,  the  radial  force,  being 
itill  positive,  gradually  decreases,  and  the  tangential  force  being 
inclined  below  the  radius,  will  act  against  p's  motion,  and  therefore 
be  negative.  As  P  moves  forward,  the  negative  tangential  forco 
gradually  decreases ;  and  when  p  arrives  at  Pg,  where  its  distance 
from  M  is  equal  to  that  of  8  from  Mg,  the  disturbing  force  being 
wholly  radial,  the  tangential  force  vanishes.     After  passine  this 

48* 


ASTRONOMT.  I 

ex&raple  at  r„  the  tsngendal  force,  dianging  ita  alio, 

.  |i.>aitivc  iiB  well  M  ibo  radiul  forc«,  Bud  both  fi^rora  ooDtiuu* 

positive,  the  radial  fari:e  gradually  decreasing  until  tbe  bodj 

it  at  f,.  where  ibe  radial  forc?e  vaiiisbcB,  the  diaturbiog  fore* 

iiig  tbe  direction  of  tbe  tuDgcDt,  and  being  still  positive. 

ftfter  passing  this  poiot,  tbe  radial   force,  chan^ng  ita  ^ga, 

wmes  negative  bb  at  p„  tbe  tangential  force  still  being  poNtim, 

1  grodually  decreasing.     This  latter  vanishes  when  p  arnvea  at  c, 

ere  the  whole  disturbing  force  is  radial  and  negative.     After 

!ing  this  point,  Ibe  nrgatire  tsdial  force  gradual^  diminisbet^ 

the  tangential  compoucnt,  changing  its  direction  as  at  p/,  be- 

iGS,  like  tbe  radial  component,  negative.     On  arriving  at  p,',  tha 

ial  component  having  gradually  decreaaed,  vanisbea,  the  whole 

turbing  force  being  tangential  and  negative. 

Pafsiog  this  point,  the  radial  oompoaent  changing  ile  sign  become) 

iiive  as  at  Fj,  tbe  tangential  component  being  still  Dcgative.    On 

ving  at  p,',  the  tangential  component  haviog  gradually  deereiM^ 

iiiiahcs,  and   the  whole   disturbing  force   is   radial   and   podltK-    i 

.fter  passing  this  point,  as  for  example  at  p,',  the  tangential  ecu^ 

oneni,  as  well  as  tbe  radial  component,  is  positive;  and,  in  fine, 

■  ben  tbe  body  returns  to  o,  the  tangential  component  vaiiiiibeB,  and 

the  radial  coroponcat  ia  poulivc. 

All  these  changes  are  indicated  on  the  diagnm  in  the  bum 
manner  bb  in  tbe  former  case. 

We  have  here  supposed  that  tbe  distance  of  u  from  a  is  gntta 
than  half  the  dbtanoe  O  e,  and  we  have  accordingly  seea  that  there 
are  ooly  two  certain  points  p,  and  p/  in  each  semicircle  where,  the 
distance  of  P  and  s  from  m  being  equal,  tbe  tangential  component 
TanisheB,  and  the  whole  disturbing  force  becomes  radial.  If  U  be 
supposed  gradually  to  approach  the  middle  point  of  so,  tbeae  pointt 
Vt  and  Pg'  will  assume  positions  gradually  nearer  and  nearer  to  the 
point  o ;  and  when,  in  fine,  M  coincides  with  the  middle  poiot  of 
B  0,  these  two  points  P,  and  V,  will  ooalesce  with  the  point  o.  In 
this  case  there  will  be  no  point  in  either  semicircle  at  which  (he 
disturbing  force  will  be  wholly  radial ;  but  there  will  still  be  the 
points  P,  and  p/,  at  which  it  will  be  wholly  tangential,  and  acoord- 
iogly  the  orbit  in  this  case  will  bo  divided  into  only  four  ara,  set*- 
rated  by  the  points  p,  and  p/  at  which  tbe  disturbing  forc«  is  eicla- 
sively  tangential,  and  the  points  o  and  C  at  which  it  is  exclusively 
radial. 

The  same  observations,  mutatis  mutanJt'i,  will  be  applicable  when 
M  lies  between  tbe  middle  point  of  the  radius  s  o  and  a. 

3182.  General  summary  of  the  rhanya  o/ direction  of  Ae  radial 
and  Iransverial  romponcnls  lif  the  diiturbiTit/  force  dvring  a  gr""^** 
period  of  the  disturbed  body.  — It  will  be  coavenieDt,  BB  well  for 
the  purposes  of  reference  bb  to  impress  tbem  oa  Om  memwy,  U 


PBOBLBM  or  inEBB  BODIES. 


671 


ooUeot  ben,  and  amnge  in  joztapouticm,  the  wvenl  ahangei  of 
direction  which  the  compoDcnts  of  (he  disturhing  force  in  the  plane 
of  the  dJBtnrbed  orbit  undergo  during  a  sjnodio  period  of  p.  This 
is  done  in  the  foUowiog  Ublo,  the  aigns  retaining  the  signiGoatioDB 
tUntdy  givea  to  them : — 


^^,..„,.,.,._.;..„^„.^ 

-r"'""*"- 

— 

«.«.fp. 

' 

I 

n.,..rp. 

» 

l 

4 
4 

4 
■J 

4 

* 

4 
4 
4 

AID 
TroBOIoFl 

Fnap/loPi 
Tm^p'taC 

noDictsiv 

-"■:;->'•■ 

mnPt-toP.- 
AlW 

t 

■+ 

+ 
+ 

4 

4 

■+ 

"ft 

+ 
4 

rnu  IV  lo  o 

4 

4 
4 
4 

4 

F»m  0  u  P, 
ProoP.ic 
Fnm  C  lo  PV 

3183.  Varying  fffefit  of  the  orlhogonal  component  during  a 
if»odie  reeoiutiim.  —  If  a  trianglo  be  imagined  to  f^  formed  by 
DDea  drawn  joining  (he  places  of  the  central  body  b,  the  diatnrbed 
bodjr  P,  and  the  disturbing  bod;  M,  the  plane  of  this  triangle  will 
is  general  be  inclined  at  some  angle  to  the  plane  of  p'b  orbit.  The 
firection  of  the  disturbing  force,  according  to  what  has  been  shown, 
vill  be  that  of  a  line  dniwn  from  p  in  the  pkne  of  this  triangle, 
■eeting  the  line  m  s  either  between  m  and  e,  at  s,  or  bejond  s, 
■eeording  to  the  relative  magnitude  of  m  s  and  up.  If  u p  be  less 
tban  H  B,  then  the  direction  of  tbo  disturbing  force  will  meet  M  a 
between  H  and  s ;  if  m  r  =  m  r,  ita  direction  nil]  be  that  of  the  line 
Pb;  and,  in  fine,  if  mf  bo  greater  than  MS,  itsdirectioD  will  meet 
the  prolongation  of  m  b  bcjond  s. 

On  considering  these  Tarious  directions  of  the  disturbing  force,  it 
will  be  evident  that  when  h  p  is  less  than  m  s  its  direction  will  lie 
on  the  same  side  of  the  plane  of  p'«  orbit  with  tbo  disturbing  tiody 
Jf,  and  the  orthogonal  coniponent  being  thcrcforo  directed  towardg 
llut  side,  will  have  a  tendency  to  bring  the  piano  of  the  disturbed 
trbit  nearer  to  M. 

When  u  p  is  greater  than  M  8,  on  the  contrary,  the  direction  of 
the  disturbing  force  meeting  the  prolongation  of  the  line  U  s  beyond 
»,  Boot  lie  OD  the  nde  of  the  plane  of  p's  orbil^  differeot  from  that 


ASTROKOMT. 

isplued;  and  tLe  orthngonnl  eompoDcnt  being  io  lint 
._d  to  the  same  eiJe,  would  Lave  a  letiJcnoj  10  duflt?Ct  (ba 
.1  ^B  orbit /i^«i  M. 

the  furmer  cii9i>,  the  orthAg^nal  cnrnpHinent  woald  decrcsH, 
io   tLe  \iiUer  it  would  increase  tbo   augle  at  wbicli  the  line 
is  iuoliLcd  to  tbo  plnne  of  p'b  orbit. 
fVhcn   M  P  =  M  8,   the   diBlurbing  force,    being  directed  from 
'-  s,  would   act   in    the  plane  of  p'b  orbit,  and   would  watt- 
llj-  hare  no  eH'ect  in  chou^ng  that  plane. 
M  bo   Bitoate  anywhere   in    the   pkne  of  p's   orbit,  which 
w   the   case  whenever  it   passes   through   the   nodes  of  ila 
and  p's  orbit,  the  three  bodies  being  in  ibo  same  plane,  the 
anal  component  of  the  disturbing  force  will  be  nothing. 
13  it  appears  that  the  orthogonal  component  will  vnnbh  at 
1  paasugc  of   M  through    p's  nodes;  and   also  at  each  of  tiii 
ts,  if  an;  suob  there  be,  at  which  M  and  P  are  equally  di»> 

184.  PrriO'Jic  atiil  trc'u/iir  pertiirbmions.  —  From  wbat  hu 
a  espluined  in  the  present  nnd  the  prcceilini;  cLnpter,  it 
ears  that  tlie  geveral  eomponenta  of  tli'  ■'.',-'  i:'  I'-.-o  priK 

a  contrary  effeola  on  the  eleraenle  nf  il  ■  wbca 

they  have  contrary  signs,   and  th:»t  they    ..  t  to 

a  succession  of  changes  of  sign  during  the  pjnodic  revolution  of 
the  dislurbpd  and  the  disturbing  bodies.  The  several  elements 
of  the  disturbed  orbit  will  therefore  be  in  a  continual  state  of 
oscillation,  from  these  nlternate  actions  of  the  compoucnts  of  the 
disiurbiog  force  in  one  direction  and  llie  other. 

If,  in  all  cases,  ihc  sum  of  tlie  eficcis  produced  by  the  action  ' 
of  each  component  while  positive  were  Cf|ual  to  the  sum  of  ill 
effects  while  negative,  the  elcmenU  would  oscillato  roand  a 
fixed  and  invariable  sUte.  They  would  pass  tbrongh  all  thur 
variations  when  the  disturbed  and  disturbing  bodies  would  have 
assumed  all  their  possible  varieties  of  position  with  relation  to 
the  central  body,  and  they  would  then  recommence  the  same  goc* 
cession  of  changes. 

The  mean  values  of  all  the  clemenla  of  the  disturbed  orbit 
would  in  this  case  bo  constant.  Thus  the  major  axis  would 
altcrnaU'ly  iiicrcnse  and  decrea.^  bcttrcen  fixed  limits,  but  its 
menu  value  would  be  always  the  same.  lu  like  manner,  the 
eccentricity  and  inclination  would  alternately  increase  and  decrease, 
having  a  constant  mean  value;  and  the  like  would  be  true  of 
the  other  eleuicals. 

llut  if,  on  the  contrary,  it  were  found,  on  comporing  the  sum 
of  the  posilivo  wiih  «lie  sum  of  the  negative  efiects  of  any  of 
the  con:poncnts,  that  the  sum  of  all  the  effects  while  positive 
were  not  exactly  ci]uA  to  the  sum  of  the  effects  while  nega^Tc, 


PROBLBM  OF  THKBS  BODIES.  678 

Iwt  tbftt  a  certain  minnte  difference  or  rosidnal  phenomenon 
alwaja  remains  nnefiaced,  it  is  evident  that  this  rcsidoum,  how- 
CTer  small  it  may  be,  mast  accumulate  until  at  length  it  will 
attain  a  magnitude  which  will  tell  in  a  very  sensible  manner, 
and,  if  a  stall  longer  series  of  periods  be  waited  for,  would  totally 
ebang^  the  elements  of  the  disturbed  orbit. 

It  must  be  observed  that  the  interval  which  leaves  this  rcsi- 
donm  uncompensated,  is  one  daring  which  the  disturbed  and 
disturbing  bodies  pass  through  all  possible  varieties  of  confiffu- 
ration,  taking  into  the  account  not  merely  their  directions  with 
relation  to  the  central  body,  but  their  positions  with  relation  to 
the  apsides  of  their  respective  orbits.  It  is  only  after  assuming 
all  the  varieties  of  relative  position  and  distance,  arising  as  weU 
from  the  relative  changes  of  direction  of  M  and  p  as  viewed 
from  8,  as  from  their  changes  of  position  in  their  respective 
orbits  with  relation  to  their  points  of  perihelion  and  aphelion, 
that  the  components  of  the  disturbing  force  complete  their  round 
of  effects,  and  recommence  another  series  of  actions.  It  is  the 
randnal  phenomena  which  remain  uneffaced  after  this  interval, 
which,  accumulating  for  a  long  succession  of  ages,  produce  the 
ultimate  changes  of  the  elements  now  referred  to. 

It  appears,  therefore,  that  there  are  two  extremely  different 
daaaes  of  inequalities  as  they  are  called,  which  arise  from 
the  operation  of  the  disturbing  force. 

let  Those  which  vary  with  and  depend  on  the  configuration 
of  the  disturbed  and  disturbing  bodies  with  relation  to  the  oen- 
tnl  body,  taking  into  the  account  not  only  their  relative  direo* 
tiooa  as  seen  from  the  central  body,  and  their  varying  distance 
from  each  other,  but  also  their  varying  distances  from  the  oen- 
tnl  body,  owing  to  the  elliptic  form  of  their  orbits. 

These  inequalities  necessarily  pass  through  all  their  phases, 
complete  their  periods,  and  recommence  the  same  suooession  of 
changes,  when  the  disturbed  and  disturbing  bodies  have  passed 
throueh  all  their  possible  varieties  of  configuration;  and,  conse 
qnently,  their  several  periods  must  bo  less  than  the  interval 
within  which  this  succession  of  configurations  is  completed. 

These  are  denominated  pbriodio  inequalities. 

2nd.  Those  which  arise  from  the  accumulation  of  the  residua] 
phenomena  already  mentioned,  as  being  in  some  cases  uneztin- 
goiahed  by  the  opposite  effects  of  the  positive  and  negative  compo- 
nenta  of  the  disturbing  force,  acting  during  that  interval  of  time 
within  which  the  bodies  assume  all  their  possible  varieties  of  oon- 
fignration.  It  will  appear  hereafter  that  these  residual  phenomena 
tre  generally  of  very  small  value, — so  small  as  to  be  rarely  sensible 
lo  ODservation  until  they  have  been  allowed  to  accumulate  for  a  long 
mccieaaion  of  periods. 


i  It  Es,  thon'fore,  evidoDt  thftt  these  latt«r  iitFtjmliiios  are  inonnpt- 

jWy  (Jowpr  iu  tlieir  ppngreswive  developmetit  thsn  thn  f  )rm«r,  and 

KnuoquRatl;  the  intcn'»l«  of  time  niibio  wliich  they  romjilfir  ihrir 

■^•ng^s  MV  prop"itionally  RUtro   prolraete<l.      I'hF.ie  havr,  unrd- 

Plseiyi  liveu  denomioBted  secvi^R  iNEQCAUTiEa. 

J      Til  must  not,  however,  be  imagincil  that  these  are  less  wally  po}. 

odio  tlian  the  former.     The  only  differeocG  in  (liat  KapMt  benrm 

the  lito  clauses  of  pheDomena  m  in  the  Icneth  of  tiieir  pfriodi. 

Wbere  tbfiKo  of  the  former  mny  be  expressad  %  ycan^  t!uM  of  & 

latter  will  be  eiprosscd  by  centaries. 


K  CHAP.  XXL 

r  LUNAR    TBEOBT. 

-  8185.  T/unar  ilieorg  on  important  fate  of  the  prfifilan  of  Am 
lo(}its.  —  The  moat  remarkable  example,  and  in  manj  respccUtbt 
inOEt  interesting,  of  the  application  of  the  principles  cxpliincd  in 
the  last  cbnpler  for  the  BOlution  of  the  problem  of  three  boJirs,  ii 
nnqaestionnbly  that  which  is  presented  by  the  lunar  theory,  in  niuth 
the  central  bndy  s  is  the  earth,  the  disturbed  body  p  the  niooo,  am! 
tho  disturbing  body  M  the  Eun. 

This  applieation  of  the  theory  of  perturbation  is  loterestirg,  not 
BO  much  because  of  the  physical  iniporlance  of  the  moon,  as  be- 
cause, by  the  proximity  of  tUat  body,  porturbationa  prwioced 
upon  it  become  conspicuously  observable,  which  in  any  other  boJj 
of  the  solar  system  would  be  iaappreciabte  by  reosoa  of  its  remote- 
ness. 

The  lunar  perturbations,  morcorer,  present  another  fcalnre  of 
interest,  as  compared  with  those  of  the  plancUi,  by  reason  of  tbi 
comparative  shortness  of  their  cycles, — phenomena,  which,  in  the 
case  of  tlie  planets,  require  a  succession  of  ages  to  complete  thdr 
periodB,  passing,  in  the  case  of  the  moon,  through  all  their  phtfei, 
«nd  returning  upon  themselves,  iu  the  course  of  a  few  years. 

3186.  /(  *u/«rfi"ra  ffri/iiiiff  pmof  of  the  truA  of  the  thwryof 
graiiiUition.  —  But  tran  seen  dan  t!y  the  moat  interesting  and  import- 
sat  circumstance  atteeding  the  lunar  theory  is,  the  remarkable  en- 
dence  it  has  afforded  in  support  of  the  theory  of  gravitation.  Tha 
perturbniions  of  the  lunar  motions  being,  for  tho  most  part,  of  eoa- 
sidernble  miigniluJo,  and  recurring  after  ,'li'irt  ii::'  n  il-,  ii-.r' 
observed,  and  tlie  laws  of  many  of  them  ascertained,  at  a  very  earij 
epoch  in  the  pmgteaa  of  astroonmical  science,  and  long  before  the 
discovery  of  gravilatitm  \ibA  4\»i;\o«ei  xXnivt  ■^■^«otJi.  ia.<a5e%.  Several 
«f  these  phenomena  were  csv^niwei^i^  *tfi««i!iiw«tt»aisSu«  -issas. 


LUNAR  THEORT 


675 


theory,  some  perfectly,  others  imperfectly;  and  those  which  remained 
unexplained  or  imperfectly  explained  by  him  have  since  been  fully 
and  satisfactorily  accounted  for,  upon  the  principles  which  form  the 
foandation  of  his  physical  theory. 

8187.  The  9un  alone  sensibly  disturhs  the  moon, — The  only  body 
in  the  system,  which  produces  a  sensible  disturbing  effect  upon  the 
moon,  is  the  sun ;  for  although  several  of  the  planets  when  in  oppo- 
sitioQ  or  inferior  conjunction,  come  within  less  distances  of  the 
earth,  their  masses  are  too  inconsiderable  to  produce  any  sensible 
disturbing  effect  upon  the  moon's  motion.  The  mass  of  the  sun, 
on  the  contrary,  is  comparatively  so  prodigious  that,  although  the 
radios  of  the  moon's  orbit  bears  so  small  a  ratio  to  the  sun's  dis- 
tance, and  although  lines  drawn  from  the  sun  to  any  part  of  that 
orbit  may  be  regarded  as  sensibly  parallel,  the  difference  between 
the  forces  exerted  by  the  sun  upon  the  moon  and  earth,  so  far  from 
being  insensible,  produces  on  the  contrary  those  perturbations  which 

it  ^  our  purpose  in  the  present 
chapter  to  explain. 

3188.  Lines  of  syzygy  and 
quadrature,  —  Let  8,  Jig,  840,  re- 
present the  place  of  the  earth; 
p„  P2,  P3,  &c.,  representing  succes- 
sive positions  of  the  moon  in  its 
orbit,  which,  for  tho  present,  we 
shall  consider  to  be  circular.  Let 
0  o  be  that  diameter  of  tho  lunar 
orbit  which  is  directed  to  the  sun, 
0  being  the  point  of  conjunction, 
and  0  the  point  of  opposition.  Let 
r4  s  p'4  be  drawn  through  s  at 
If.  right  angles  to  00;  the  points  P4 
p'4  will  then  be  the  points  of  quad- 
rature. 

The  line  O  0  is  called  the  line 
OF  SYZYQIES ;  and  the  line  P4  p'4 

the  LINE  OF  QUADRATURES. 

We  shall,  for  the  present,  con- 
sider only  that  component  of  the 
sun's  disturbing  force  which  is  in 
the  plane  of  the  moon's  orbit ;  and 
shall,  therefore,  speak  of  the  sun  as 
if  it  were  placed  in  the  prolongation 
of  tho  line  sc. 

The   moon  being  supposed   to 

move  synodically  in  the  direction 

jng.  sio.  c  Pi  P^  &c.;  wo  shall  distiu^iftVk 


n  qusdRint,  p,  o  as  tbn  eeconi,  O  T*,  m  th«  Utird,  laA 

„ardi  (juadrant  of  the  syimdic  revolution. 

8,    Dirrrtion  of  the  tUiturhiny  /arei:  of  the  tun. If  UttOp- 

.  Ja»  ntooD  at  aoy  point,  Euch  13  r,  in  tbc  first  qoadmit,  ud 
1  drav  F|  ^1  at  right  angles  to  s  c,  the  direction  of  Uic  nii'i 
rlnog  force  acting  at  P,  will  be  fcnnd  by  takiog  s  2-,,  =8  ey„ 
Iraffing  I-,  z,  irhiob  will  then  be  the  direetioD  ^  the  distnrlmig 

la  this,  we  have  to  obserTe  that  P,  and  y,  may  be  oooM- 
ually  dtiitant  from  the  sun.     liet  their  oDiamoD  diftune 
d  by  >,  and  lot  tbe  bod's  dial&aoe  from  e  be  «xpnMei 
uoon'e  distance  by  r. 
O  by  the  formula  [2]  (3174)  bave 

J       J 
03^1=  sy,  XCI  +  p  +  ^^>• 

But  Btncc  tbe  mnon'a  dialanco  bears  an  insigniScant  proportiM 
that  of  tbe  sun,  being  only  a  400th  part  of  itj  wc  may  ooBOte 

=  I'y  and  Donsequeatly  ^  =  I,  and  therefore  we  shall  hare 

Sr,  =  3sy^. 

Whatever,  therefore,  may  be  the  synoilic  position  of  the  moon, 
tiiis  supplies  an  ea-iy  and  simple  method  of  determining  the  dii«o- 
tioa  of  the  sun's  disturbing  foroe  upon  it.  Thus,  if  the  mooD 
be  at  Pi,  draw  P|  y,  at  right  angles  to  8  c,  and  let  6  3-(=  Ssji 
■od  the  line  Ti  ^t  "'^  be  the  direction  of  tbe  disturbing  fone 
at  F,. 

It  is  evident  that,  as  the  moon  approaches  its  western  qnaJni- 
ture,  the  distance  of  the  perpendicular  P,yn  P,yj,  &c.,  from  8  Bon- 
atkotly  diminishes ;  and,  therefore,  the  distance  ^x^,  &Xt,  &^i  wbicb 
is  always  three  times  that  distance,  also  constantly  diminishes,  M 
that  tbe  point  where  the  direction  of  the  disturbing  force  meets  the  ' 
line  of  syzygies,  constantly  approaches  s,  as  the  moon  approacba 
Ft;  and  when  the  moon  arrives  at  P„  the  perpendicular  on  oc 
puses  through  s.  When  tbe  mooa  arrives  at  ltd  wcEtcm  (jnaJra- 
turc,  the  disturbing  force  of  the  enu.  is  therefore  directed  aloog  the 
line  p,  8  to  tbe  earth.  After  the  moon  passes  tbe  weatcra  (jnadta- 
ture,  and  moves  through  tbe  second  quadrant,  the  perpendiculars 
^t  y'»  ^1  y^r  ^"1  y'ti  &e.,  meet  the  line  of  syzjgics  above  s  ;  and  as 
the  moon  advances  the  distance  of  j/„!/i,!/„  &o.,  from  8, 
Btantly  increases.  Now,  the  direction  of  the  disturbing  force  being 
etill  determined  by  tbe  same  principle,  it  will  in  all  cases  meet  the 
line  of  syzygies  at  a  point  above  s,  at  a  distance  from  s  always  three 
times  the  diataDce,  By*,,  b;/,,  sy„  &c.     Thus,  when  the  t 


LUNAR  THEORT.  677 

likoi  BocoeBriTiely  (be  positions  F^s,  1^21  ^u  ^-9  ^^  distnrluDg  foroe 
takes  Bocoessively  the  directions  i^,  x'^  P'a  ^^y  P^i  x^i,  fto. 

Without  panning  these  considerations  fnrther,  it  will  be  eyident 
ika%f  in  moving  through  the  first  quadrant,  the  direction  of  the  dis- 
tnrbinff  force  intersects  the  line  of  syijgies  below  s ;  and  in  moving 
thioo^  the  second  quadrant^  intersects  it  above  s ;  and  the  same 
VBuoning  will  show  that,  in  moving  through  the  fourth  quadrant, 
Ibe  disturbing  force  intersects  the  line  of  sjzjgies  below  s  in  the 
same  manner  as  in  the  first  quadrant ;  and  in  moving  through  the 
third  quadrant,  it  intersects  it  above  s  in  the  same  manner  as  in 
tlie  lecond  quadrant ;  and  it  is  further  evident,  that  at  corresponding 
poinls  in  the  third  and  fourth  quadrants  the  direction  of  the  dis- 
turbing force  intersects  the  line  of  syzvgies  at  the  same  points  as  in 
the  second  and  first  quadrants. 

8190.  Points  where  (he  dvsturhing  force  %$  te?u>lly  radial  and 
wholly  tangential  —  From  what  has  been  explained  it  appearSy 
that  the  disturbing  force  at  quadratures  being  directed  to  the 
earth,  is  wholly  radial  and  positive. 

It  is  easy  to  show  that  at  syzygics  it  is  also  wholly  radial| 
but  negative ;  for  at  this  place  the  sun's  attraction  is  obviously 
at  right  angles  to  the  tangents  of  the  moon's  orbit  at  0  and  o, 
and  as  the  whole  attraction  is  thus  perpendicular  to  the  tangent, 
and  the  disturbing  force  is  equal  to  the  difference  of  the  attraot- 
iDg  force  exerted  oy  the  sun  upon  the  moon  and  upon  the  earth, 
it  18  clear  that  disturbing  force  is  also  perpendicular  to  the  tan- 
geot,  and  therefore  radial,  since  the  moon's  orbit  is  here  assumed 
to  be  sensibly  circular. 

To  determine  the  points  at  which  the  disturbing  force  of  the 
•nn  assumes  the  direction  of  a  tangent  to  the  moon's  orbit,  let 
y^  be  that  point  in  the  first  quadrant  We  shall  then  have  the 
ngle  8  Pg  0^  =  90^,  and  consequently 

■ad  oonsequently, 


—  =  tan.P280  =  \/^- 


Byg 

And  it  appears  by  the  trigonometrical  tables  that  the    angle 


whose  tangent  is   y /  2  is  fA?  44'  7". 


Thus  it  follows  that  the  synodic  position  of  the  moon  in  the 
int  qoadnuit  at  which  the  cUstnrbing  force  is  wholly  tuifgmtial^ 
m.  49 


IBV  ASTROKOMT. 

n^iig  in  tbe  direction  p,x,  against  tbc  idooq'b  modoD,  !■  kt  (bi 

diatance  of  5-1°  4-1'  7"  from  couj  unction.* 

It  will  fullow  iu  the  same  maiiQBr,  ihat  the  distarbing  {area 
in  tba  second  quadrant  nlll  be  whuUj  tangential  at  a  poiDt  ^, 
whose  distance  from  opposilion  o  is  bi"  44'  7";  aod  in  Ilk* 
manner,  it  will  be  tangential  at  points  in  the  third  and  fint 
quadrants  which  are  at  tike  distances  from  oppoeition  and  cod- 
j  unction. 

Thus  it  appears  that  in  the  synodic  orbit  of  the  moon  then 
are  four  points,  viz,,  oppoeition,  conjuaclion,  and  qnadratures,  at 
which  the  sun's  disturbing  force  is  wholly  radial,  betog  directed 
from  the  earth,  and  therefore  negative  at  opposition  and  eon- 
junction,  and  directed  towards  it,  and  therefore  posilire  at  quad' 
rntures;  and  fuur  other  pointa  at  dislaDcea  of  5-1°  W  7"  n 
either  side  of  oppoailian  and  conjunction,  at  which  it  is  whullj 
tangential,  being  in  the  directlun  of  the  moon's  motion  and  then- 
fore  positive  in  the  second  and  fourth  qnadranls,  and  conCraij 
to  the  moon's  motion  and  therefore  negative  ia  the  first  aod  I 
third  quadrants.  j 

3191.   Intetmtit*  of  the    disturbing  /ortet  at    ly^fffiet  and  1 
qaadraturet.  —  Let   the  intensity  of  the  disturbing  force    at  coa- 
junotion  be  d',  at  opposition  d",  aud  at  cjuadratures  D. 

If  we  take  the  radius  of  the  moon'a  orbit  as  tlie  nni^  the 
distance  of  the  sun  from  the  moon  in  quadrature  will  be  400, 
in  GODJuDctlon  399,  and  in  apposition  401,  and  the  bdd'i  at- 
traction upon   the  moon  in  these  three  poationa  will  be  ^^ 

■j-gftj,  and   ■        ;  and  since  the  disturbing  force  at  oonjonctioa 

ind  opposition  are  the  differenoea  between  the  whole  aUncliau 
exerted  by  the  sun  upon  the  moon  and  upon  the  earth,  we  shall 
have, 

°'  =  "<(l55'-450.)  =  ''"™"""'5'*'<' 
''■■=»'<(w-45l>)=»"»''»»'"'«l»x'- 

The  disturbing  force  D  exerted  at  p,  will  be  to  the  sun'f 
entire  attraction  as  p,  s  is  to  the  distance  of  the  earth  from 
the  flun,  or,  what  is  the  same,  aa  r  to  /,  and  consequently  w« 
■hall  have, 

*  Sir  John  Herschel  pves  for  tliia  angle  the  nine  M"  IV.  vUok  b 
Mrtaiid;  enooMus.— Bm  (h^tUnu  of  Aatrononj,  pap  4M,  edit.  lUH 


LUNAR  THEORY. 


679 


Br  r  1 


400*^ 


isequently, 


D  =  00000000156  X  8. 


pears  from  these  yalaes  of  d',  d",  aod  D,  that  the  three  radial 
Qg  forces  exerted  bj  the  sun  upon  the  moon  at  coDJactioii| 
yif  and  quadrature,  are  in  the  following  proportion, 

d':d":d::63:62:31-2. 

it  appears  that  the  disturbing  force  at  conjunction  is  greater 
opposition  in  the  proportion  of  68  to  62,  and  that  the  negative 
Qg  force  at  sjzjgies  is  about  double  the  positive  disturbing 
quadratures. 

ber  words,  it  appears  that  the  disturbing  force  of  the  sun  acts 

the  moon's  attraction  upon  the  earth  at  conjunction  more 

cally  than  at  opposition,  in  the  proportion  of  63  to  62 ;  and 

both  cases,  its  action  in  diminishing  the  earth's  attraction 

on  the  moon  is  twice  as  great  as  its  ac- 
tion in  increasing  the  emi's  attraction 
upon  it  in  quadratures. 

8192.   The  sun's  disturbing  force  at 

rl  angles  with  syzygy  varies  in  the 
*i  ratio  of  the  moon's  distance  from 
the  earth,  —  It  is  easy  to  show  that  if 
the  moon's  distance  from  the  earth  be 
supposed  to  vary,  whik  the  sun's  dis- 
tance remains  the  same,  and  still  bears 
a  high  ratio  to  the  moon's  distance,  the 
sun's  disturbing  force  will  vary  in  the 
direct  ratio  of  the  moon's  distance  at 
equal  angular  distances  from  syzygy. 

Let  p  and  y^^fig>  841,  represent  the 
moon  at  two  different  distances,  s  P,  and 
8  p',  from  the  earth.  To  find  the  lines 
representing  the  disturbing  force  at  p 
and  p'  draw  py  and  p'y  at  right  angles 
to  the  line  drawn  from  8  to  tho  sun,  and 
let  8  X  =:  3  sy,  and  8  a/  =  3  8y,  and 
draw  the  lines  p  x  and  ^  a/.  Theso  two 
lines  will  then  represent  in  quantity 
and  direction  the  disturbing  forces  of  the 
Q  the  moon  at  P  and  p'. 

t  is  evident,  since  sx  is  three  times  sy,  and  so/  is  three 
fj  that  the  lines  Px  and  p'x'  are  parallel,  and  are  therefore 
)nal  to  8  p  and  8  p';  that  is,  the  disturbin^^  foT^i^  ^\»^  v^\ 


Fig.  841. 


580  ASTBOBOMT. 

p  19  proportional  to  tte  distancM  ot  the  moon  from  the  euth  »t 
these  two  points. 

It  will  be  Been  hereafter  that  this  principle  is  attended  with  sojoe 
important  consequences  in  the  lunar  theory. 

3193.  Analyta  of  the  varialtom  of  tign  of  the  eompotiettit 
of  the  disturbing  force  during  a  ij/nodic  period.  —  From  Wut  hu 
been  explained  in  the  preceding  pBragmphs,  it  will  be  easj  to  tnn 
the  BuccCBsive  changes  of  direction  and  sign  of  the  radial  and  tan- 
gential components  of  the  disturbing  force  of  the  son,  during  u 
entire  lunBtion  or  synodic  period  of  the  moon. 

Let  Cjfig.  842,  represent  ihe  position  of  the  moon  in  conjunetiaB; 
O,  ite  position  in  opposition ;  F„  it^  position  in  western,  and  ?*«  io 
eastern  quadrature. 


Let  P,  be  ila  pof-iiicm  in  the  first  quiidmnt  when  tic  radial  com- 
ponent  vanishes,  and  tlic  whulo  disturbing  force  is  tangential,  this 
point  being  at  the  distance  nf  54°  44'  7"  from  c.  Let  r,.  P„  and 
1^1  be  the  corrc'pi^niiiTig  p.-iuls  in  the  pc.'PqJ,  (Lini,  and  fount 
quadrants. 


LCSAR  THEORY.  681 

Fron  wli&t  fau  been  Already  explained  it  tppein  that,  tLe  dis- 
torbins  force  >t  c  beiae  at  right  anglea  to  the  tangent,  tho  tao- 
gantiar component  it  nothing;  and  since,  through  the  first  quadrant 
0  P|,  tho  direction  of  the  disturbing  force  fornii  an  obtuse  angle  with 
the  di^^etion  of  the  noon's  motion,  its  tangential  componcDt  will  bo 
in  a  diredioQ  contrary  to  the  moon's  motion,  and  It  will  tfaereforo 
)m  negative.  This  compmeut  TaniBheB  at  p„  where  the  whole  dii- 
tarluDg  force  becomea  ndial,  and  therefore  at  right  anglea  to  the 
hogent,  and  after  pasaing  p„  the  direction  of  tho  disturbing  force 
broing  ao  acute  angle  with  the  direction  of  the  moon'R  motion,  the 
hngmtial  component  is  in  the  direction  of  the  moon's  motion,  and 
Ibarefore  pow^ve;  and  continues  to  be  positive  throughout  the 
neodd  quadrant  until  the  moou  arrives  at  npposition  o,  where  the 
diitarbing  force  again  becomes  radial,  and  being  at  right  angles  to 
tbe  tangent,  the  tangential  component  vsnifhcs.  After  pawing  o, 
the  distorfaing  force  forma  an  obtuse  angle  with  tbe  direction  of  the 
mnon'e  motion,  and  ita  tangential  component  is  therefore  contrary 
in  direction  to  tha  motion  of  the  moon,  and  consequently  negative. 

It  coDiinues  nrgarive  through  the  third  quadrant  until,  the  moon 
WTiiiog  at  Pi,  tbe  direction  of  tbe  di«tnrbing  force  becomes  radial 
•ad  at  tight  angles  b>  tho  tangent,  and  the  tangential  component 
■gun  vaoiabes.  AUn  passing  this  point  the  disturbing  foroe  forma 
U  aeule  angle  with  tbe  direc^on  of  the  moon's  motioo,  and  its  tas- 
ntntial  oompooent  therefore  being  in  the  direction  of  such  motion  is 

rritiTe,  and  continue  pontiTe  throughout  the  fourth  quadrant  until 
ranialtaa  at  conjun«tion. 

Tbus  il  appears,  tiiat  the  tangential  oomponent  is  negative  in  the 
ItsI  and  thinl  qundranta,  throughout  which  It  has  therefore  a  ten- 
dency to  retard  the  moon's  motion;  and  that  it  is  positive  in  the 
woood  and  fourth  quadrants,  throoghont  which  therefore  it  boa  a 
tendency  to  aucelcrot^  the  moon's  motion. 

Let  08  DOW  trace  the  changes  of  direction  and  aign,  which  aSect 
die  ndial  component  of  the  disturbing  force. 

It  liaa  been  already  shown  that  at  coDJnnction  the  radial  compo- 
iMMiiik  ncflMtirn,  and  therefore  directed  from  the  earth.  This  cir- 
aiuBilMMa  atiMS  from  the  fact  that  the  sun'a  attraction  on  the  moon 
at  C,  h  poler  llian  ita  attraction  upon  tbe  earth  at  b,  and  the  di»- 
turluBg  mca  being  the  exceas  of  the  attraction  towards  the  sun  at 
C,  above  the  attraction  towards  the  sun  at  s,  ia  directed  from  e.  Aa 
tbe  moon  moves  from  c  to  p,  Uie  direction  of  the  disturbing  force 
liM  oataide  tho  tangent,  and  consequently  its  radial  component  ia 
directed  from  s  ano  is  therefore  negative.  It  gradually  decreases 
trom  0  to  Pi,  because  tbe  angle  under  the  disturbing  force  and  the 
tragent  gradually  decreases.  This  angle  vanishes  at  P„  where  tho 
disturbiug  force  coincides  with  tbe  tangent,  and  where  therefore  ita 
ndial  cowpateot  nniabcB.  Thus  it  appeara  t\ial  \:ki«  tw!Cv(\  wn&i- 
49* 


582  ASTROKOMT. 

poneDt  which  b  negative  at  c,  contionally  decreaaea  from  c  to  P|  ' 
where  it  i8==0. 

After  passing  Pi,  the  direction  of  the  disturbing  force  fallixiff 
within  the  tangent,  its  radial  component  is  directed  towards  s,  and 
18  therefore  posiUvc;  and  the  angle  which  the  direction  of  the 
disturbing  force  makes  with  the  the  tangent,  increaaing  from  P|  to 
P„  the  radial  component  continually  increases  untal  at  Pg  the  di- 
rection of  the  disturbing  force  being  at  risht  angles  to  the  tangent, 
the  whole  disturbing  force  becomes  radiu.  A&r  passing  P|,  the 
angle  under  the  direction  of  the  disturbing  force  and  the  tangent 
again  becomes  acute,  and  the  radial  component  being  poaitiTe, 
decreases  and  continues  to  decrease  until  at  p,  the  angle  under  the 
direction  of  the  disturbing  force  and  the  tangent  vanishes,  and  there 
accordingly  the  radial  component  also  vanishes,  the  whole  disturbing 
force  being  tangential. 

After  passing  p„  the  direction  of  the  disturbing  force  falling  oat- 
aide  the  tangent,  the  radial  component  is  again  directed  from  the 
centre,  and  is  therefore  negative ;  and  the  angle  under  the  diaturbiog 
force  and  the  tangent  continually  decreases  until  the  moon  arrives  it 
opposition  o,  where  it  becomes  a  right  angle,  and  the  whole  dis- 
turbing force  becoming  radial,  is  directed  from  s,  and  is  therefore 
negative.  After  passing  opposition,  the  angle  under  the  disturbing 
force  and  tangent  again  becomes  acute  and  continually  diminishes, 
and  therefore  the  radial  component  continually  decreases,  being  still 
negative  until  at  p^'  the  angle  under  the  direction  of  the  disturbing 
force  and  tangent  vanishes,  the  whole  disturbing  force  becoming 
tangential,  and  the  radial  component  being  therefore  =  0.  After 
passing  p'3,  the  direction  of  the  disturbing  force  again  falls  within 
the  tangent,  and  from  i*',  to  p'j  it  forms  an  acute  angle  with  the 
tangent  which  continually  increases  until  at  p'^  it  becomes  a  right 
angle.  The  radial  couijjuncnt  thtToforo,  from  l^'j  to  p'g,  is  positive 
and  continually  iucroascs  until  at  p'^  the  whole  disturbing  force  is 
radial.  After  passing  p'2,  the  direction  of  the  disturbing  force  again 
forms  an  acute  angle  with  the  tangent,  and  the  radial  eomponcnt  is 
therefore  still  positive;  and  as  this  angle  continually  decreases,  the 
radial  component  decreases  until  the  moon  arriving  at  p'„  the  dis- 
turbing force  takes  the  direction  of  the  tangent,  and  the  radial  com- 
ponent is  =  0.  After  passing  i*'„  the  direction  of  the  disturbing 
force  lying  outside  the  tangent,  the  radial  component  is  directed 
from  the  earth,  and  is  therefore  negative,  and  the  angle  formed  by 
the  direction  of  the  disturbing  force  with  the  tangent  continually 
increasing,  the  negative  radial  component  continually  increases  until 
the  moon  arrives  at  conjunction  whore  the  whole  disturbing  force  is 
negative  and  radial. 

It  appears,  therefore,  that  through   the  arcs  c  p,  and  c  p'„  ex- 
tending to  51^  41'  7"  on  each  side  of  conjunction,  and  op^,  ov\ 


LUNAii  THEORT.  688 

'  extending  to  the  same  distance  on  each  side  of  opposition^  the  radial 
component  of  the  disturbing  force  is  negative,  being  greatest  at  con- 
junction and  opposition,  and  gradually  decreasing  as  the  distance  of 
the  moon  from  those  points  increases  until  it  vanishes  at  the  points 
p„  p',,  IV,  and  p',. 

It  appears  further,  that  throughout  the  arcs  of  the  synodic  orbit 
included  between  Pt  and  p,,  and  between  p^i  and  p^„  which  are 
bisected  by  the  points  of  quadrature  p,  and  i^i,  the  radial  compo- 
nent of  the  disturbing  force  is  positive,  beine  greatest  at  the  points 
of  quadrature  P2  and  P^s*  i^d  gradually  diminishing  from  those 
points  to  the  extreme  points  of  uie  arcs  P|  p„  and  P^,  p'„  where  it 
vanishes. 

Since,  therefore,  a  negative  radial  component  acts  in  antagonism 
with  the  central  attraction  of  the  earth,  and  a  positive  radiid  com- 
ponent coincides  in  direction  with  that  attoiction,  it  follows,  that 
the  radial  component  of  the  sun's  disturbing  force  has  the  effect  of 
diminishine  the  intensity  of  the  earth's  attraction  throughout  the 
■iCB  P|  c  P\  and  P,  o  p^^;  and  that,  on  the  contrary,  it  has  a  ten- 
dency to  increase  the  earth's  attraction  throughout  the  arcs  Pj  P^  P| 
and  y,  p^t  ^r 

The  successive  changes  of  sign  of  the  radial  component  r,  and 
the  tangential  component  t,  of  the  sun's  disturbing  force,  are  indi- 
cated on  Jiff,  842,  in  a  manner  that  will  be  readily  understood  after 
what  has  been  explained  above. 

8194.  JSffeeU  0/ the  disturbinff  force  on  the  mo(m' 8  motion.  The 
tmnwMl  equation, — ^It  now  remains  to  explain  the  manner  in  which 
the  disturbing  force  of  the  sun  affects  the  moon's  motion  and  the 
fiDnn  of  its  orbit 

We  shall  first  explain  those  lunar  inequalities  which  are  inde- 
pendent of  the  elliptic  orbit;  and,  in  doing  this,  we  shall  regard  the 
undiatnrbed  orbit  as  a  circle,  having  the  earth  at  its  centre.  When 
these  inequalities  have  been  explained,  we  shall  consider  those 
which  aflSect  the  elliptic  orbit  of  the  moon. 

After  what  has  been  explained,  it  will  be  apparent  that  the  total 
effeetof  the  radial  component  of  the  disturbing  force  during  a  synodic 
lerolation,  will  be  to  decrease  the  intensity  of  the  earth's  attraction 
upon  the  moon. 

It  has  been  already  shown  that  the  intensity  of  the  negative 
ndial  component  of  the  disturbing  force  at  syzygies,  is  about  twice 
that  of  the  positive  radial  component  at  quadratures.  It  follows, 
therefore,  that  at  c  and  o  the  disturbing  action  of  the  moon  dinrin- 
ishet  the  earth's  attraction  twice  as  much  as  that  by  which  the 
positive  disturbing  action  at  pg  and  p'a  increases  it;  and  it  will  be 
apparent  that  nearly  the  same  proportion  will  prevail  between  the 
intensities  of  the  negative  action  of  the  disturbing  force  through  the 
aies  P,  c  p^i  and  p,  o  p',,  and  its  positive  action  through  the  ana 
P,  p|  pj  and  p^i  P^t  p's-    It  appears;  therefore,  t\iat  \lh«  \\i\AT!an9^«a  A 


5S4  ASTRONOMY. 

tlic  positive  radial  components  do  not  amount  to  more  than  one-half 
those  of  tho  negative  radial  components  of  the  disturbing  force 
during  an  entire  pjnodic  period. 

But  besides  this  excess  of  intensity  of  the  negative  over  the 
positive  radial  components^  it  is  to  be  considered  that  while  the 
negative  radial  components  are  in  operation  through  four  arcs  of 
54^  44'  7"  of  the  synodic  revolution,  the  positive  radial  compo- 
nents are  in  operation  only  through  the  four  arcs  complementary 
to  these, — that  is,  through  four  arcs  whose  magnitude  is  35^ 
15'  53". 

The  total  ciTcct,  therefore,  of  the  radial  components,  during  an 
entire  synodic  period,  must  be  to  diminish  tho  earth's  central  attrac- 
tion upon  the  moon  — firttt,  because  the  intensity  of  the  negative 
radial  components  is  greater  than  that  of  the  positive  in  the  pro- 
portion of  nearly  2  to  1 ;  and,  secondly,  because  the  total  length 
of  the  arcs,  through  which  the  former  act,  is  greater  than  that  of 
the  arcs  through  which  the  latter  act,  in  the  proportion  of  54  to 
35  nearly.  The  total  effect,  therefore,  of  the  radial  component  of 
the  disturbing  force  is  to  diminish  the  earth's  attraction  upon  the 
moon.  Now  it  appears,  from  the  general  principles  of  centnl 
force,  which  have  been  so  fully  explained  in  former  chapters  of  this 
volume,  that  the  angular  motion  of  a  body,  revolving  at  a  given 
distance  round  a  centre  of  attraction,  will  be  more  or  less  rafiid 
according  to  the  greater  or  less  intensity  of  that  attraction.  AVhat- 
ever,  therefore,  diminishes  the  central  attraction  of  the  earth  upon 
the  moon,  must  produce  a  corresponding  diminution  of  the  rate  of 
tho  moon's  mean  motion  round  the  earth.  Since,  therefore,  the 
disturbing  force  of  the  pun  diminishes  the  central  attraction  of  the 
earth,  it  necessarily  retards  the  motion  of  the  moon  round  the 
earth,  or,  what  is  the  same,  it  increases  the  length  of  its  peri».Hl. 

But  it  remains  to  be  seen  how  far  this  effect  may  bo  modified  by 
the  tangential  component  of  the  disturbing  force.  Now,  from  what 
has  been  expLiiuod,  it  appears  that  the  tangential  component  is 
negative  in  the  first  and  third,  and  positive  in  the  second  and  fourth 
quadrants,  and  therefore  it  retards  the  moon's  motion  in  the  former, 
and  accelerates  it  in  the  latter,  and  these  effects  in  the  two  qunJ- 
rants  are  very  nearly  erjual ;  the  consequence  is,  that  the  contnry 
effects  of  the  tangential  force,  in  accelerating  and  retarding  the 
nxxni's  motion,  neutralize  each  other,  and  leave  the  effect  uf  the 
radial  component  unimpaired. 

It  appears,  therefore,  that  the  mean  apparent  motion  of  the  moon 
is  thus  remlorcd  less  by  the  sun's  disturbing  force,  than  it  would  be 
if  that  forc<;  did  not  act ;  and  if  that  force  be  subject  to  any  varia- 
tion, it  is  obvious  that  the  mean  apparent  motion  of  the  moon  niu.-t 
be  Bubjeet  to  a  corresponding  variation,  increasing  and  decreasing 
with  the  increase  and  decrease  of  tho  disturbing  force.  Ihit  since 
the  sun's  disturbing  foiec  Xseon^  ;i  c^^TtaAu  ^ro^ortion  to  the  sun's 


LUNAR  TUBORT.  585 

whole  attnetioiii  it  must  increase  and  deoreaae  with  such  attraction. 
Now,  rinoe  the  sun's  distance  from  the  earth  varies,  being  least 
when  the  earth  is  in  perihelion,  and  greatest  when  it  is  in  aphelion, 
and  since  the  sun's  attraction  on  the  earth  increases  in  the  same 
proportion  as  the  square  of  the  earth's  distance  from  it  decreases,  it 
follows,  that  the  sun's  attraction  on  the  earth  and  moon,  and  there- 
fore its  dbturbin|;  force,  is  greatest  when  the  earth  is  in  perihelion, 
and  least  when  it  is  in  aphelion,  and  that  it  continually  decreases 
while  the  earth  passes  from  aphelion  to  perihelion. 

Now,  since,  from  what  has  been  just  explained,  the  mean  appa- 
rent motion  of  the  moon  is  diminished  by  every  increase  of  tho 
ion's  disturbing  force,  it  will  follow  that  this  mean  apparent  motion 
will  be  least  when  the  earth  is  ii;  perihelion,  and  greatest  when  it 
it  in  aphelion  ;  and  that  it  will  gradually  increase  while  the  earth 
is  passing  from  perihelion  to  aphelion,  and  gradually  decrease  while 
the  earth  is  passing  from  aphelion  to  perihelion. 

If  we  suppose  an  imaginary  moon  to  revolve  round  the  earth 
vniformly  in  the  same  time  as  the  real  moon  does  variably,  the 
appsrent  motion  of  this  imaginary  moon  would  be  the  mean  appa- 
rent motion  of  the  moon,  and  its  place  would  be  the  mean  place  of 
the  moon. 

The  difference  between  the  places  of  this  imaginary  moon  and 
tlie  true  moon,  produced  by  the  inequality  of  the  moon's  mean 
Bodos  which  has  been  just  explained,  is  called  the  annual  eqwjb' 
tum^  because  this  difference  must  continually  increase  for  one  half 
year,  and  diminish  for  another  half  year,  according  as  the  true 
notion  exceeds  or  falls  short  of  the  mean  motion. 

This  inequality  or  variation  of  the  moon's  mean  apparent  motion  was 
diecovered  by  observation  at  a  very  early  period  in  the  progress  of 
Mtronomical  science,  and  long  before  its  physical  cause  was  disclosed 
by  the  discovery  of  gravitation.  Its  discovery  by  observation  was 
dne  to  Tycho  Brahd,  about  the  year  1590.  The  greatest  value  of 
this  annual  equation,  or,  what  is  the  same,  the  greatest  difference 
between  the  mean  and  true  places  of  the  moon,  so  far  as  they  are 
alieoted  by  this  cause,  is  about  10'. 

3195.  Acceleration  of  the  moon^$  mean  motion.  —  It  might 
Tery  naturally  be  expected  that  a  mean  between  the  greatest 
and  least  values  of  the  moon's  mean  motion,  as  above  explained, 
would  be  equal  to  the  moon's  mean  motion  when  the  earth  is 
at  its  mean  distance  from  the  bud.  Thus,  if  fii'  express  the 
moon's  mean  apparent  motion  when  the  earth  is  in  aphelion, 
and  M '  its  mean  apparent  motion  when  in  perihelion,  and  M  be 
the  mean  between  these,  we  shall  have 

M  =  i  (m'  -f  m"). 
NoW|  if  m  express  tho  mean  motion  of  the  moon,  subject   to 


►- 


ASTKOSOMT. 


Hie  Jistorbing  aolioo  of  the  son,  when  the  earth  is  at  it*  nem 
diBtanpe  from  the  sun  it  might  be  expcote'l  that  we  should  have 
i»  =  M,  and  if  tbia  were  the  case,  M  wonld  necessarily  be  invi. 
liable,  becsupc,  ag  will  hereafter  appear,  the  earth's  'mewi  di*. 
tanoe  fmra  tbo  son  la  subject  to  no  eeeular  variation,  ftod  ooo- 
Bequcnily  the  disturbing  force  of  tbe  Bun  at  this  distanoe  maSt 
be  eijuallj  invariable.  It  ig  fnand,  however,  that  M  is  not  onlj 
not  ccinnl  to  m,  bnt  that  it  ia  no't  invariable. 

It  IB  found  to  be  greater  than  «,  and  variable  in  a  manner 
depending  on  the  inenuality  of  the  earth's  diatancca  fram  tbe 
nun  at  tbe  apsidefl;  the  more  nncqual  these  distances  are,  tbe 
Kreater  is  M  found  to  be.  But  since  the  ineqaality  of  ihes« 
distances  depends  on  the  eccentricity  of  the  earth's  orbit,  and 
since  this  eccentricity  is,  as  will  appear  hereafter,  subject  to  t 
Blow  secular  variation,  it  follows  that  m,  or  the  moon's  mesn 
apparent  motion,  is  subject  to  a  oorreapoading  secular  variation. 
It  will  appear  that,  for  (hoasanda  of  years  back,  end  fi^r  a  cor- 
reapondiog  period  to  come,  the  ecccntricily  of  the  eanfa's  orbit 
haa  been,  nod  will  be,  subject  to  a  slow  dcorease ;  the  cmae- 
E  qneDCO  of  vhicb  is,  that  the  noon's  mean  apparent  motioa, 
which  increases  aa  the  inc<iHiility  of  tbe  apsidsl  dislances  de- 
crc3><e,  baa  been,  and  is  still,  subject  to  a  slow  Rccular  increase, 
which,  like  the  annua]  equation,  was  discovered  as  a  fitct  bj 
observation  long  before  the  physical  cause  was  known,  and  WM 
designated,  in  astronomical  science,  aa  tbe  acceleration  of  At 
moon't  mean  motion. 

Its  cause,  as  just  explained,  was  traced  to  the  secular  variatioa 
of  tbe  eccentricity  of  the  earth's  orbit  by  Laplace,  in  1787. 

3196.  E^ect  upon  the  form  of  ike  moon's  orbit.  — Tbe  oom- 
bined  effect  of  the  two  components  of  tbe  diatnrbing  force  itpOB 
the  form  of  the  moon's  orbit,  the  undisturbed  orbit  being  sop- 
posed  to  be  circular,  is  to  elongate  it  in  the  direction  of  tks 
Une  of  quadratures,  and  to  contract  it  in  the  directioD  of  tbs 
line  of  syiygies  so  aa  to  convert  it  into  a  sort  of  ova],  tU 
longer  axis  of  which  is  at  right  angles  to  tbe  line  of  direetion 
of  the  sun.  It  conseqaentlj  follows,  that  as  the  earth  mOTct 
rouod  the  sun,  tbia  oval  continually  shifts  the  direetion  of  its 
axis,  the  longer  axis  constantly  turning  so  as  to  keep  itself  it 
right  angles  to  the  radius  vector  of  the  earth. 

To  explain  this,  it  is  only  necessary  to  oonsider  the  getwnl 
conditions  which  determine  the  curvature  of  tbe  pftth  of  «  body 
moving  under  the  influence  of  a  central  attraction,  and  to  oom- 
pare  them  with  the  components  of  the  disturbing  force  at  dif- 
ferent parts  of  the  synodic  revolution.  The  curvature  of  tba 
path  of  such  body  depends  in  general  on  tbe  intensit;  of  tlw 
central  attraction  and  the  velocity  of  the  body.      Whatever  <t 


LUKAB  THEORY.  687 

minuhes  the  central  attnotioa  or  increases  the  velocity,  most 
diminish  the  curvature  of  the  path  of  the  body,  and  vice  versd. 
Now  it  has  been  shown  that,  throughout  two  arcs  of  the  lunar 
orbit  extending  to  54^  44'  7"  at  each  side  of  the  line  of  syzy- 
gies,  the  radial  component  of  the  disturbing  force  is  negative, 
and  therefore  diminishes  the  central  attraction,  and  consequently 
also  diminishes  the  curvature.  But  it  has  also  been  shown  that 
the  tangential  component  is  positive  while  the  moon  approaches 
the  syzygics,  and  negative  after  it  passes  them.  The  motion 
of  the  moon  is  therefore  accelerated  by  this  component  until  it 
arrives  at  syzygies,  and  retarded  after  it  passes  these  points. 
The  velocity  of  the  moon,  therefore,  being  most  augmented  at 
sysygies  by  the  tangential  component,  the  curvature  of  its  path 
is  there  diminished. 

It  appears,  therefore,  that  throughout  the  arcs  extending 
540  ^^p  *j'/  ^Q  either  side  of  the  syzygies,  both  components  of 
the  sun's  disturbing  force  have  a  tendency  to  diminish  the  curva- 
tore  of  the  moon's  path. 

On  the  other  hand,  throughout  the  arcs  which  extend  35^  15'  6^" 
on  each  side  of  the  quadratures,  the  radial  force,  being  positive, 
augments  the  central  attraction  of  the  earth,  and  therefore  in- 
creaaes  the  curvature  of  the  orbit;  and  at  the  same  time  the 
tangential  component  of  the  disturbing  force,  being  negative  as 
the  moon  approaches  the  quadratures,  diminishes  the  velocity, 
and  consequently  increases  the  curvature  of  the  moon's  path. 

For  these  reasons,  the  curvature  of  the  moon's  orbit  is  greatest 
at  the  quadratures  and  least  at  the  syzygies,  which  is  equivalent  to 
stating  that  the  lunar  orbit  has  an  oval  form  arising  from  these 
caQseSi  the  longer  axis  of  the  oval  being  in  the  direction  of  the  qua- 
dntares^  and  the  lesser  axis  in  the  direction  of  syzygies. 

8197.  Moon's  variation,  —  If  the  radial  component  be  alone  con- 
sidered, it  is  easy  to  see  that  the  moon,  moving  in  such  an  orbit, 
would  have  a  varying  angular  motion,  which  would  be  greatest  at 
ajaygies  where  the  moon  is  nearest  the  earth,  and  least  at  quadra- 
tarea  where  it  is  most  distant  from  the  earth.  This  will  follow 
immediately  from  the  principle  of  the  equable  description  of  areas, 
which  is  never  affected  by  a  radial  disturbing  forc^>,  since  that  prin- 
dple  rests  on  no  other  condition  than  that  the  revolving  body  be 
affected  only  by  a  force  directed  to  a  fixed  centre.  It  is  clear,  from 
what  has  been  proved  in  (2614),  that  the  angular  velocity,  varying 
inversely  as  the  square  of  the  moon's  distincc  from  the  earth,  will, 
in  aach  an  oval  orbit  as  has  just  been  described,  be  greatest  where 
the  distance  is  least,  —  that  is,  at  syzygics;  and  least  where  the 
diatance  is  greatest,  —  that  is,  at  quadratures.  So  far,  therefore,  as 
relates  to  the  radial  component  of  the  disturbing  force,  the  moon's 
apparent  motion,  as  seen  from  the  earth,  which  is^  in  (suotx  VUk 


■■fdir  ■otioB  itmnd  the  eartli,  it  grettart  at  ejiiygies,  lad  lent  it 

Bat  if  W  Ilka  rata  meetaatt,  tiaa,  Uie  effect  of  Ibe  tangentul  aan- 
MHB^  Ihii  nriUton  nt  Hm  wpfanat  matiaa  iriU  be  BtiH  grMa. 
nk  flonpoMa^  ■aaortoy  to  irint  ks  bMa  iliowa,  eontiaiBH)' 
tweleralM  Uw  aDon't  BuAoa  ii  ■nwnniiBg  Afl  syEygies,  ud  eni> 

utit  it  in  qiproMUDS  tbs  qoauKtaica,  bo  ihtt,  lo  far 

OB  it,  llw  moon's  ymoAtj  will  be  greatest  at  ijrfp», 
■Bd  iBMl  It  qndratura. 

ThM  lh»  tm  compoDenta  of  the  son's  disturbing  lone  con- 
tht  tt  roidw  the  mooo's  sf^annt  notion  greitcst  t(  coe- 
Jnaofiaa  ■&!  tmontion,  nnd  lea*  nt  qiadntans. 

TUb  hegMtitj  of  (be  Boaa'a  ■«»«■«  awimi.  whH  lawt 
Ihnoi^  all  ita  phiaei  m  the  sjnouo  period,  is  callnl  the  nvw- 
tmt,  aad  vat  dhseoveied  ^mmI  tba  Mme  time  with  iho  umi 
•qnatioB  bj  T^o  Brabi. 

If  wa  niipate  sn  imaginaiy  araon  to  petfonn  tbe  i^Mdli 
period  with  a  naifoTm  angular  motioo,  wbik  the  motion  of  di 
true  moon  b  enbjccl  to  this  slterosle  acceler&lion  stid  taudk  . 
tion  at  sjsy^es  sod  qnsdratures,  the  distance  between  the  tn 
moons  will  be  the  variation,  sod  its  greatest  amount  riD  h 
about  32'. 

8198.  ParaUactie  inequality. — In  this  explanation,  Iwana^ 
we  have  assumed  that  uie  distnrbiiig  forces  are  equal  *  mr 
JDuction  and  opposition.  Now,  it  has  been  already  ahowa  AH^ 
at  these  points,  they  are  slightly  unequal — the  duturbiBg  faM 
at  conjnnotion  exceediog  that  at  oppositioa,  io  the  [iiiiJiiiliM 
of  about  63  to  62.  It  followB,  therefore,  that  the  efieot  of  At 
distorbiog  forces  will  not  be  exactly  equal  at  the  two  gyijglaj 
and  a  smsll  inequslity  is  tbua,  as  it  were,  superposed  npoa  !■ 
variation,  or,  so  to  epeak,  a  variation  of  tile  van'aiian  n  fn-  | 
dnoed,  which  is  called  the  parallactic  mequtUi^. 

8199.  iTitqualitiet  dtpendtng  oa  Me  effijpfK  /brm  ^  it 
btnar  orinL  —  la  the  preceding  paragiaphs  we  bava  owHal 
the  ooQBidenitioQ  of  the  elliptio  chaiaoter  of  the  moon's  aKL 
We  shall  now  explain  those  ineqnalilieB  which  depend  on  fla 
Taryiog  length  of  the  moon's  radius  vector. 

3200.  ^uatvM  of  Ae  centre.  —  The  first  inequali^  of  M 
oIsBs  which  we  shall  notioe  is  one  which  appertaioa  to  the 
problem  of  two  bodies,  rather  than  that  of  three  bodies,  and  wUtk 
has  been  already  noticed  in  relation  to  elliptic  motion  in  geneiaL 
The  equable  description  of  areas  by  the  moon  in  ita  elliptit 
orbit,  csuses  its  angular  motion  at  perihelion  to  be  .greater  Uaa 
ac  other  points',  &i^d,  «a  It  moves  from  perihelion,  tbis  angdc 
motion  gradually  &nAu\^«A,  uA  Qi»!><asraM&  ^  K-oKosak^  nnlil  il 
arrivaa    at  apheuon,  w\ie»  "*  '»  Vm^    "Ttooi.  w^n^vn.  >n  ^^ 


LUNAR  THEORY.  589 

1ieItoii|  on  the  contrary,  the  angalar  motion  gradually  and  continaally 
increases.  If  we  suppose  an  imaginary  moon  to  move  from  peri- 
helion through  aphelion  hack  to  perihelion,  with  a  uniform  angular 
Tdodty,  the  motion  of  this  moon  would  he  tho  mean  motion  of  the 
moon,  its  place  the  mean  place,  and  its  anomaly,  or  its  distance 
from  perihelion,  the  mean  anomaly ;  and  the  distance  hetween  this 
imaginary  moon  and  the  true  moon  is  called  the  equation  of  the 

Starting  from  perihelion,  the  motion  of  the  true  moon  heing 
greater  than  that  of  the  imaginary  moon,  the  true  moon  is  in  ad- 
vance of  the  imaginary  moon,  and  it  continues  to  gain  upon  the 
imaffinaiy  moon  to  a  certain  point,  after  which  the  mean  moon 
besinSy  in  its  tnnii  to  gain  upon  the  true  moon,  and  overtakes  it  at 
apibelion ;  the  distance  between  the  two  moons,  mean  and  true,  at 
aaj  pointy  ia  the  equation  of  the  centre.  From  aphelion  to  perihe- 
&m,  on  the  contrary,  the  mean  moon  precedes  the  true  moon,  and 
the  distanoe  between  them  increases  to  a  certain  point,  after  which 
tke  mean  moon  begins  to  overtake  the  true  moon,  and  does  over- 
lake  it  on  retnmiDg  to  perihelion. 

The  equation  of  the  centre  is,  therefore,  positive  from  perihelion 
to  aphelion,  and  negative  from  aphelion  to  perihelion. 

8201.  Method  of  investigating  the  variations  of  the  elliptic 
AmaUs  of  the  lunar  orbit.  —  After  what  has  been  explained  in  the 
praaent  and  preceding  chapters,  there  will  be  no  difficulty  in  tracing 
the  effects  produced  by  the  sun's  disturbing  force  upon  the  magni- 
iade,  form,  and  position  of  the  moon's  elliptic  orbit.  The  effects 
pndooed  in  general  upon  any  elliptic  orbit  whatever,  by  positive 
and  negative,  radial  and  tangential  disturbing  forces  (317  c/  ^2')f 
and  the  successive  changes  of  direction  and  intensity  of  the  radial 
aad  tangential  components  of  the  sun's  disturbing  force  acUng  on 
the  moon,  as  explained  above,  being  fully  comprehended,  it  is  only 
Becessary  to  apply  the  general  principles  to  the  particular  case  of 
tke  moon  in  order  to  explain  all  the  phenomena.  For  this  purpose 
ii  will  be  necessaiy  to  consider  successively  the  cases  in  which  the 
moon's  perigee  assumes  every  variety  of  position  with  relation  to 
the  line  of  syzygios,  and  in  each  position  to  investigate  the  effects 
prodnoed  upon  the  elements  of  the  instantaneous  ellipse  in  the 
diffBrent  positions  which  the  moon  assumes  during  an  entire  revolu- 
tion in  its  orbit 

8202.  Moon's  mean  distance  not  sithject  to  sertilar  variation,  — 
It  may  be  stated,  generally,  that  the  effects  of  the  disturbing  force 
of  the  sun  upon  the  moon's  mean  distance  or  major  axis  of  its  orbit 
lentraliee  each  other;  the  increase  which  it  produces  on  that  ele- 
ment in  some  synodic  positions  being  exactly  compensated  by  the 
decreue  it  produces  id  others. 

Jo  the  Srst  place,  it  must  be  observed  that  since  l\i^  wiwcAtvsnVj 
ju-  50 


688  ASTBONOMT. 

tDgnlar  motion  round  the  earth,  is  greatest  at  sysygieSy  and  least  at 
quadratures. 

But  if  we  take  into  account,  also,  the  effect  of  the  tangential  com* 
ponent,  this  variation  of  the  apparent  motion  will  be  still  greater. 
This  component,  according  to  what  has  been  shown,  oontinnally 
accelerates  the  moon's  motion  in  approaching  the  sysygies,  and  oon- 
tinually  retards  it  in  approaching  the  quadratures,  so  that,  so  &r 
as  depends  on  it,  the  moon's  velocity  will  be  greatest  at  sysygies, 
and  least  at  quadratures. 

Thus  the  two  components  of  the  sun's  disturbing  force  com- 
bine to  render  the  moon's  apparent  motion  greatest  at  con- 
junction and  opposition,  and  least  at  quadratures. 

This  inequality  of  the  moon's  apparent  motion,  which  pasKi 
through  all  its  phases  in  the  synodic  period,  is  called  the  vario' 
tion,  and  was  discovered  about  the  same  time  with  the  annoil 
equation  by  Tycho  Brah^. 

If  we  suppose  an  imaginary  moon  to  perform  the  synodic 
period  with  a  uniform  angular  motion,  while  the  motion  of  the 
true  moon  is  subject  to  this  alternate  acceleration  and  retuda* 
tion  at  sysygies  and  quadratures,  the  distance  between  the  two 
mooDS  will  be  the  variation^  and  its  greatest  amount  will  be 
about  32'. 

3198.  Parallactic  tnequaliff/. — In  this  explanation,  however, 
wo  have  assumed  that  the  disturbing  forces  are  equal  at  con- 
junction and  opposition.  Now,  it  has  been  already  shown  that, 
at  these  points,  they  are  slightly  unequal — the  disturbing  force 
at  conjunction  exceeding  that  at  opposition,  in  the  proportion 
of  about  03  to  62.  It  follows,  therefore,  that  the  eflfect  of  the 
disturbing  forces  will  not  be  exactly  equal  at  the  two  syzygics; 
and  a  small  inequality  is  thus,  as  it  were,  superposed  upon  the 
variation,  or,  so  to  speak,  a  variation  of  the  variation  is  pro- 
duced, which  is  called  the  parallactic  inrqualitf/, 

3199.  Inequalities  depending  on  the  elliptic  forta  of  the 
lunar  orbit.  —  In  the  preceding  paragraphs  we  have  omitted 
the  consideration  of  the  elliptic  character  of  the  moon's  orbit. 
We  shall  now  explain  those  inequalities  which  depend  on  the 
varying  length  of  the  moon's  radius  vector. 

3200.  Equation  of  the  centre, — The  first  inequality  of  this 
class  which  we  shall  notice  is  one  which  appertains  to  the 
problem  of  two  bodies,  rather  than  that  of  three  bodies,  and  which 
has  been  already  noticed  in  relation  to  elliptic  motion  in  general. 
The  equable  description  of  areas  by  the  moon  in  its  elliptic 
orbit,  causes  its  angular  motion  at  perihelion  to  be  greater  than 
at  other  points;  and,  as  it  moves  from  perihelion,  this  angular 
motion  gradually  diminishes,  and  continues  to  diminish,  until  it 
arrives  at  aphelion,  vfhcre  it   is   least.     From   aphelion  to  peri- 


LUNAR  THEORY.  589 

heUoDy  on  tbe  contrary,  the  angalar  motion  graduall j  and  continnally 
mcreaaes.  If  we  suppose  an  imaginary  moon  to  move  from  peri^ 
helion  through  aphelion  back  to  perihelion,  with  a  uniform  angular 
Telocity,  the  motion  of  this  moon  would  be  the  mean  motion  of  the 
moon,  its  place  the  mean  place,  and  its  anomaly,  or  its  distance 
from  perihelion,  the  mean  anomaly ;  and  the  distance  between  this 
immg^nary  moon  and  the  true  moon  is  called  the  equation  of  the 

Starting  from  perihelion,  the  motion  of  the  true  moon  being 
gremter  than  that  of  the  imaginary  moon,  the  true  moon  is  in  ad- 
Ttooe  of  the  imaginary  moon,  and  it  continues  to  gain  upon  the 
imaginaiy  moon  to  a  certain  point,  after  which  the  mean  moon 
besiDa,  in  its  turn,  to  gain  upon  the  true  moon,  and  overtakes  it  at 
apbelioii ;  the  distance  between  the  two  moons,  mean  and  true,  at 
any  point,  ia  the  equation  of  the  centre.  From  aphelion  to  perihe- 
Ikm,  on  the  contrary,  the  mean  moon  precedes  the  true  moon,  and 
the  diatanoe  between  them  increases  to  a  certain  point,  after  which 
the  mean  moon  begins  to  overtake  the  true  moon,  and  does  over- 
tike  it  OQ  returning  to  perihelion. 

The  equation  of  the  centre  is,  therefore,  positive  from  perihelion 
to  aphelioD,  and  negative  from  aphelion  to  perihelion. 

8201.  Method  of  investigating  the  variations  of  the  elliptic 
efemeMfa  of  the  lunar  orbit,  —  After  what  has  been  explained  in  the 
preient  and  preceding  chapters,  there  will  be  no  difficulty  in  tracing 
the  effects  produced  by  the  sun's  disturbing  force  upon  the  magni- 
tude, form,  and  position  of  the  moon's  elliptic  orbit.  The  effects 
produced  in  general  upon  any  elliptic  orbit  whatever,  by  positive 
and  negative,  radial  and  tangential  disturbing  forces  (317  et  Meq,\ 
and  the  successive  changes  of  direction  and  mtensity  of  the  radial 
and  tangential  components  of  the  sun's  disturbing  force  acting  on 
the  moon,  as  explained  above,  being  fully  comprehended,  it  is  only 
neoeaaary  to  apply  the  general  principles  to  the  particular  case  of 
the  moon  in  order  to  explain  all  the  phenomena.  For  this  purpose 
it  will  be  necessaiy  to  consider  successively  the  cases  in  which  the 
moon's  perigee  assumes  every  variety  of  position  with  relation  to 
the  line  of  syzygies,  and  in  each  position  to  investigate  the  effects 
produced  upon  the  elements  of  the  instantaneous  elli^e  in  the 
difierent  positions  which  the  moon  assumes  during  an  entire  revolu- 
tioo  in  its  orbit 

8202.  Moon's  mean  distance  not  sithjWt  to  secular  variation.  — 
It  may  be  stated,  generally,  that  the  effects  of  the  disturbing  force 
of  the  sun  upon  the  moon's  mean  distance  or  major  axis  of  its  orbit 
neatralise  each  other ;  the  increase  which  it  produces  on  that  ele- 
ment in  some  synodic  positions  being  exactly  compensated  by  the 
decrease  it  produces  in  others. 

In  the  first  phice,  it  must  be  observed  that  since  the  ^^"^Vri^V^ 
III.  50 


690  ASTKONOUT. 

of  the  lunar  orljit  is  very  small,  the  radial  component  produeei  no 
effect  on  the  moon's  orbital  velocitj,  and,  tbrrcrurc,  none  apon  tht 
oognitudc  of  ils  major  axis. 

The  tangential  component  being  negative  in  the  fint  ind  third, 
and  positive  in  the  second  aad  fourth,  quadrants,  diminiahea  ths 
axis  in  the  former  and  increases  it  in  the  latter.  If  it  otn  be  shinrn 
thatj  on  the  whole,  the  increase  is  eqnol  to  the  decrease,  it  will  fol- 
low that  the  magoitude  of  the  mean  distonoe  oi  major  Bemi-ixil 


suiTcra  no  ultimate  chasge. 
Tor  this  purpose  it  will  w 


etTccts 

iu  differcL 

I  [iiwiiion* 

of  the 

lunar  orb 

t  relative!; 

to  the 

sviygies 

auJ  (luid- 

ratorcs 

If  the  line  of 

aphides  k 

in  syz 

vgii'H,  as   repruscnteJ 

in  yy 

iii:i,  when   pi-rigi'* 

eoiiiuncUt 

1,   and  in 

yy.8-14«L.,.  u 

„,(,,-.  is  i« 

intensity  of  llic  -Jisturbing  force  is 
tances  from  the  ufwdes,  il  fnllaws  t 
of  the  mean  distautt  ^ircxiuttd  by  t 


10  mnn:  at  equal  angular  <]is- 
,t  in  ta^-L  rase  the  diiuiouli''" 
:  tunjrintial  couipuaeut  io.  ttw 


LXySAJt  THBORT. 


Mcond  And  fourtb  qiudraDta. 

If  the  apsides  b«  in  quadrature,  as  represented  in  ^ij.  S45,  the 
wme  will  obriouBlj  be  true. 

In  tbese  osea,  therefore,  the  m&jor  axis  of  the  orbit  Buffers  no 
nltiinftte  ohange  ^m  the  action  of  the  disturbing  force. 

Bnl  if,  SB  iafy.  846,  the  line  of  apsides  ^  a  be  inclined  at  an 

obliqae  angle  to  Uie  line  of  syzjgies  o  O,  the  elliptic  orbit  will  not 

be  By m metrically  divided  by 

the  four    Byuodic    quadranta 

I  P|,  F]  0,  o  !>„  and  p")  0,  and 

Q  that  case  the  decrease  and 

I  increase  of  the  axis  produced 

1  in  the  alternate  quadrants  will 

I  no  longer  be  equal,  and  a  com- 

I  plete  compeoBation  will  not,  as 

I  before,  be  effected  in  a  single 

Snodic  revolution.  But  if 
e  orbit  be  taken  in  two  posi- 
I  tiong  in  which  the  Lne  of 
I  apEidcs  n  a  and  p'  a'  is  equally 
I  inclinea  on  different  sides  of 
*  the  line  of  syzygica,  the  effect 
of  the  disturbing  force  on  the 
mean  distanco  in  a  complete 
synodic  revolution  in  one  posi- 
tion will  bo  compensated  by 
Ac  eqnal  and  contrary  effect  produced  in  the  other  position.  This 
will  be  apparent  by  considering  that  the  intensities  of  the  disturbing 
JbrM  at  equal  inclinations  to  the  line  of  syzygies  are  proporliooaL 
to  the  moon's  distance  from  the  earth.  It  follows  from  this  that 
tin  efleetsof  tbc  disturbing  force  in  the  quadranta  c^P|  and  af/j/„ 
toA  in  the  quadrants  P,  a  P*]  and  P,  a'  v',  arc  equal,  and  in  the  same 
■Mnner  that  the  effects  are  equal  in  the  other  corresponding  quad- 
nuts.  It  will,  therefore,  be  apparent  that,  (Akiug  the  orbit  in  the 
two  poritions,  the  increase  and  decrease  which  the  major  axis  suffers 
in  two  complete  synodic  periods  ore  equal,  and  ttiac,  therefore,  the 
major  asis  suffers  no  ultimato  change  of  magnitude. 

Bat  since,  in  the  revolution  of  the  earth  and  moon  ronnd  the 
■on,  the  line  of  apsides  takes  successively  every  iuclination  to  the 
line  of  nyEjgics,  it  will  necessarily  assume,  ut  regular  intervals, 
the  equal  inelinntinns  at  wbich  tiio  effi'cls  of  the  disturbing  force 
upon  the  axis  of  the  orbit  arc  mutually  compensatory,  and  it  fol- 
lows, therefore,  that  no  ultimate  decrca^  of  uiugnitudc  of  the  axis 
takes  place. 

It  remains,  therefore,  to  investigate  the  effects  of  the  dietaiUvk^ 


Fig.  US. 


602  A8TR0N0MT. 

force  of  the  san  on  tbe  other  elements  of  the  lunar  orint;  that  itp 
upon  the  direction  of  the  apsidea,  or,  what  ia  the  same,  on  the  longi- 
tude of  perihelion  and  the  eccentricity. 

As  these  effects  will  vary  according  to  the  varying  position  of 
the  line  of  apsides,  with  relation  to  the  line  of  ayiygies,  we  shall 
consider  successively  the  variation  of  each  of  the  elements  daring  a 
synodic  revolution  of  the  moon,  when  the  apsides  are  in  BpjgteBj 
in  quadratures,  and  between  these  points. 

First  Case.  i 

WHEN  PERIGEE  IS  IN  CONJUNOTION. 

3208.  Motion  of  the  apsides, — Let  the  lines  P|  p^a  and  p/  P|1m 
drawn,  making  angles  of  54^  44'  T'  with  the  line  of  sysygiee  co^ 
Jig,  843.  Let  us  consider,  first,  the  effect  of  the  radutl|  and, 
secondly,  the  effect  of  the  tangential  component. 

First,  Tbe  radial  component,  being  negative  while  the  moon 
moves  through  tbe  arcs  F  i  o  P„  and  p,  o  P^a  (3193),  a  regresBfS 
motion  will  be  imparted  to  the  apsides  in  tbe  former  and  a  progrei- 
sive  motion  in  the  latter  (3193). 

The  same  compoDeDt  being  positive  while  the  moon  mo?e8 
through  the  arcs  p,  P3  and  p'3 1*',,  a  progressive  motion  will  be  im- 
parted to  the  apsides  in  P|  P2  and  p',  p'„  and  a  regressive  motion  in 
Pg  Ps  and  p'3  p'j. 

To  determine  the  effect  produced  upon  the  apsides  during  tbe 
whole  synodic  revolution,  it  will  be  necessary  to  take  into  account 
the  varying  intensity  of  the  disturbing  force  in  these  several  arcs. 

Since,  at  equal  inclinations  to  the  line  of  syzygies,  the  intensity 
of  the  disturbing  force  is  in  the  direct  ratio  of  the  moon's  distance 
from  the  earth  (3192),  it  is  evident  that  its  effect  through  the  aro 
P,  o  p's  will  be  greater  than  its  effect  through  the  arc  p',  c  P„  and 
that  its  effect  through  the  arcs  Pg  P,  and  p'3  p'j  will  also  be  greater, 
though  in  a  much  less  degree,  than  its  effect  through  the  arcs  p,  P| 
and  v^2  P'l-  I^ot  besides  the  greater  intensity  of  the  disturbing 
force  throughout  the  arc  P,  o  p'g,  its  effect  is  augmented  by  the 
slower  motion  of  the  moon  supplying  a  longer  interval  for  its 
action. 

It  follows,  therefore,  that  the  progressive  motion  imparted  to  the 
apsides  while  the  moon  moves  from  P3  to  p'3  is  much  greater  than 
the  regressive  motion  imparted  while  it  moves  from  p'l  to  P, ;  and 
that  the  regressive  motion  imparted  while  it  moves  through  the  area 
Pj  P3  and  p'3  p'g  very  little  exceeds  the  progressive  motion  imparted 
while  it  moves  through  the  arcs  P,  Pj  and  p'g  p',. 

The  consequence  is,  that,  in  a  complete  synodic  revolution,  the 


LUNAR  THEORY.  598 

mgressive  motion  consiclerably  exceeds  the  regressire ;  and;  thore- 
Mre,  on  the  whole,  the  apsides  are  moved  forward. 

Secondly.  The  tangential  component  being  negative  from  o  to  Pg 
and  from  O  to  p'a,  and  positive  from  pg  to  O  and  from  o  to  p^a,  it 
imptrts  a  regressive  motion  to  the  apsides  from  p^i  to  Pi,  from  p,  to 
P^  and  from  p's  to  p's,  and  a  progressive  motion  from  P^  to  P^s,  from 
p^a  to  P^„  and  from  Pi  to  P,,  (3193). 

It  may  be  shown,  as  in  the  former  case,  that  the  progressive  mo- 
tion in  a  complete  synodic  revolution  exceeds  the  regressive  motion, 
and,  therefore,  that  on  the  whole  the  tangential  component  imparts 
a  progressive  motion  to  the  apsides. 

It  follows,  therefore,  that  when  perigee  is  in  conjunction,  the 
distorbing  force  of  the  snn,  acting  during  a  complete  synodic  revo- 
lution of  the  moon,  causes  the  line  of  apsides  to  move  forward  in 
the  direction  of  the  sun's  motion,  so  that,  at  the  end  of  a  synodic 
levolation,  the  longitude  of  perigee  will  be  greater  than  it  was  at 
lis  eommenccment,  —  the  longitude  of  that  point,  however,  having, 
dnrinff  sooh  revolution,  alternately  increased  and  decreased. 

82(>4.  Effects  on  the  eccentricity. — To  ascertain  the  variation  of 
Hm  eecentricity  of  the  lunar  orbit,  produced  by  the  sun's  disturbing 
inree  in  the  same  position  of  the  apsides,  we  shall,  as  before,  consider 
int,  the  effect  of  the  radial,  and,  secondly,  that  of  the  tangential 
•omponent 

Fint,  The  radial  component  being  negative  from  p^i  to  Pi  and 
from  Pa  to  P^s)  and  positive  from  p,  to  P3  and  from  p's  to  P^i,  it  fol- 
lowBy  that  it  will  cause  the  eccentricity  to  increase  from  0  to  Pi  and 
from  P^  to  o,  and  to  decrease  from  p,  to  p„  while,  in  the  other  half 
of  the  synodic  revolution,  it  will  cause  it  to  decrease  from  o  to  P^s, 
aad  from  p,  to  c,  and  to  increase  from  p',  to  P^i,  (3193).  Now  it  is 
tvident  that  the  effects  of  the  disturbing  force  through  the  arcs 
C  Pi,  Pi  P„  and  Pj  O,  are  respectively  equal  to  its  effects  through  the 
aici  0  P^„  p'l  p's,  and  p',  o,  and,  therefore,  that  the  increments 
end  deorements  which  the  eccentricity  receives  during  a  complete 
ijnodic  revolution  are  equal,  and  that  so  far  as  depends  on  the 
ladial  eomponent  of  the  disturbing  force,  it  suffers  no  ultimate 
variation. 

Secondly.  Since  the  tangential  component  is  negative  in  the  first 
and  third,  and  positive  in  the  second  and  fourth  quadrants,  it  will 
foUow,  from  what  has  been  proved  (3156),  that  this  component  will 
aaiiae  the  eccentricity  to  decrease  throughout  the  first  and  second, 
and  to  increase  throughout  the  third  and  fourth  quadrants. 

But  it  will  be  evident,  from  the  same  reasoning  as  has  been  used 
in  the  former  case,  that  the  intensity  of  the  disturbing  force  in  the 
first  and  second  quadrants,  being  respectively  equal  to  its  intensity 
in  tiio  fourth  and  third,  the  decrease  of  the  eccentricity  in  the  first 
qoadrant  will  be  equal  to  its  increase  in  the  fourth,  and  its  decreasQ 

60* 


fe. 


ASXftOIVDHV. 


1  be  equal  to  its  inorease  in  tbe  third ;  da 

CDDsequencc  of  which  will  be  thnt,  ia  a  complete  revoIa^oD,  Uie 
occeatricity  nill  BuSer  do  change  from  tbe  operation  of  the  t&Dgea- 
tial  compoocnt  of  the  di^turbiog  force. 

It  follows,  therefore,  that  mhca  the  mooo's  porij^  is  in  oodjudc- 
txoa,  tbe  eccentricity  of  its  orbit,  at  tbe  eod  of  caofa  synodic  rcrolu- 
tioQ,  will  be  tbe  same  as  at  the  begianing,  but  that  during  bocI) 
nvolntion  it  will  alternately  increase  and  decrease  witbia  oertiia 
narrow  limits. 

Second  Case. 

■  WHBH   PEBIOEB   IS  IN  OFPOSlTtON. 

I  3205.  Jtfotion  o/the  aptidct.  —  As  before,  let  the  lines  p,  t^,  ud 
^1  ^t'  fig-  844,  be  drawn,  making  angles  of  51°  44'  7"  wilb  t)» 
line  of  Bj'zygies  c  o,  and  let  ns  cooEider,  first,  os  in  the  former  cue, 
the  effect  of  tbe  radial,  and,  secondly,  tbe  efiiHit  of  the  tangentid 
oomponont. 

tFirU.  The  radial  component  being  oega^Te,  while  the  mom 
moves  from  p*,  to  F„  and  from  Pj  to  F,,  a  progreBsiTe  motion  will 
be  imparted  to  the  apsides  in  the  former,  and  a  regressive  motjon 
in  the  latter,  (3103).  The  same  component  being  positive,  while 
the  moon  moves  from  P,  to  P,,  and  from  p',  to  p*,,  a  regressive  00- 
tion  will  be  imparted  lo  the  apsides  from  P,  to  Pj  and  from  p',  to  P*], 
and  a  progressive  motion  from  p,  lo  p,  and  from  p",  to  p",;  and  it 
will  appear  by  the  same  reasoning  as  in  the  former  case,  that  tbe 
total  effect  through  the  arcs  in  which  the  motion  is  progressive,  will 
exceed  consideraoly  tbe  total  eFTcet  through  tbe  arcs  in  which  tbe 
motion  ia  regressive,  and  therefore  that  tbe  effect  of  the  radial  com- 
ponent during  a  complete  synodic  revolution  will  be  lo  carry  forwaid 
the  line  of  apsides. 

SeconiUy.  The  tangential  component  being  negative  in  the  first 
Nid  third,  and  positive  in  the  second  and  fourth  (luadraats,  it  will 
impart  a  progressive  motion  to  tbe  apsides  from  p',  to  Pg,  and  a  re- 
gressive motion  from  P  to  p",  (3193). 

It  will  follow,  as  in  the  former  cose,  that  the  progressive  motion 
arising  from  this  component  in  a  complete  Rjnodio  revolutioo 
exceeds  tbe  regressive  motion.  It  follows  therefore,  precisely  as  in 
the  former  case,  that  when  perigee  b  in  opposition,  the  sun's  dit- 
turbing  force,  during  a  complete  synodic  revolution,  gives  a  pro- 
gressive motion  to  the  line  of  apsides,  that  line  however,  during 
Bncb  revolution,  receiving  an  alternate  motion  of  progression  and 
regression  within  certain  limits. 

3206.  EffecU  on  ihe  ecccntridfjf.  —  These  effects  may  be  explained 
hj  reasoniog  precisely  eimilar  to  that  used  in  the  formei  case. 


LUNAR  THEORT.  596 

I%nt.  The  radial  oomponent  being  ncgativo  from  p^,  to  p,  and 
from  Pf  to  P^a  and  positive  from  Pi  to  p,  and  from  p^,  to  Pi,  it  wiU 
eanse  the  eccentricity  to  decrease  from  o  to  Pi  and  from  p,,  to  o, 
and  to  increase  from  P|  to  P3 ;  while  in  the  other  half  of  the  synodic 
KYolation,  it  will  cause  it  to  increase  from  o  to  p',  and  from  p',  to 
Cy  tod  to  decrease  from  P^,  to  P^,  (3193);  and  it  is  evident,  as  before, 
that  Uie  effects  in  each  half  orbit  being  compensatory,  no  ultimate 
Tariatioi)  is  produced  by  this  component  upon  the  eccentricity  in  a 
oomplete  synodic  revolution. 

Secondly.  The  effects  of  the  tangential  component  are,  in  like 
manner,  shown  to  be  compensatory  in  this  case  by  reasoning  so  com- 
pletely similar  to  the  former  that  it  need  not  be  repeated. 

Third  Case, 
when  the  apsides  are  in  quadrature. 

8207.  Motion  of  the  apsides.  —  Let  the  lines  p,  p',  and  p',  p„ 

Jiff.  845,  as  before,  be  drawn,  making  angles  of  54^  44'  7"  with  the 

line  of  syiygies  0  O.     We  shall,  as  in  the  former  case,  consider  first 

tbe  effect  of  the  radial,  and  second  that  of  the  tangential  component. 

FinL  The  radial  component  being  negative  from  p',  to  P|  and 
from  Ps  to  p^s,  and  positive  from  p,  to  P,  and  from  P^,  to  p^„  it  fol- 
lows that  a  regressive  motion  will  be  imparted  to  the  apsides  while 
llw  moon  moves  from  0  to  Pi,  from  p,  to  o,  and  from  p^,  to  p^i,  and 
that  a  progressive  motion  will  be  imparted  to  it  in  the  intermediate 
area,  that  is  from  p,  to  p,,  from  o  to  p's*  and  from  p'l  to  0. 

But,  from  the  principle  already  so  often  referred  to,  in  virtue  of 
which  the  intensity  of  the  disturbing  force  at  equal  inclinations  to  the 
line  of  syiyfl^ies  is  proportional  to  the  distence  of  the  moon  from  the 
earth,  it  wiU  be  evident  that  the  totel  effect  of  the  radial  component 
in  imparting  a  regressive  motion  to  the  apsides  from  p^,  to  p^i  will  be 
much  greater  than  its  total  effect  in  imparting  a  progressive  motion 
from  P|  to  Pa,  while  the  difference  of  ite  effects  in  the  other  arcs  will 
be  comparatively  small.  It  will  follow,  therefore,  that  after  an 
entire  revolution  the  effect  of  this  component  in  imparting  regres- 
Hon  will  greatly  predominate  over  its  effect  in  imparting  progression^ 
and  that,  on  the  whole,  the  apsides  will  be  made  to  regress. 

Secondly,  The  tengential  component  being,  as  before,  negative 
in  the  first  and  third,  and  positive  in  the  second  and  fourth  quad- 
lanta,  it  will  impart  to  the  line  of  apsides  a  progressive  motion 
through  the  arc  OPgO,  and  a  regressive  motion  through  the  are 
o  P^,  o  (3163). 

It  is  evident,  as  before,  that  in  this  case  the  regressive  effects 
predominate  over  the  progressive,  and  that,  therefore,  the  effect  of 
this  oomponent  throughout  a  complete  synodic  revolution  is  to  im- 
jart  to  the  apsides  a  regressive  motion. 


696  A8TR0N0MT. 

3208.  Effect  on  the  eccentricity, — We  sball,  as  before,  first  OGI- 
Bider  the  effect  of  the  radial^  and  secondly  of  the  tangential  oom- 
ponent 

It  will  appear,  from  what  has  been  already  explained  (3163), 
that  the  radial  component  being  positive  from  P|  to  V^  and  from  ii 
to  F^i,  the  eccentricity  will  increase  from  Pi  to  P,  and  from  V^  to  p'» 
and  will  decrease  from  Pg  to  p,  and  from  p',  to  p't;  and  the  radial 
component  being  positive  from  p,  to  p',  and  from  P^,  to  P|,  the 
eccentricity  will  increase  throughout  the  former  and  decrease 
throughout  the  latter  aro. 

If,  then,  the  several  arcs  of  the  ellipse  in  which  the  eccentricity 
increases  be  compared  with  those  in  which  it  decreases,  they  will  be 
found  to  be  perfectly  equal  and  symmetrical,  so  that  the  intensity 
of  the  radial  components  which  produce  increase  will  be  equal  on 
the  whole  to  those  which  produce  decrease;  consequently,  the  effects 
of  this  component  on  the  eccentricity  will  be  compensatory. 

Secondly,  Since  the  tangential  component  is  negative  in  the  first 
and  third,  and  positive  in  the  second  and  fourth  quadrants,  it  will 
follow  from  what  has  been  explained  (3163),  that  the  eocentridty 
will  continually  increase  through  the  same  ellipse  Pt  O  p't,  so  thit 
here  again  the  effects  of  the  component  are  compcn5«atory. 

It  follows,  therefore,  that  when  the  line  of  apsides  is  in  quadra- 
ture, the  eccentricity  at  the  end  of  a  complete  synodic  revolution  is 
precisely  what  it  was  at  the  commencement,  suffering,  nevertheless, 
variations  of  increase  and  decrease  during  such  revolution. 

3209.  The  motifm  of  the  ajmdes  ffreairr  in  xy::yjics  than  in 
quadrature.  —  It  has  been  already  shown  (3191)  that  the  intensity 
of  the  disturbing  forccf  directed  from  the  earth  when  the  moon  is  in 
syzygies,  is  twice  as  great  as  its  intensity  directed  to  the  earth  when 
in  quadrature. 

So  far,  therefore,  as  depends  on  the  radial  component,  it  may  be 
inferred  that  the  progressive  motion  imparted  to  the  apsides  when 
in  syzygies,  will  be  greater  than  the  regressive  motion  imparted  to 
them  in  quadrature. 

But  if  the  effect  of  the  tangential  component  on  the  line  of 
apsides  in  quadrature  be  compared  with  its  effect  in  syzygies,  it  will 
be  found  to  be  nearly  the  same.  The  effect,  therefore,  of  the 
greater  intensity  of  the  radial  component  not  being  affected  by  that 
of  the  tangential,  the  progressive  motion  imparted  by  the  disturbing 
force  to  the  apsides  in  syzygies  is  found  to  be  greater  than  the 
regressive  motion  imparted  to  them  in  quadrature ;  in  fact,  it  is 
found  that  in  each  synodic  revolution  of  the  moon,  when  the  ap- 
sides arc  in  syzygies,  a  progressive  motion  of  11°  is  imparted  to 
them,  while  the  regressive  motion  imparted  to  them  in  each  synodic 
revolution,  when  in  quadrature,  is  only  9*^.  If,  then,  two  such 
syuodic  rcvoluLious  be  compared,  one  in  syzygies  and  the  other  in 


LUNAR  THBORT.  597 

qnadratarey  the  result  will  be  a  progression  of  the  apiudes  amount- 
ing to  IP  —  9*^  =  2^ 

Several  circumstances  attending  the  moon's  motion  combine  in 
producing  this  difference  in  the  effects  of  the  apsides  in  the  two 
positions.  The  synodic  motion  of  the  moon  is  slower  at  apogee 
than  at  perigee  in  the  ratio  of  9  to  13 ;  that  is  to  say,  while  the 
moon  departs  from  the  sun  at  perigee  through  13^,  it  will  depart 
at  apogee  through  only  9^.  The  consequence  of  this  is,  that  the 
dower  synodic  motion  at  apogee  leaves  a  longer  time  for  the  opera- 
tion of  the  sun's  disturbing  force  upon  the  earth  than  at  perigee. 
ThuBf  thia  force  is  not  only  more  energetic  at  apogee  than  at  peri- 
eeei  since  its  intensity  is  proportional  to  the  mean  distance  from 
ue  earth,  but  the  more  intense  force  acts  for  a  longer  time. 

When  perigee  is  in  conjunction,  the  motion  of  tibe  apsides  being 
progressive,  and  at  the  rate  of  11^  in  each  synodic  revolution,  while 
tiie  progressive  motion  of  the  sun  in  the  same  time  is  about  27^,  it 
follows  that,  in  each  synodic  revolution,  the  sun  will  depart  from 
perigee  through  a  distance  of  27''—  ll""  =  IG"". 

But  when  the  sun  is  in  quadrature,  the  regressive  motion  of  the 
apndes  in  each  revolution  being  9^,  while  the  progressive  motion 
m  the  sun  is,  as  before,  27^,  the  sun  and  perigee  will  depart  from 
each  other,  in  each  synodic  revolution,  through  27^  -f  9^  =  36^. 

It  appears,  therefore,  that  the  separation  of  the  sun  and  perigee, 
in  eacm  synodic  revolution  when  perigee  is  in  syzygies,  is  greater 
than  when  it  is  in  quadrature,  in  the  proportion  of  36  to  16,  or 
9  to  4. 

It  is  evident  from  this,  therefore,  that  another  cause  operates  in 
favoor  of  the  more  continued  action  of  the  disturbing  force  in  pro- 
ducing a  progressive  motion  in  syzygies  than  in  producing  a  regres- 
nva  motion  in  quadratures,  inasmuch  as,  from  what  has  been  just 
explained,  the  sun  separates  itself  from  the  position  favourable  to 
the  action  of  the  disturbing  force  more  than  twice  as  rapidly  in 
qnadratores  than  in  syzygies. 

Fourth  Case. 
when  the  apsides  are  oblique  to  the  line  of  syztoies. 

8210.  Motion  of  the  apndes, — ^It  has  been  shown  that  when  the 
apsides  are  in  syzygy  the  disturbing  force  imparts  to  them  a  pro- 
gresaive  motion  at  the  rate  of  about  11^  in  each  synodic  revolution, 
and  thai  when  they  are  in  quadrature  it  imparts  to  them  a  regres- 
give  motion  at  the  rate  of  about  9^  in  each  synodic  revolution.  It 
might  therefore  be  expected,  that  if  the  line  of  apsides  assume  suo- 
eeesively  increasing  inclinations  with  the  line  of  syzygies,  from  0^ 
to  90^9  the  progressive  motion  of  11^  imparted  to  the  apsides  at 
Bjtjffea  would  gradually  decrease^  and  at  some  intermediate  incli- 


■  Mveen  0°  ni  90*  voold  become  nothbg,  tft«r  wttich  1U> 
m  inpwtcd  to  Ibe  ipndM  beowning  nercssive,  would  gtvliullj 
«  WKil  U  beoDOMS  9°  in  each  sjnodto  rcrolalioD,  when  tte 
"■fM^N  is  in  qnadratitie. 

tvondtticna  wliich  determine  the  eSect  of  each  eoiepoDa^ 
*-*~*SBg  tone  vpon  th«  direction  of  the  line  of  k^idot,  )S' 
^   _  >l  of  ■>ijg«,  be  clearly  fixed  in  Ihe  mind,  the  itndtnt' 

Vill  b««i  BO  Aficttlty  u  KO-  .Jiis  id  &ct  will  be  the  om. 

Fw  Ibis  pwpoM^  it  ■  ooIt  b        BnjF  to  draw  the  elliptic  whit  wiA 
■   ""         '  'l  ndioed  lo  ll™  jiae  of  eyzygica  at  sniccessiTely  ia- 

s.  Hid  to  enmine  and  compare  carefullj  (he  dideresl 
ed  by  eaeb  conipo'oent  of  the  distarbing  fume  npoa 
I  at  diferent  eloBgattoiu  from  the  euq,  in  each  positioD  of 
.  _  Im  IB  Rhiwa  to  Bjiygj.  It  will  be  foond  thu  when  tin 
•  air  afadea  nake*  a  xtry  gmall  angle  wiih  the  line  of  ijirpe^ 
A«  afert  of  tbe  disturbing  force  is  Tcr;  little  less  than  at  sTifgi^ 
ind  that,  iccotdjnglj,  a  prngressiT*  motion  is  impirted  lo  the  ip- 
aide^  \erj  little  lets  Ihia  11°;  and  on  tie  other  hand,  th&l  wbeD 
tbe  Hne  dF  apsides  makes  with  that  of  ^j^es  an  angle  bat  little 
leaa  than  !K>°,  the  regressiTe  motitHi  imparted  to  tbe  apsides  is  litlb 
kwtbaBS^ 

It  will  not  be  neoessaij  here  to  mnl^ply  the  details  of  lliit 
anatjsip,  bj  going  throagh  tbe  particulars  of  all  ench  caKs;  bolit 
inaj  be  OMfuI  to  illostnte  the  mode  of  investigating  them,  bj 
showing  the  effects  of  tbe  disturbing  force  on  tbe  line  of  apsidH, 
when  tbit  line  ja  inclined  to  that  of  syijgies  at  the  angle  of  &4* 
44  7",  at  which  tbe  efTects  of  tbe  disturbing  force  in  imparting  pr» 
gKBtire  and  r^reesive  motion  lo  the  apsides  are  compensatory,  or 
nearlj  so,  and  where,  therefore,  the  apsides  at  the  end  of  a  ajae&t  I 
tprolntion  bare  the  sanu  direction  as  at  its  co  mm  once  meat.  ' 

8211.    What  As  MsiA 
pwv«6  54*'44'r  if/taa 
I  Ae  pouU  of  eoH/wKfCm.— 
I  Let  o  o,  ;^.  g47,  be  lbs  fiaa 
I  rf  sjijgies,  o  being  tb«  pot 
1  of  eonjnnotioB  wbn  life 
moon'a  perigee  p  is  bi'Vt 
I  7*  before  it,  and  whet,  en»- 
seqnently,  the  apogee  a  it  it 
I  tbe    same    angtuar  iSstaMt 
I  from  tbe  point  of  otmoH&t 
The  line  of  npsKlM  viO 
in  ooincide  with  tbe  tint 
which  in  the  preoediog  dia- 


LUNAR  TIlKJ^nV.  .000 

through  8  at  right  angles  to  the  line  of  apsides,  will  lie  in  advance 
of  the  line  p'l  p,,  which  is  inclined  to  the  line  of  syzjgies  on  the 
other  side  of  it  at  the  angle  54^  44'  V, 

We  shall  consider,  ^r<^,  the  effect  of  the  radial,  and  secondly ,  of 
the  tangential  component. 

Firti,  From  what  has  been  already  proved  (3163),  it  appears 
that  a  positive  radial  component  will  render  the  apsides  regressive 
while  the  moon  passes  from  m  to  n,  and  progressive  while  it  passes 
from  n  to  m,  and,  consequently,  that  a  ncpitive  radial  component 
will  produce  a  contrary  effect.  By  combining  these  with  the  condi- 
tions which  determine  the  changes  of  sign  of  the  radial  component, 
explained  in  the  present  chapter,  it  may  bo  easily  inferred,  that  the 
apMdes  will  be  progrci^sivo,  while  the  moon  moves  from  p  to  v^  from 
m  to  P^3,  and  from  i^'i  to  n,  and  that  they  will  be  regressive  while 
the  moon  moves  through  the  arcs  Pj  m,  a  p',,  and  n  Pj ;  and  it  will 
be  easy  to  perceive  that  the  aggregate  length  of  these  arcs  is  not 
only  Dearly  equal,  but  that  their  distances  from  s  are  nearly  the 
same,  consequently  the  extent  of  the  orbit  through  which  the  radial 
component  renders  the  apsides  progressive,  is  nearly  equal  to  that 
through  which  it  renders  it  regressive.  The  effects  of  this  compo- 
nent are  therefore  compensatory. 

Secondly,  It  appears  from  what  has  been  proved  (3163)  that  a 
positive  tangential  component  renders  the  apsides  progressive  while 
the  moon  moves  from  |}  to  a,  and  regressive  while  it  moves  from  a 
to  Pf  and  that  a  negative  tangential  component  has  contrary  effects. 
By  combining  these  with  what 'has  been  proved  in  the  changes  of 
flign  of  the  tangential  component  in  the  present  chapter,  it  will  be 
easy  to  infer  that  this  component  will  render  the  apsides  progressive 
from  Pg  to  0,  from  a  to  p'l,  and  from  o  to  />,  and  regressive  from  p 
to  p2,  from  0  to  a,  and  from  ^^io  Q)  and  by  comparing  these  arcs 
as  before,  it  will  be  obvious  that  they  are  nearly  equal  in  length  and 
at  nearly  equal  distances  from  s,  and  that  consequently  the  effects 
of  this  component  of  the  disturbing  force  are  also  compensatory. 

It  follows  therefore,  generally,  that  in  this  position  of  the  moon's 
perigee  no  motion  is  imparted  to  the  line  of  apsides  in  a  complete 
synodic  revolution,  but  that  alternate  motions  of  progression  and 
regression  of  equal  total  amount  are  imparted  to  it  during  each 
revolution. 

3212.  When  the  moan's  perigee  t$  64°  44'  7"  behind  the  point 
of  opposition,  —  This  case  is  represented  in  Jig.  848,  the  moon's 
apogee  being  the  same  distance  behind  the  point  of  conjunction  o. 

We  shall,  as  in  the  former  case,  consider,  Jirst,  the  effect  of  the 
radial,  and  secondly,  that  of  the  tangential  component. 

First.  Upon  the  same  principles  as  were  applied  in  the  preceding 
case,  it  will  follow  that,  by  the  effect  of  the  radial  component,  the 
apsides  will  be  progressive  while  the  moon  moves  from  m  to  p',; 


ASTBOROMT. 


^P  j^^^^^^^^^^^^H^^^^k   '^^  tnooo  mores  from 

^^^^^^^^^^^^^^^^^^^^\  m,  from  p',  to  p',  and  frtm  a 

o  p, ;  and,  &s  befon,  if  tben 

ittts  be  compared  both  u  U 

length  sod  dieUDCo  from  t, 

it  will   be   foand    that  de 

I   effects  of  tbis  compoaent  on 

lincB  of  apstdea  an  com- 

I  pensatory. 

Sei^nd/j,.      By    the   umt 

'   principles  03  before,  it  will 

foUow  that,  bj  tbe  dbd  of 

_  the  taDgeDtialcoiDp«iat,lb 

L  Fig.  848.  apsides  will    be   fnffmdm 

K  '  while  the  mooD  tnomfin 

'      Ti  to  o,  from  p'l  to  P*,,  and  from  o  to  P,,  and  regresBiro  vhili  & 

moon  moves  from  m  to  Pj,  from  p'l  to  c,  and  froro  Pj  to  f,-  ui, 

u  before,  it  will  be  appareat  by  oomparing  tbeee  arra  thai  thM 

effect*  on  iLo  apsides  are  compensatory. 

It  follows   therefore,  as  before,  that  in  this  case   the  dilluin| 
force,  in  a  complete  synodic  revolution,  produces  no  cfaaoge  ill  lb 

^  position  of  the  line  of  apsides,  and  that  tbis  line  oseil]aie«  witb  ai 
mltemate  regressive  and  progresBive  jnotion  during  sueh  revolnlini. 
3213.  Whenpfrigniibi* 
14'  7"  bf/ore  the  point  rf 
opposition.  — In  thia  mm, 
bioh  is  represented  in  fj. 
19,  tbe  point  of  apogee  Bill 
i  at  tbe  Bamc  angular  dit- 
tance  before  the  point  of  «ttt- 
junction  c. 

Fir&l.   In  the  Nme  maoixr 
s  in  the  former  cose,  it  will 
I   beapparent  that  by  theeffccB 
I  of  the  radial  component  the 
]   line  of   apsidea  will   be  pro- 
gressive from  p',  til  p'y  from 
to  I'l,  and  from   P,  U>  a, 
and  regressire  Itoid  n  UtVi 
Fig.  849.  &om  V I  iota,  and  from  P,  to 

F,;  and,  in  the  eime  maa- 
ser  as  before,  the  efiecta  thnngh  these  area  will  be  shown  to  be 
OOmpeDsatory. 


LDXAR  TUEORT. 


601 


tengcntinl  component  the  apsides  will  be  rendered  pn^rossive  vLilo 
Iba  moon  moves  from  o  to  p',,  from  p',  to  c,  and  from  p,  to  P^  and 
that  they  vill  be  i^gressiTO  while  it  mores  from  Pj  to  o,  from  p',  to 
!>„  and  from  o  to  p,j  and  it  will  appcu  as  before  that  the  effects 
are  compensatory. 

It  follows,  therefore,  in  general,  as  in  the  former  cases,  that  in 
this  pcaitioQ  of  perigee  the  Hoc  of  apsides  suffers  no  change  of 
direction  from  the  action  of  the  disturbing  force  after  a  complete 
synodic  reToIution,  but  that,  during  Buc-h  revolution  as  before,  it 
oscillates  on  either  side  of  its  nieiin  position. 

8214.  When  perigee  it  54"  44'  7"  lehiml  conjunction. — In  this 
case,  which  is  represented  in 
fg.  850,  the  line  of  apogee  is 
at  the  same  angular  distaocD 
behind  the  point  of  opposition. 
Fint.  By  the  effects  of  the 
radial  component  the  apsiJca 
will  be  rendered  progressive 
while  the  moon   moves  from 


,  from  p'. 


»  to  P],  and  regressive 
I  while  it  moves  from  p,  to  Pi, 
I  from  n  to  P*!,  and  from  p'l  to 
i  before,  it  may  be 
'  shown  that  the  effects  in  tbcso 
cases   respectively  are    com- 
pensatory. 

Bfr  SSI-  SecmiUi/.  By  the  effects  of 

the  tangential  force  it  appears, 
in  like  manner,  that  the  apsides  will  be  rendered  progressive  from  o  to 
Vu  from  p'l  to  c,  and  from  p^  to  Pg,  and  regressive  from  P|  to  o,  from 
p'l  to  p'„  and  from  o  to  Pj;  and  that,  iu  like  manner,  these  effects 
mre  compensatory. 

It  follows,  therefore,  that  in  this  po>^ition  of  the  moon's  perigee 
no  effect  is  produced  by  the  disturbing  force  upon  the  direction  of 
the  line  of  apsides  after  a  complete  synodic  rcvoluiion,  bat  that  line, 
u  before,  during  such  rcvoInUon  oscilhitcs  on  the  one  sido  and  on 
the  other  of  its  mean  position. 

8215.  Summarif  o/tim  motions  of  the  aptiiitt. — After  what  has 
been  explained  above,  the  motion  of  the  line  of  apsides  iu  all  its 
positions  with  relation  to  the  line  of  syzygies  may  be  easily  inferred. 
It  must  be  remembered  that  the  lines  of  syzygies  and  apsides  being 
both  affected  with  a,  mean  progroasivc  motion,  thatuf  syzygies,  how- 
ever, being  much  more  rapid  than  Ihitt  of  apsides,  it  will  fallow  thai, 
the  lino  of  Bjzjgics  .iftL-r  each  successive  synodic  revolution  will 
giiin  npon  the  line  of  upsides,  advancing  uonstaatly  before  It. 


ASTROSOMT. 


I* 

^^r     Let  DS  tlien  imagine,  first,  tbat  the  tiioi>&'e  pengee  i 

^Hiyiiiiction. 

^^^  Tlie  lino  of  ap-^itii'S  will  tiien,  according  to  what  bas  hm 
^^  proved,  after  ooe  synodic  revolution  be  :lfi'ecl«^l  by  a  prcgnssite 
motion.  After  the  next  aynodic  revolution  tbe  liuc  of  trxypts  will 
have  advanced  before  tbat  of  apeides,  nod  the  progressive  nioiioQ 
ioiparteil  to  tbc  latter  will  be  leas  tbao  before,  md  afler  mch  anis 
ce*sivQ  synodic  revolution  tbe  line  of  eyzygios  advancing  furlberind 
further  iu  advance  of  the  lino  of  ipaides,  the  progreswre  motion  im- 
partud  to  the  Ittier  will  becomo  le^s  and  less  until  tbe  line  of  ijij- 
giea  having  advanced  to  the  distanee  of  o4°  44'  7"  from  the  line  uf 
apeidca  the  progressive  motioa  cea^o?,  and  the  line  of  apsidM 
b«caraes  etatioonry. 

After  ibis,  tbe  line  of  syiygics  advancing  to  a  still  greater  ingii- 
lar  distance  from  the  apsides,  the  motion  imparted  aft^r  each  ki> 
Ixn'i'-n  to  the  latt«r  becomes  regressive,  and  its  regressive  atnonsl 
itiercaties  every  successive  synodio  revolution  until  tbe  line  of  aptda 
comes  into  quadrature,  when  the  regressive  motion  of  the  apadn 
produced  in  a  complete  synodto  revolution  becomes  &  nuudttU' 
After  tbifl  vrben  the  lino  of  sjxj^ea  has  advanced  more  thu  90° 
from  the  line  of  op-sides  the  regressive  motion  imparted  in  eacb  re- 
VolutioD  becomes  lesa  nud  less  UQtil  the  line  of  apsides  has  approach e'l 
within  54"  44'  T"  of  opposition,  when  tbe  regressive  motion  vanishea 
and  the  line  of  apsides  again  becomes  stationary;  after  this  it 
becomes  pmgrcssive,  tbe  amount  of  its  progressive  motion  con- 
tinually increases  until  the  point  of  perigee  comes  into  oppositioa, 
where  it  is  a  maximum.  While  pciigre  passes  successively  from 
opposition  to  conjunction  tbc  Bauie  variations  of  the  motion  of  the 
apsides  takes  place,  but  in  a  contrary  order. 

I'hus  it  appears  that  the  are  of  each  synodic  revolution  throujtb 
■which  the  disturbing  force  produces  a  progressive  effect  b  51°  44'  7" 
X  2^  1IJ9°  28'  14"j  while  tbo  arc  through  which  it  producea  a 
regressive  motion  is  only  35=  15'  53"  X  2  =  70*  31'  46".  Tb« 
predominance  of  the  progressive  over  the  regressive  effect  result! 
therefore  from  the  greater  range  through  which  the  former  b  pro- 
duced, combined  with  the  fact,  tbat  within  tbb  range  tbc  iolcnsity 
of  the  disturbing  force  is  equal  to  twice  its  intensity  through  tbe 
shorter  arc,  over  which  the  motion  is  regressive. 

3216.   EgtclKof  the  ,/Ulwrbinif  force  iijion  (Ac  eerenlrieity.- 
remains  now  to  examine  the  effects  produced  upon   the  eccentricity 
of  tbe  moon's  orbit  by  tbe  disturbing  force  when  the  line  of  apsides 
has  (be  same  positions. 

It  has  been  already  shown,  that  when  the  line  of  .ipsidcs 
Wzygics  and  quadratures,  the  effects  of  the  disturbing  force  upon 
the  eccentricity  are  compensatory,  and  that  this  element  at  tb«-e 
points  umlcrgoea  uo  change  of  magnitude.     If,  therefore,  ii  be 


LUNAR  THEORY.  603 

subject  to  no  variation,  it  is  plain  that  at  these  points  it  must  be 
cither  a  maxinmm  or  a  miuimum,  since  it  is  neither  on  the  increase 
or  dt.'crease. 

3217.  When  perif/ce  is  54°  44'  7"  before  the  point  of  conjunction. 
—  We  shall  consider  as  before,  ^r*/,  the  effects  of  the  radial,  and 
r^ouiUi/y  those  of  the  tangential  component  upon  the  eccentricity. 

First,  It  appears  from  what  has  been  proved,  that  a  positive 
radial  component  will  cause  the  eccentricity  to  diminish,  while  the 
moon  moves  from  perigee  to  apogee,  and  to  increase  while  it  moves 
from  apogee  to  perigee,  and  that  a  negative  radial  component  will 
have  a  contrary  effect.  It  will  follow,  therefore,  in  this  case  by  com- 
bining this  principle  with  the  conditions  determining  the  change  of 
sign  of  the  radial  component  explained  in  the  present  chapter,  that 
it  will  cause  the  eccentricity  to  increase  while  the  moon  moves  from 
pj  to  p'l,  fig,  847,  and  to  decrease  while  it  moves  from  p',  to  Pj. 
Bat  it  will  be  evident  by  comparing  the  lengths  of  these  two  arcs, 
and  their  distances  from  8,  that  the  effect  of  the  disturbing  force 
will  be  much  greater  in  the  former  than  in  the  latter,  and  conse- 
qnently,  that  the  increase  of  the  eccentricity  in  the  former  must 
greatly  exceed  the  decrease  in  the  latter,  and  therefore,  that  the 
effect  of  the  radial  component  in  an  entire  synodic  revolution  will 
be  to  increase  the  eccentricity. 

Secondljf,  It  appears  from  what  has  l>een  explained  that  the 
effect  of  a  positive  tangential  component  will  be  to  decrease  the 
eccentricity  while  the  moon  moves  from  in  to  n,  and  to  increase  it 
while  it  moves  from  n  to  m,  and  that  a  negative  tangential  com- 
ponent will  have  contrary  effects.  Hy  combining  this  with  the 
changes  of  sign  explained  in  the  present  chapter,  it  will  follow  that 
the  eccentricity  will  be  increased  while  the  moon  moves  from  pj  to 
«iy  from  o  to  p'2)  and  from  n  to  c,  and  that  it  will  be  decreased 
while  it  moves  from  c  to  P2,  from  m  to  o,  and  from  i^^  ^  ^y  ^^^  ^Y 
comparing  these  arcs  both  with  relation  to  their  extent  and  their 
distance  from  s,  it  will  be  apparent  that  the  increase  of  the  eccen- 
tricity must  exceed  the  decroat^e,  and  that  consequently  the  result  of 
a  whole  synodic  period  will  be  to  cause  the  eccentricity  to  increase. 

It  appears,  therefore,  that  both  components  of  the  disturbing  force 
in  thb  position  of  the  line  of  apsides  will  cause  the  eccentricity  to 
increase  during  each  synodic  revolution,  being  subject  nevertheless 
during  such  revolution  to  alternate  increase  and  decrease. 

3218.  When  ptrii/'C  is  54°  44' 7"  W///t(/  opposition.  —  First. 
By  the  effects  of  the  radial  conipHient  it  m.'iy  be  shown,  as  before, 
that  the  eccentricity  will  ton>taiitly  incroaso  while  the  moon  moves 
from  P,  to  v\.ffj.  ^^4'^,  niul  an  ill  continually  decrease  while  it  moves 
from  p',  to  P„  and  it  will  be  obvious,  from  crm^iJeriog  the  mag- 
nitude of  these  arcs  and  their  disUinces  from  8,  that  the  decrease  of 
the  eccentricity  will  considerably  exceed  the  increase;  and  that^ 


ASTKuNOMT. 

tbis  oomponent  of  the  disturbing  force  vHIg 

.-.olution,  caase  the  eccfintriotty  to  dePTeaae. 

oniUi/.      By   the   cffccls   of   Ihc   tangnutial   force,   it  maj  be 

nil,  as  before,  that  the  cccenlridty  n-ill  be  increasod  vbile  tha 

on  movea  from  Pi  lo  o,  from  m  to  p'j,  and  from  c  to  n,  and  tbst 

*ill  bo  deereascd  while  the  moon  moyca  from  n  lo  Ti,  from  o  to 

id  from  v\  to  c,  aod  by  cooiporing  these  anrs  it  vill  be  obrioas 

ho  tnUl  decrease  vill  exceed  the  total  iocrease. 

results  therefore  from  this,  that  both  componeDts  of  the  S\>- 

■j?  force  in  this  position  of  perigee  causes  the  eoceatricity  to 

complete  Bynodic  revolution. 

icH  yeriyfe  U  54°  44'  7"  hi  fore  oj'pnntion.  —  Finl.  — 
^^j  .Jt  BuowD  na  before,  that  the  radial  coniponeot  wilt  eau^  the 
^ntrioily  continQsily  to  increasn  nbilc  the  moon  moved  itnta  f, 
Vf,Jig.  840,  and  to  deereaae  continually  while  it  moves  from  Pi 
J  p*,,  and  by  eompnring  these  arcs  as  before,  it  will  be  appued 
bftt  the  inerensc  grently  exceeds  the  decrease,  and  Iherefoie,  lo  lie 
I  relates  to  the  radial  component,  the  eccentricity  duiiog  nch 
jrnodia  revolution  will  suffer  an  increase. 

Second^.  By  the  effects  of  the  tangential  component,  the  «eefr 
tricity  will  increase  while  the  moon  moves  from  c  to  p,,  from  »  lo  o 
and  from  I'',  to  m,  and  will  decrease  while  it  moves  from  p,  tn  i, 
from  o  to  I'iBnd  from  m  to  C,  and  by  comparing  those  arcs  as  before, 
it  will  be  apparent  that  the  increase  will  ezeeed  the  decrease. 

It  follows,  therefore,  that  the  effect  of  both  components  in  tbi) 
pofiitJon  of  tbe  apsides  during  an  cutiro  synodic  revolution  is  to 
cause  the  eccentricity  to  increase. 

3220.  When  perii/ce  u  54"  44'  7"  bt-hi'tid  ronjunctwn.  —  FirtL 
In  thia  case  it  may  be  shown  that  the  radial  component  will  cana 
the  eoeentricity  to  decrease  while  tho  moon  movea  from  f,  to  p". 
Jig.  S50,  and  to  increase  while  it  toovcs  from  v',  to  r„  and  by  cnni- 
paring  these  ares,  it  will  appear,  ns  before,  that  tbe  decrease  will 
greatly  exceed  the  increase,  and  that,  therefore,  on  the  wbole,  is 
each  synodic  revolution  tbe  radial  eomponcnt  will  cause  tbe  ecwo- 
tricity  to  decrease. 

Second)!/.  By  the  effect  of  the  tangential  force,  the  eecentridlj 
win  increase  while  tbe  moon  moves  from  m  to  P,,  from  o  to  n,  and 
from  P*!  to  c,  and  will  decrease  while  it  moves  from  P,  to  o,  fron  * 
to  p'g,  and  from  0  to  fn,  and  by  comparing  these  arcs  as  before,  il 
vill  be  apparent  that  tbe  decrease  will  exceed  tbe  increase. 

It  follows,  therefore,  that  the  result  of  the  wbole  disturbing  force 
in  thit  position  of  the  apsides  ia  to  cause  a  decrease  of  the  ecccn- 
trieity  in  each  synodic  revolution. 

3^21.  £.rlreme  anil  viean  valves  of  frcrmtrinly.  —  It  appeals, 
tnerefore,  generally,  that  when  perigee  is  in  eonjuDctinn,  tlie  ecccn- 
trjcily  does  not  vary,  and  that  as  the  point  of  oonjunciion  rcce^n 


LUNAR  THEORY.  C05 

from  perigeCy  tbe  eccentricity  decreases,  and  continues  to  dccreaso 
nntil  tbe  point  of  conjunction  is  90*^  from  perigee,  when  tbe  eccen- 
tricity' again  becomes  stationary,  its  decrease  ceasing.  Wben  tbo 
conjunction  advances  more  tban  90°  from  perigee,  tbe  eccentricity 
again  increases  and  continues  to  increase  until  tbe  point  of  conjunc- 
tion has  moved  180°  before  perigee,  wben  tbe  increase  ceases. 
After  tbis,  tbe  eccentricity  again  decreases,  and  continues  to  decrease 
until  tbe  point  of  conjunction  gains  anotbcr  quadrant  on  perigee, 
wben  tbe  increase  ceases  and  tbe  decrease  commences,  wbicb  is  con- 
tinued tbrougb  anotber  quadrant.  It  appears,  tborcfore,  tbat  tbe 
eccentricity  is  a  maximum  wben  tbe  apsides  arc  in  quadrature,  and 
a  minimum  wben  tbey  arc  in  coDJuDction,  and  tbat  consequently  it 
gradually  increases  wbile  tbo  apsides  move  from  conjunction  to 
quadrature,  and  gradually  decreases  wbile  tbcy  move  from  quadra- 
ture to  conjunction. 

If  ^  express  tbe  value  of  tbe  eccentricity  wbile  tbe  apsides  are 
in  quadrature,  and  t!*  tbeir  value  wben  in  conjunction,  tbe  mean 
Talue  being  e,  it  is  found  tbat 

e':c:e"=  1-50:  1-25:  100; 

80  that  tbe  extreme  range  of  variation  of  tbe  eccentricity  of  tbe 
moon's  orbit  is  as  3  to  2. 

IFFfiCTS  OF  THE  DISTURBING  FORCE  UPON  THE  LUNAR  NODES  AND 

INCUNATION. 

From  wbat  bas  been  proved  in  general  (3158.  tt  8eq.)y  it  will 
appear  tbat  wben  tbe  moon  is  less  distant  than  tbe  eartb  from  tbe 
ran,  tbe  ortbogonal  component  of  tbe  disturbing  force  will  bave  a 
tendency  to  draw  it  out  of  tbe  plane  in  wbicb  it  is  moving  towards 
the  side  on  wbicb  tbe  sun  is  placed,  and  tbat  wben  tbe  moon  is 
more  distant  tban  tbe  eartb  from  tbe  sun,  tbe  ortbogonal  component 
will  have  a  tendency  to  draw  it  out  of  tbe  plane  in  wbicb  it  moves 
to  the  side  opposite  to  tbe  sun. 

Bat  it  bas  also  been  proved  tbat  tbe  nodes  will  bave  a  progres- 
rive  or  regressive  motion,  according  to  the  direction  of  tbe  ortbogonal 
force  in  tbe  successive  quadrants  of  its  orbit  between  node  and 
node. 

It  will,  therefore,  be  necessary  to  consider  successively  tbe  effects 
of  the  disturbing  force  in  tbe  various  positions  wbicb  tbe  lines 
of  sjzygies  and  quadratures  may  assume  with  relation  to  tbe  lino 
of  nodes. 

First  Case. 

8222.    When  Uie  line  of  ai/zyrjies  u  in  the  line  of  nodes. — In  this 
it  is  evident  tbat  the  ortbogonal  component  of  tbe  disturbing 

51* 


ASTRONOMT, 


i>e  notliiDg,  since  tbe  wbolc  tLttraction  of  the  ma  la  ii  tiM 
1  i-lie  moon's  orhii.,  and,  coiutqnenllj,  no  part  of  Uie  attn^ 
iH  act  at  tigbt  angles  to  that  plauu. 

Second  Case. 
1'2S,    When  the  line  of  noiJa  is  in  qaadratart. — Let  A.  CO  A 
851),  rcpreKDt  the  moou's  orbit,  and  a  D  A  tho  ecliptic  seeo  it 


Fig.  SSI, 

ovn  plane  ami  projected  into  a  straight  line.  Let  a  b«  t!i< 
ending  and  d  tbe  dcaeonding  node,  and  let  the  point?  of  sytj^ 
supposed  to  be  at  C,  and  O  tbe  points  of  the  moon's  orbit  mirt 
tant  from  the  ecliptic,  while  tho  points  of  quadraturo  p,  and  r"] 
■ic  at  tbe  Dodca  a  and  d. 

It  has  been  already  shown,  that  when  tbe  moon  is  in  qaadntorci 
iho  whole  dirturbing  force  la  radial,  nnd  being  directed  to  the  ?nii 
and  in  the  plane  of  tbe  iiioiin's  orbit^  it  can  have  no  compoEent  ptr- 
pendicnlor  to  that  plane,  and  therefore  tbe  disturbine  force  at  these 
points  can  have  no  tcndcDcy  to  change  the  plane  of  the  moon's  orbit. 
While  the  nif)on  moves  frora  A  through  c  to  n,  its  distance  from 
the  EUD  being  less  than  that  of  the  earth,  and  the  sun  being  eup- 
poscd  to  be  below  the  plane  of  the  orbit,  the  orthogonal  componeat 
of  the  disturbing  force  will  everywhere  have  a  tendency  to  draw  the 
moon  nearer  to  the  plane  of  the  ecliptic  A  B ;  and,  according  to  whit 
baa  been  proved  C^>I<>1),  It  follows  that,  through  the  entire  semi- 
eirele  Acu,  the  orthogonal  component  will  impart  a  regressive 
notion  to  the  line  of  ni>i]cs,  and  from  a  to  c,  it  will  cause  the  inch- 
nation  to  decrease,  and  from  c  to  D  to  increase. 

While  the  moon  moves  from  D  through  o  to  A,  being  at  a  greater 
distance  than  the  earth  from  the  sun,  the  orthogonal  component  has 
a  tendency  to  repel  tbe  moon  further  from  tbe  sun,  which,  in  thi^ 
case,  will  have  the  effect  of  drawing  the  moon  from  the  semicircle 
SO  A  towards  the  plane  of  the  ecliptic  da;  and,  consecjnenlly, 
according  to  what  has  been  proved  (SlCl),  its  efTeels  will  be  to 
impart  a  rcgrcs,sive  motion  to  the  line  of  nodes  throughout  the  seaii- 
eircle  noA,nnd  to  cause  the  inclination  to  decrease  from  D  to  0, 
and  to  iucrea.so  from  o  to  A. 

Thus  it  appears  thai,  in  (his  position  of  tbe  lines  of  (juadrature 
and  syzjgies,  a  continual  motion  of  regression  is  imparled  to  the 
nodes,  eit-ept  at  the  points  a  and  d,  where  the  effect  is  nothing. 
(Jnramencing  from  a,  the  regression  of  the  nodes  continually  in- 


LUNAR  THEORY.  607 

creases  with  tlie  increase  of  the  orthogonal  force,  until  the  moon 
arrives  at  c,  when  the  regression  is  a  maximum ;  it  then  decreases 
and  continues  to  decrease  until  the  moon  arrives  at  D,  where  it 
vanishes ;  it  again  increases  from  D  to  o,  where  it  is  again  a  maxi- 
mum,  and  decreases  from  o  to  A,  where  it  vanishes. 

The  change  of  inclination  produced  by  the  disturbing  force  being 
nothing  at  a,  the  inclination  decreases  continually  from  A  to  0,  and 
increases  from  c  to  D.  It  is,  therefore,  a  minimum  at  c.  After 
passing  D)  it  decreases  from  D  to  o,  and,  consequently,  is  a  maximum 
at  D.  After  passing  o,  it  increases  from  o  to  A,  and  is,  consequently 
a  Diinimum  at  O. 

-Thus  it  appears  that  the  inclination  is  least  at  conjunction  and 
opposition,  and  greatest  at  quadratures,  —  that  is,  in  the  present 
position  of  the  lines  of  syzygies  and  quadrature,  it  is  least  when  the 
moon's  latitude  is  greatest,  and  greatest  when  the  moon's  latitude 
b  nothing. 

TuiRD  Case. 

3224.  When  the  line  of  ^yzygxci  is  less  than  90°  he/ore  the  line 
of  nodes,  —  This  case  is  represented  in^^.  852,  where,  as  before,  A 


Fig.  852. 

ascending  and  d  the  descending  node,  o  and  o  being  the  extremities 
of  the  line  of  syzygies,  and  P2  and  p'2  those  of  the  line  of  quadratures, 
the  points  £  and  e'  being  those  at  which  the  moon's  orbit  is  most 
distant  from  the  ecliptic,  and,  therefore,  the  middle  points  of  the 
semicircles  a  d  and  d  a. 

From  what  has  been  explained,  it  is  evident  that  the  orthogonal 
component  at  p,  and  p'2  will  be  nothing,  since  at  these  points  the 
disturbing  force  is  radial ;  and  it  has  been  already  shown  that  at  the 
nodes  A  and  d  the  orthogonal  component  is  also  nothing. 

While  the  moon  moves  from  p'2  through  A  and  0  to  P2  the  dis- 
turbing force  tends  to  draw  it  from  the  plane  of  its  orbit  towards 
the  ecliptic,  and  while  it  moves  from  P2  through  D  and  o  to  p',  the 
disturbing  force  tends  to  draw  it  up  from  the  plane  of  her  orbit ; 
therefore  in  moving  from  p'2  to  A  the  disturbing  force  draws  it  from 
the  plane  of  the  ecliptic,  and  while  it  moves  from  A  to  Pj  through  0 
and  E  the  disturbing  force  draws  it  towards  the  plane  of  the  ecliptic. 

While  the  moon  moves  from  pg  to  D  it  draws  the  moon  from  the 
plane  of  the  ecliptic,  and  while  it  moves  from  D  through  0  and  J$ 
to  Ft  it  draws  it  towards  the  plane  of  the  ecliptic. 


ASTROSCMV. 

ng    icGO  results  nith  wbal  bu  been  prmcd  in  :il61, 

tbitt  iihile  tbo  moon  moTea  from  A  to  r,  ftod  inm  s 

^.^^ivfl  .notion,  aod  wliUe  it  moves  from  p,  to  d  suJ  bom 

A  a  progratfiive  motion,  is  imparted  lo  tho  line  of  nodct. 

I.  will  apiieai*  \iy  inspection  of  the  figure,  iLat  tlie  an;  A  P,  ii 

T  than  the  bio  PiD,  and  tliat  tho  arc  dp'i  is  greater  thui  i',i, 

Bonseqnently ,  it  follows  that  ite  sam  of  the  arcs  tbraugli 

a  retrogiadf  motion  is  imputed  is  much  greater  than  tbe  nim 

t  tLrou:..  ch  a  progres^vc  motion  is  impxrled.'uid 

t —  .-ynodio  rcTolutioQ  has  been  coiupli-tal,  lEta 

I  nbole  will  hive  retrograded. 

ti  GJiio,  from  wbat  has  been  stated  that  &om  t'i  to  i:  tsd 

I*.  bq  inultnaUon  will  decrease,  and  from  E  to  r,  and  fram 

increase.     But  since  tbe  arcs  p'.e  and  Pis' ore  r- 

3  J        or  than  e  p,  and  £'  p'„  tbe  Eum  of  tbe  funnei  will 

jn-dtcr        D  tbe  Bum  of  tbe  latter,  and  consequentlj  tbe  ara 

ongb  nbicn  tbe  inclination  decreases  being  much  greater  thu 

se  tbrnu^b  whicb  it  increases,  tbcre  vJII  be  on  tbe  whole  a  dr- 

crease  of  tUc  iuL-Iioation   uftor  tbe   ejn&die   revolution  liis  Wu 

completed. 

Fourth  Case. 

3225.  Whm  Ike  line  of  ty^tjgies  u  more  than  90°  bffore  the  iki 
of  voJei.  —  In  tbis  case  while  the  moon  moves  from  !■',  to  P^^fl- 
853,  the  disturbing  force  bas  a  tendency  to  draw  it  down  tonink 


Fig.  853. 

the  ecliptic,  and  from  r,  to  p",  it  bas  an  opposite  effect.  It  follows, 
therefore,  that  wbiio  the  moon  moves  from  v't  to  i>  tbe  line  of  nodes 
regresses,  and  while  it  moves  from  u  to  r^  it  progresses.  While  ii 
moves  from  r,  lo  A  it  regresses,  and  while  it  moves  from  A  to  i^i  it 
progresses. 

iiy  comparing  the  lengths  of  these  arcs,  as  before,  it  will  appear 
that  those  where  regress  is  produced  eseccd  those  where  progress  ii 
produced,  and  it  follows,  therefore,  that  in  an  entire  sjnodio  revolu- 
tion the  ]ine  of  nodes  regresses.  It  also  follows  that  while  the 
moon  moves  from  p",  to  £  and  from  Pj  to  e*  the  incUnatiou  is  de- 
creased, and  while  it  moves  from  e  to  Pj  and  from  £*  to  p',  the 
inclination  is  increased,  and  bj  comparing  the  magnitudes  of  these 
arcs  It  will  be  evident  that  in  tbe  entire  eynodio  revolution  an  ia* 
crease  of  the  inclination  takes  place. 


LUNAR  THEORY.  W9 

The  Bame  conclusions  would  follow  if  ti  '.  moon's  orbit  were 
supposed  to  be  inclined  to  the  ecliptic  in  the  other  direction. 

Thus  it  appears  in  general  that  when  the  Hne  of  nodes  is  in 
ejzygies  no  change  takes  place  cither  in  the  position  of  that  line  or 
iu  the  magnitude  of  the  inclination.  While  it  passes  from  sjzjgies 
to  quadrature  the  line  of  nodes  regresses  and  the  inclination  dimin- 
ishes ;  when  it  is  in  the  line  of  quadratures  the  line  of  nodes  re- 
gresses, but  the  inclination  is  unchanged;  and  when  it  is  between 
quadratures  and  syzjgies  the  line  of  nodes  still  regresses  and  the 
inclination  is  increased.  Thus  when  the  sun  has  described  in  its 
apparent  motion  nearly  one  half  a  revolution  of  the  ecliptic,  there 
is,  on  the  whole,  a  regression  of  the  node  and  an  alternate  increase 
and  decrease  of  the  inclination ;  and  during  its  motion  through  the 
other  half  of  the  ecliptic  similar  changes  are  produced  in  the  same 
order.  It  follows,  that  the  inclination  is  a  maximum  when  the  line 
of  nodes  is  in  syzygies,  and  a  minimum  when  it  is  in  quadratures. 

3*226.  General  summary  of  the  lunar  inequalities. — 
From  all  that  has  been  stated  in  the  present  chapter  it  appears  that 
the  principal  lunar  inequalities  are  as  follows : — 

1**.  The  annual  equation,  which  depends  on  the  variation  of 
the  disturbing  force  due  to  the  varying  distance  of  the  earth  from 
the  sun  in  its  elliptic  orbit. 

2^.  The  variation,  which  depends  on  the  difference  of  the 
disturbing  force  arising  from  the  synodic  place  of  the  moon. 

3°.  The  acceleration  of  the  moon's  mean  motion,  depend- 
ing on  the  effect  produced  upon  the  disturbing  force  by  the  secular 
variation  of  the  eccentricity  of  the  earth's  orbit. 

4?.  The  parallactic  inequality,  depending  on  the  difference 
between  the  disturbing  forces  of  the  sun  in  conjunction  and  oppo- 
sition. 

5**.  The  equation  of  teie  centre,  an  inequality  which,  how- 
ever, cannot  properly  be  called  a  perturbation,  inasmuch  as  it  depends 
only  on  the  elliptic  form  of  the  lunar  orbit,  which  would  subsist 
without  any  disturbing  force. 

6°.  The  alternate  progression  and  regression  of  the 
apsides,  depending  on  the  synodic  place  of  the  moon. 

7°.  The  mean  progression  of  the  apsides,  being  the  excess 
of  the  progression  over  the  regression  during  a  synodic  period. 

8**.  The  variation  of  the  eccentricity,  depending  on  the 
synodic  place  of  the  moon. 

0**.  The  alternate  regression  and  progression  of  the 
MODES,  arising  from  the  effect  of  the  orthogonal  component  of  the 
disturbing  force. 

10°.  The  mean  regression  of  the  nodes,  arising  from  the 
excess  of  the  regressive  over  the  progressive  motion  during  the 
pynodic  revolution. 


I 


ASTHOXOMT- 
ALTEKNATE  INCMEABE  ASD  DECREASl  OWVttiW 

!  oombinetltffiwlfiof  IJicseveatli  and  eighti  of  tic  preceding  iti' 
uticB  depi'uding  on  the  s}*Dodic  position  of  perigee  are  cnlltd  tr 
.fiiDmon  Dame,  evfction.  Tbis  ie  the  greatest  inequality  to  nliieb 
luono'a  pkoc  ia  subject,  prodaciog  a  Tanatioa  ia  the  nioou'i 
gilude,  the  estreme  range  of  >flii(.-li  is  2  J".  It  vm  diBOOTcrodb; 
rMiTAtioD  nbout  ibe  year  A.  D.  140,  by  Plolcmj. 
Tbe  ineqnalily  arising  from  iLo  nltcrnnte  regreBGion  and  pro- 
«noD  of  tlie  nodes  and  the  alternate  increase  and  decrease  of  ibe 
liottljon  were  discovered  by  TytUo,  about  tbe  year  1590.  This 
Iho  greatest  of  tbe  ineqaalitics  which  nfTuct  tba  moon'i  latitude, 
f  raoge,  however,  is  limiteJ  to  about  IC. 

8227.  Other  liiscr  inequalilirs. — The  precijding  inequalities, 
•nnerous  ae  tbey  tuoj  seem,  are  neverlbeless  only  the  principal 
eta  of  lunar  perturbations.  There  arc  many  others  vliicb  depcod 
difiercnees  of  intensity  of  the  disturbing  force,  which  have  not 
A  been  taken  into  account;  for  exuciple,  tbe  rate  of  the  pn> 
Ksion  of  the  upsides,  as  well  as  tbe  diminution  of  the  lunar  orbit, 
iSccled  by  the  difference  of  the  intensities  of  tbe  disturbing  forca 
.1,  conjunotioD  and  oppoeitioo. 

TIju  Ynpi:iri,in  of  tW  inltnsitj  of  this  f,ir<-c  (!i.g  to  tbe  Dcccntrlcilf 
of  the  carlb'a  orbit,  affects  abo,  to  a  sensible  extent,  the  variation 
of  the  motion  of  tiie  apsides,  and  tlio  variation  of  tbe  eccentricity. 

The  parallactic  inequality  is  also  atfected  by  the  position  of  the 
moou  in  relation  to  the  apsides  of  the  earth's  orbit. 

There  arc  itl.so  several  small  inequalities  affecting  the  plane  of 
the  moon's  orbit,  depending  on  the  cecenlrieiiy  of  tbe  orbits  of  llie 

In  fact,  the  niimborof  corrections,  or  equations  as  they  are  called, 
which  are  applied  to  the  moon  in  tbe  eoiuputatioa  of  its  true  place 
are  not  less  than  forty. 


CHAP.  xxir. 

TUEORY  OP  THE  JoVIAN    SvSTEM. 

32Cft,  AiiaJnij;/  of  (l,c  Jovian  tolhct'-rrei'Irinlsi/Mcm. — What  the 
moon  is  to  the  cjirtli,  each  of  the  Jovian  satellite's  is  to  Jupiter,  and 
the  snn  stands  in  the  same  phywieal  relation  to  both  these  systems. 

Jt  might,  therefore,  be  e.\-|ii'eled  that  the  same  series  of  inequali- 
ties which  arise  from  the  di.sturbing  forec  of  the  sun  acting  on  the 
earth  and  moon,  wouliJ  bo  equally  r''<'*'"CL'd  in  the  ease  of  each  of 


JOVIAN  THEORY.  611 

Jupiter's  satellites,  and  that  sacli  distarbances  do  act  and  that  like 
inequalities  are  produced  cannot  be  doubted. 

3229.  Why  the  same  inequalities  are  not  manifested,  —  But 
when  we  come  to  calculate  the  quantities  of  these  inequalities  in  the 
case  of  Jupiter,  they  are  found  to  be  so  utterly  insignificant  in  their 
nnmerical  values,  that  they  are  altogether  incapable  of  being  appre- 
ciated by  the  nicest  observation,  except  in  the  case  of  the  fourth 
satellite,  in  whose  motions  inequalities  of  very  minute  amount, 
analogous  to  the  moon's  variation,  evection,  and  annual  equation 
are  barely  observable,  the  inequality  corresponding  to  the  annual 
equation  in  this  case  amounting  to  no  more  than  2',  and  the  other 
inequalities  being  much  less. 

The  cause  of  this  insignificant  amount  of  the  disturbing  force  of 
the  sun  will  be  easily  understood. 

The  whole  Jovian  system  subtends  at  the  sun  a  visual  angle  less 
than  one-half  the  apparent  diameter  of  the  sun  as  seen  from  the 
earth,  and  consequently,  lines  drawn  from  the  sun  to  all  points  in 
that  system  will  be  practically  parallel,  and  with  the  exception  of 
the  fourth  satellite,  as  already  mentioned,  the  variation  of  the  dis- 
tances of  the  different  satellites  from  the  sun  is  so  utterly  insignifi- 
cant, compared  with  the  whole  distance,  that  the  corresponding 
Tariation  of  the  intensity  of  the  sun's  attraction  upon  the  satellites 
and  the  central  body  is  so  minute  as  to  produce  no  perceptible  dis- 
turbing effect.  In  a  word,  the  sun's  attraction  upon  the  Jovian 
system  may  be  regarded  as  a  force  acting  with  equal  intensities  in 
parallel  lines  on  all  parts  of  the  system,  exactly  as  the  force  of 
gravitation  would  act  upon  any  small  group  of  heavy  bodies  placed 
near  the  surface  of  the  earth. 

3230.  Mutual  perturbations  of  the  satellites. — In  this  secondary 
system,  therefore,  contrary  to  what  might  be  expected,  there  is  no 
analogy  whatever  to  the  lunar  theory,  and  all  the  perturbations 
which  are  observable  are  those  due  to  the  mutuaT  gravitation  of  the 
four  satellites  one  upon  another. 

The  investigation  of  these  perturbations  is  greatly  simplified  by 
the  following  conditions  which  prevail  in  the  system : 

First.  That  the  undisturbed  orbits  of  all  the  satellites  are  very 
nearly  circular,  those  of  the  first  and  second  being  exactly  so. 

Sfx'ondly,  That  they  arc  very  nearly  in  the  common  plane  of  the 
planet's  equator;  and 

Thirdly.  That  the  mean  motions  of  the  three  inner  satellites 
are  commensurable  in  the  remarkable  manner  already  expressed, 
(2762.) 

3231.  Retrogression  of  die  lines  of  conjunction  of  the  first  three 
tatellites.  —  As  some  of  the  most  remarkable  consequences  of  the 
mutual  disturbing  forces  in  this  system  depend  upon  the  relation 
between  the  mean  motions  of  the  three  inner  satellites  just  men.- 


ASTROSOMT, 

Bhall,  in  the  first   instance,  ciplaiD  tho  et[-.ti  of  tibii 

upon  lie  euocessivo  positions  ansnoied  by  their  linai  of 

Let  tbc  throe  inner  ))atfllitc9  be  ex- 
pressed by  s',  s",  b'",  nod  their  periods  bj 
p,  I*",  r"'. 

By  the  line  of  eonjancUon  of  sn;  t«o 
BDtellitefl  is  lo  be  uuJerstood  that  line 
nliiuh  vould  be  drawn  through  Ibt^ 
pliices  from  the  e^'ntre  of  Jupiter,  where 
ihey  have  the  eame  direction  as  seen  fmu 
that  cctitre. 

Thus,  if  J,  fy.  854,  be  Ihe  centre  of  lie 

phnct,  and  e',  that  of  the  first  satellite, 

the  scconil  ratcllite  will  be  in  conjuoclien 

Fl([.  B64.  with  it,  if  it  be  at  s",.     Now,  if  the  Iwo 

sittellitea  move  each  in  its  proper  orbit,  in 

direction  of  tho  arrows  irom  this  position,  the  angular  rnolioo 

860"  390" 

he  first  will  be and  that  of  the  second    '  „    and  sioee  r*  is 

p  !■ 

less  than  p",  the  latter  angular  motion  will  he  more  rapid  than 
the  former,  and  the  first  satellite  will  continually  gain  upon  tho 
second,  and  after  the  lapse  of  the  interval  called  their  synodic 
period,  the  first  will  overtake  the  second,  and  they  will  be  again  in 
conjunction. 

The  new  direction  of  their  line  of  conjunction,  relatively  to  the 
former,  will  depend  upon  the  relation  which  subsists  between  iheir 
periodic  times,  and,  consequently,  between  their  mean  motions. 
Now  it  appears  that  the  mean  motions  of  the  first  and  second  are 
very  nearly,  though  not  exactly,  in  the  proportion  of  2  to  1.  Uj 
reference  to  the  tabubr  synopsis  of  the  elements  of  the  Jovian 
system,  in  (2999)",  it  will  be  seen  that  the  proportion  of  their  peri- 
odic times  is  as  17G9  to  3551,  that  is,  as  1000  to  2007.  It  follows, 
therefore,  that  the  mean  motion  of  the  first  satellite  is  a  little  mere 
than  twice  as  rapid  as  the  mean  motion  of  the  second.  If  the  mean 
motion  of  the  first  were  eiactlj  twice  the  mean  motion  of  the  second, 
the  first  would  make  two  complete  revolutions  while  the  sceoud 
would  make  one  J  and,  therefore,  the  second  having  revolved  once 
in  its  orbit,  and  returned  to  s"i,  the  first  would  have  revolved  twici', 
and  would  also  have  returned  to  s',,  and  in  this  case,  their  line  of 
conjunction  would  always  have  the  same  fised  direction  J  s',  s"|. 
But  since  the  periodic  time  of  the  first  is  a  littie  less  than  half  that 
of  the  second,  the  first  will  overtake  the  second  before  it  h.is  (juito 
completed  two  revolutions,  and  tho  consequence  will  be,  that  theii 
next  line  of  eoujuuction  .i  s',  h"i  will  be  behind  the  former  ;  so  lh;it 
JD  a  single  synodic  revolution,  their  liue  of  conjunctioD  will  haw 


JOVUN  THEORY.  613 

xetrograded  through  the  angle  s"^  J  s"„  and  in  the  same  manner, 
in  another  synodic  period,  it  will  have  retrograded  through  an  equal 
angle,  and  will  assume  the  direction  j  s'  s",,  and  in  the  same  manner 
at  every  snccessivc  conjunction  it  will  have  retrograded  through  an 
equal  angle,  the  mean  motion  of  the  satellite  being  supposed  to 
remain  the  same. 

3232.  Change  of  direction  of  line  of  conjunction  in  each  syno' 
die  revolution,  —  To  determine  this,  lot  ^  be  the  angle  formed  by 
the  line  of  conjunction  at  the  termination  of  each  revolution  with 
the  direction  it  had  at  the  commencement,  such  angle  being  mca- 
aarcd  from  the  latter  position,  in  the  direction  of  the  motion  of  the 
satellites,  so  that,  in  fact,  ^  will  express  the  increase  of  longitude 
which  the  line  of  conjunction  may  receive  in  the  synodic  period. 
Let  if  express  the  synodic  period  of  the  satellites  s'  and  is".  Wo 
shall  then  have  (2589.) 


Wfl  p/  — -  1)//  ■*■  p// 1 ; 


ytf 


SGO^ 


-^1 

ind  since  ^'  moves  through    J^    in  the  unit  of  time,  and  the  ad- 

tiDce  of  the  line  of  conjunction  in  the  time  t'  is  equal  to  the  anglo 
through  which  ^'  moves  in  that  time,  we  shall  have 

▼  I'"  1»  ' P 

In  lilce  manner,  if  t"  express  the  same  angle  for  the  line  of  con- 
junction of  the  satellites  s''  and  s"',  we  shall  have 


^"  =  3C0°  X 


p" 


8233.  Application  to  the  thre^  iim^r  sntcUitcs.  — Now  in  the  case 
of  these  three  satellites  we  have  by  (2091).)     Table  V. 

p' :  p*'  IP"' =  17691 :  35512  :  71516, 

from  which  it  appears  that 

=  0-9027  ;:?7;^^  =  0-9855; 


p"_j/  p"'  — p' 

and  consequently 

f  =  357°-37  ^"  354°-78. 

It  appears,  therefore,  that  in  each  synodic  revolution  of  s'  and 
if  their  line  of  conjunction  advances  through  357°*37,  and  is, 
therefore,  2®-23  behind  its  first  position ;  and  that  in  the  case  of 
if'  and  b'",  the  corresponding  line  advances  through  354°-78,  and 
ify  therefore,  5^-12  bcKind  its  first  position. 

8234.  Regreision  of  the  UneA  of  conjunction  of  the  three  sateJi- 

III  [rl 


ASTBOKGUT. 

«  equal  —  Hut  tbe  eyoo^c  periods  t  and  i',  of  e^,  s",  lad  &", 
f"  m  2677), 

!r'  =  S-525  T"  =  7-050; 

r-tnil  conacqncDtl;  tbe  aoglea  of  regression  of  (he  tvo  lines  of  «»■ 
juDution  ID  Ihc  snme  time  are  as 

2  23  X  7050 : 5-12  X  3030  : :  167  :  156, 
I  to  that  (An  rale  of  rr^reition  of  the  fteo  linet  of  rwijmetuai  u  ikc 

S'ZZb.  Line  of  ronjanftion  of  the  Jirit  an-i  teeond  in  appo>!tia% 
to  iJuil  of  lite  trfnnil  and  third.  — It  follows  from  tliia  llial  ibc  m 
lioes  of  0011  j miction,  thus  rogree»iig  at  tbe  same  Rtt«,  miut  ilmn 
Iw  inclined  to  cncli  ottier  at  tbe  saioe  angle.  Now  it  is  found  ij 
observation,  that  lliis  Invariable  angle  is  ISO",  ao  that  rt?  Ixiu  <•/ 
^  tonjunctu/n  of  thefini  and  tecond  tatfllittt  it  altmj/t  in  immeiii»k 
B:ttipo>iVi(ni  to  the  line  of  amjutiction  of  the  Kcond  and  third  ulri- 
htct,  OS  leenfrom  thr  planet. 

AVc  shall  now  ece  the  remarkable  consequences  of  tbcfc  rcbluiu 
in  tbeir  effects  upon  the  mutual  perturbations  of  tbe  eatellitef. 

3236.  EJicti  of  t/Kir  miifual pfrturlaiion»  vpon  iKe  formt  of 
their  orbit*.  —  The  undietHrbed  orbits  of  the  first  and  secoud  »lel- 
litcs  arc  sGDHibl;  circular,  the  eccentricity  of  the  orbit  of  the  ihiri 
being  estremely  small  (29991.  Table  V.  Their  mutnal  disturbing 
forces  render  the  orbits  elliptical.  The  major  axis  of  the  ellijitej 
are  the  same  as  the  diameter  of  the  undisturbed  orbits,  vbich  ue 
derired  from  the  periodic  times  by  ibc  harmonic  lair.  Tbe  fbnu 
of  the  orbits,  or,  irhat  is  the  same,  their  eccentricities,  are  inn- 
liable,  but  their  lines  of  apades  are  moveable, 

3237.  Molioa  of  the  apsida  f'pial  to  ihal  of  the  Hurt  of  ^njtiiu- 
tion.  —  Tbe  moliuus  imparted  to  the  apsides  being  exclusively  tb« 
effects  of  the  disturbing  force,  and  that  force  being  most  eff«etin 
where  the  satellites  arc  in  conjunction,  and  varying  in  its  ictentiij 
and  direction  with  the  angular  distance  of  the  disturbed  from  ibe 
disturbing,  as  seen  from  the  central  body,  it  is  eridcnt  that  tbe 
position  of  the  line  of  apsides  must  be  always  the  same  in  re1iii«ii 
to  the  line  of  coojunetinn,  and,  conscqnenlly,  that  tbe  motion  of  Uw 
lines  of  apsides  must  be  the  same  as  thlit  of  the  lines  of  eotij unction, 
both  Bs  to  rate  and  direction.  The  line  of  apsides  of  s'  and  g",  tui 
that  of  s"  and  s'",  must,  therefore,  have  a  regressive  motion  ei»ci]j 
equal  to  that  of  the  lines  of  conjunction  ;  and  since  the  motions  <^ 
tbe  latter  are  equal,  the  motions  of  the  lines  of  apsides  of  the  tbna 
orbits  must  likewise  be  equal. 

3238.  TAi  Urrrx  of  ,ip,i,ht  caini-i^ie.  irilk  the  lines  of  <r>nj\nrii>m. 
— In  the  exposition  of  the  general  theory  of  perturbations,  it  bu 
boeo   dcraonitratcJ   that  when   the  disturbed  and  disturbing  bmlid 


JOVIAN  THEORr. 


615 


ire  in  conjnnction,  the  eccentricity  of  the  diElurbeJ  orbit  varies,  if 
the  line  of  aprndca  be  inclined  to  that  of  conjunction,  and  is  only 
invariable  when  these  lioes  coincide.  Now,  in  the  present  cose,  the 
eccentricities  of  the  disturbed  orbita  are  subject  to  no  variation ;  and 
it  follows,  consequently,  that  the  lioes  of  apsides  of  the  disturbed 
orbits  most  always  coincide  with  the  lines  of  conjunction. 

3239.  Putilwta  of  the  perijovet  and  apojoves  of  the  three  orhilt. 
—  But  Ibis  being  admitted,  the  apsides  may  he  presented  in  either 
of  two  opposite  directions.  If  we  consider  s'  as  disturbed  by  s", 
either  the  perijove  or  apojova  of  s*  (as  the  apsides  of  the  satellites 
tre  called,)  may  be  in  conjunction  with  s".  It  results,  hovever, 
firom  what  bas  been  proved,  that  if  the  perijove  be  in  oonjunctioD, 
the  disturbing  force  of  s"  will  render  the  apsides  of  s'  regresuve, 
and  if  the  apojove  be  in  conjunction,  it  will  render  that  motion 
progressive.  Bat  since  the  motion  of  the  apsides  of  e'  is  regressive, 
the  perijove  must  be  in  conjunction. 

If  we  consider  s"  disturbed  by  s',  wo  have  the  case  of  an  exterior 
disturbed  body,  the  latter  being  at  a  distance  from  the  centre  greater 
than  half  that  of  the  exterior  body.  In 
this  case,  the  motion  imparted  to  Uie  ap- 
sides of  s"  would  be  progressive,  if  B  's 
perijove  were  in  conjunction,  and  regressive 
if  its  apojove  were  in  that  position.  But 
since  the  motion  of  tfac  apsides  is  actoally 
\  regressive,  the  apojove  of  s"  must  be  in 
\  conjunction  with  u*. 

I      In  the  same  niaoner  it  may  be  shown, 
J  that  in  conseqnenc  of  the  diatnrbing  forces 
lutoally  exerted  by  s"  and  s'",  the  former 
/  must  ho  in  perijove  and  the  latter  in  apo- 
jove when  in  conjunction. 

By  combining  these  consequences  with 
the  relative  positions  of  the  lines  of  con- 
jnnction  of  s*  g"  and  of  b"  e"'  abeady  in< 
dicatcd  (3235),  it  will  bo  apparent  that 
the  perijove  of  ^  aad  the  apojove  of  s", 
when  b"  and  s"  arc  in  conjunction,  are  in 
opposition  with  the  perijove  of  s"  and  the 
apojove  of  b"',  when  s"  and  a'"  are  in  con- 
jnnetion,  so  that  the  relative  position  of  the  three  orbits  in  this  case 
H  Uuat  which  is  represented  in  fg.  855,  where  p'  is  the  perijove, 
awt  a!  the  apojove  of  a',  p"  and  a"  those  of  s",  and  p'"  and  a'" 
those  of  8"'. 

8240.  Valae  of  the  eccentrinti/, — Since  tho  motion  of  the  apsides 
■nd  the  eccentricity  are  exclusively  due  to  the  disturbing  force, 
vhich  in  this  case  is  given,  the  constant  value  of  th«  coK'bta\W^ 


ng.  8S5. 


i^ 


AfiTHOSOMy. 


I 


Kill  M  depend  on  tho  motion  of  tbe  apeidce.  tbkt  1)m  Utter  liAtg 
given,  the  former  may  be  determined.  Now,  the  regwssive  malien 
of  the  a[isidc3  being  cxaclly  equal  to  that  of  ibe  line  of  conjunclioo 
is  knoirn,  and  therefore  Uic  value  of  the  eccentriciCy  ata  be  ieta- 
mined. 

The  cccentricily  wliich  thns  aripea  exclusivelj  from  tie  ageMj 
of  tbe  dishirbiDg  forces,  though  less  than  the  cecentririiies  m  tfat 
undisturbed  orbits  nf  the  planets  gcnerallj,  is  oeverthelesa  nolis- 
eonsiderable,  exceeding,  for  eiample,  that  of  the  orbit  of  Venni- 

3'241.  Remariabh  precision  in  the /ulfilmatt  of  thtte  lata.^ 
These  TeraHrkahlo  laws,  of  which  there  is  no  other  example  to  ^ 
Bolnr  RjRtem,  are  fulSlled  with  such  precision,  that  in  the  thoofu^ 
of  revolutions  of  the  satellites  which  have  taken  place  since  tlicir 
discovery,  not  the  smallest  deviation  from  them  haa  ever  been  ub- 
Bcrvod,  except  such  fts  has  nrUen  from  the  flight  elliplicilj  of  tke 
undisturbed  orbit  of  tbe  third  gatellile.  The  greatest  and  mcst 
'Irregnbr  perturbations  of  the  planet  or  the  satellitea,  provided  ihej 
fiome  on  gradually,  da  not  inlerropt  the  plaj  of  these  Uvs,  d« 
change  the  rcblinii  of  ihe  motions  n'Siilling  from  Ihcm.  Thf  cfT'cl 
of  a  resisting  medium  will  not  affect  them,  though  each  of  IIkm 
causes  would  alter  the  motions  of  all  the  satellites,  and  t]ioagh 
similar  causes  would  wholly  destroy  the  conclusions  which  ini[b«- 
maticians  have  drawn  as  to  tbe  stability  of  the  soUr  systfm,  Kith 
regard  to  the  elements  of  the  orhita  of  the  planets.* 

3242.  Effect*  of  the  eccentricity  of  the  umUMurhed  orbit  of  lie 
third  satcl/ite.  —  In  tbe  preceding  paragraphs,  the  orbit  of  the  third 
satellite  b'"  is  considered  as  having  no  other  ecce n trie! t;  except 
that  which  proceeds  from  the  effects  of  perturbation.  It  has,  how- 
ever, a  certain  small  original  eccentricity  independent  of  then 
effects,  the  consecjucscc  of  which  is,  that  when  its  conjanctioD  «iib 
s"  takes  place  near  the  perijove  of  its  undisturbed  orbit,  the  effect 
of  its  disturbing  force  on  s"'s  orbit  is  somewhat  more  considenUe 
than  in  other  synodic  positions.  The  consequence  of  this  is  to  pro 
ducc  a  small  variation  both  in  the  eccentricity  of  s"'s  orbit,  and  ii 
the  motion  of  its  apsides,  which  variation  will  depend  on  the  eloo- 
gallon  of  the  line  of  conjunction  from  the  apsides  of  s""b  nndii- 
turhed  orbit. 

Tbe  variation  of  tho  angular  motion  of  s'",  consequent  on  the 
small  elliptic! ty  of  its  orbit,  also  produces  a  corresponding  variatioo 
in  the  rale  of  the  regression  of  the  line  of  conjunction. 

Similar  irregularities  are  incidental  to  the  orbit  of  s'",  proceeding 
from  the  same  causes.     The  disturbing  force  excited  by  s"  on  s*", 


t.  •Koa  first  given  by  Laplam,  ia 


JOVIAN  THEORY.  617 

beiDg  tbat  of  an  interior  upon  an  exterior  body  (3180),  has  on  the 
whole  the  effect  of  increasing  the  effective  attraction  of  the  central 
body ;  and  this  effect  is  chiefly  due  to  the  action  when  s"  and  s'" 
tre  at  or  near  the  line  of  conjunction ;  consequently,  where  that 
line  ia  near  the  perijove  of  s""s  undisturbed  orbit,  the  disturbing 
force  of  s"  is  most  effective,  and,  as  that  line  revolves,  the  angle 
under  it  and  that  of  the  apsides  of  8""a  undisturbed  orbit  continu- 
ally varying,  the  effect  of  s'"s  disturbing  force  alternately  increases 
and  decreases.  This  is  attended  with  an  irregularity  in  the  major 
axisy  and  consequently  in  the  mean  motion  of  s'"  which  depends  on 
its  synodic  position. 

The  disturbing  force  of  an  exterior  exerted  on  an  interior  body 
tends,  on  the  whole,  to  diminish  the  effective  attraction  of  the 
central  body  (3177).  It  follows,  therefore,  that  s'"  exerts  upon  s" 
a  disturbing  force  which  produces  an  irregularity  depending  on  the 
synodic  position  of  the  perijove  of  s""s  undisturbed  orbit. 

Each  of  the  small  inequalities  noticed  above,  depending  on  the 
eccentricity  of  s""s  undisturbed  orbit  reacting  on  the  other  satellites 
fl  and  s'',  produce  corresponding  small  inequalities,  which  if  at- 
tempted to  be  introduced  in  the  general  theory  of  the  system  would 
render  it  extremely  complicated.  Their  almost  infinitely  small 
amounts,  however,  render  them  comparatively  unimportant 

3243.  Perturbations  of  Oie  fourth  satellite.  — The  theory  of  the 
perturbations  produced  and  sustained  by  the  fourth  satellite  s""  has 
nothing  in  common  with  that  of  the  three  others,  inasmuch  as  no 
■neb  remarkable  commensurability  prevails  between  its  mean  motion 
and  those  of  the  others.  As  it  sustains  small  inequalities  from  the 
action  of  the  sun  similar  to  the  lunar  disturbances,  so  it  also  pro- 
duces and  sustains  a  system  of  inequalities  analogous  to  those  of  the 
planets.  Thus  this  satellite  s'"'  presents  at  once  an  example  on  a 
small  scale  of  the  application  of  the  principles  of  both  the  lunar 
and  the  planetary  theories. 

To  explain  the  theory  of  the  fourth  satellite,  we  shall  first  suppose 
that  the  undisturbed  orbit  of  s"'  is  circular,  while  that  of  ?>'"  has  a 
sensible  eccentricity.  We  shall  assume  (what  will  be  more  fully 
explained  hereafter)  that  a  slow  progressive  motion  is  imparted  to  its 
apsides  by  the  spheroidal  shape  of  Jupiter,  this  motion  being  such 
that  the  apsides  make  a  complete  revolution  in  about  11,000  revo- 
lutions of  8"". 

Owing  to  the  periods  not  being  nearly  commensurable,  like  those 
of  the  inner  satellite,  the  line  of  conjunction  of  s'"  and  s""  will,  after 
a  few  hundred  revolutions  of  the  satellites,  have  assumed  every 
possible  direction.  Now,  since  the  mutual  disturbing  action  of  the 
two  satellites  is  greatest  when  the  perijove  of  s"''  is  at  or  near  con- 
junction, the  question  b  what  will  be  the  form  of  orbit  that  will  bo 


52* 


_    1  on  b"'  by  Iho  clialwri-ing  force,  subject  to  Uu  « 

I   of  Its  eccentricitj  being  iuvnrkble. 

Now  it  iH  evident,  from  all  thot  Las  been  explained,  ibat  if  ibe 
^ijove  of  it"  be  in  ooDJunction,  the  ilisturbing  furoe  of  g""  will 
OtUBO  it«  Hp«iiles  to  regress,  and  (he  mte  of  tbis  regTCSsion  vill  fa« 
grcntfr  as  ibc  eccentricitj  is  smaller  (3151).  It  ms;  therefore  be 
Bucb  BB  to  ocDtraliiQ  the  progressive  motion  vbich  U  jniparta]  to 
apsidca  by  the  spheroidal  shape  of  the  ceotral  planet,  and  tbert- 
fbro,  suvb  as  to  reodor  tbc  actual  progressive  motion  of  s"'s  tf^ies 
equa)  [0  tbat  G""'a.  But  the  motion  of  e;""'s  apsides  vill  be  alH 
affected,  thoiigb  in  a  very  slight  degree,  by  the  action  of  s"  in  tlie 
uuic  posidon,  and  will  receive  firom  that  action  a  small  increase  of 
ila  progreasivfl  motion. 

Wbcn  the  increased  progressivo  motion  of  the  llae  of  apaidea  of 

^'"  is  equal  to  the  dimiuishod  progrest-ivc  motion  of  the  line  of 

I     uwidca  of  e"*,  this  state  of  the  ejalem  will  be  permanent,  and  tb« 

P    the  progressive   motion  of  tbe  apsides  of  s"^  will  be  somevU 

P     increased,  and  tbe  orbit  of  s"*  will  have  a  compression  coire»pcwl- 

ing  in  direelion  to  tlic  pcrijovc,  anJ  no  elor^tiiin  in  the  =ame  dint- 

tiuu  as  the  apojovo  of  s>"". 

la  tbis  reasouing  wc  have  assumcJ  lliat  the  undisturbed  orbit  of 
tbe  third  Eatellite  is  circular,  but  similar  effects  will  ensue  if  it  btxt 
a  small  eccentricity. 

L«tusnextsupposcthattheuDdiBtijrbedorbitofs""iacircular,»lule 
that  of  s"'  bas  a  small  eccentricity.  The  disturbing  force  will  be  the 
greatest  at  theapojoveof  b'",  and  tbis  will  cause  the  lincof  apsidnof 
b'"  to  progress;  that  is  to  say,  it  will  increase  the  progressive  motion 
already  given  to  it  by  the  spheroidal  shape  of  tbe  central  planet 
If  then  it  be  required  to  determine  the  form  of  the  orbit  of  s^ 
which  will  have  at  every  revolution  tbe  same  eccentricity,  and  also 
bave  its  hue  of  apsides  always  corresponding  with  that  of  s"',  and 
therefore  progressing  more  rapidly  than  tbe  spheroidal  shape  of 
Jupiter  alone  would  make  it  do,  it  is  necessary  to  suppose  that  the 
perijove  of  s""  is  turned  towards  the  npojove  of  s'",  and  by  sup- 
posing the  eccentricity  small  enough,  the  disturbing  force  will  im- 
part to  it  progressive  motion  as  rapid  as  may  be  desired.  Thus  the 
effect  of  the  eccentricity  of  the  orbit  of  a'"  is,  that  its  line  of  apsides 
will  progress  rather  more  rapidly,  and  that  the  orbit  of  a""  will  be 
compressed  on  the  side  nearest  the  apnjove  of  s'",  and  elongated  on 
the  opposite  sido. 

We  have  here  assumed  that  the  undisturbed  orbit  of  s""  is  ci^ 
cular,  but  a  similar  distortion  wilt  be  produced  even  if  it  have  a 
email  eccentricity. 

In  effect  the  undisturbed  orbits  of  both  satellites  are  ellipses  of 
flmail    eccenlT^cUj,  aai  t.\\&  ^^::cedui^  conelusions   expressed  witb 


PLANETARY  PERTURBATIONS.  610 

rcferenbe  to  undisturbed  circular  orbits  will  be  equally  applicable  to 
them. 

Besides  the  eccentricity  of  the  undisturbed  orbit  of  s'%  it  has 
also  an  eccentricity  impressed  upon  it  by  the  disturbing  force,  oppo- 
site in  kind  to  that  of  s""s  orbit;  and  besides  the  eccentricity  of 
the  undisturbed  orbit  of  s'",  it  has  impressed  upon  it  an  eccentricity 
of  the  same  kind  as  that  of  s'"'. 

In  the  same  manner,  the  orbits  of  s'  and  s''  have  small  eccen- 
tricities impressed  upon  them,  similar  in  their  kind  to  those  of  ef" 
and  s"". 

3244.  Complicated  perturbations  of  this  system. — The  inequali- 
ties which  have  been  here  briefly  noticed  as  produced  in  the  Jovian 
system,  by  the  mutual  perturbations  of  the  satellites,  and  which  are 
only  the  principal  inequalities  of  this  system,  are  so  closely  connec- 
ted, and  so  completely  entangled,  that  though  they  admit  of  being, 
for  popular  purposes,  explained  under  the  point  of  view  here  pre- 
sented, it  would  not  be  possible  to  reduce  them  in  this  way  to  com- 
putation ;  a  mathematical  process  of  the  most  abstruse  kind,  which 
would,  at  the  same  time,  include  the  motions  of  all  the  four  satel- 
lites, would  alouc  be  sufficient  for  this  purpose. 

Enough,  however,  has  been  done  if,  in  what  has  been  said  above, 
a  general  idea  may  be  obtained  of  the  theory  of  these  disturbances 
in  the  most  curious  and  complicated  system  that 'has  ever  been 
reduced  to  calculation.* 


CHAP.  XXIII. 

THEORY  OF  PLANETARY  PERTURBATIONS. 

3245.  The  theory  srmpUJied  by  those  of  the  moon  and  the  Jovian 
^fttem.  —  The  investigation  and  solution  of  the  more  general  and 
oomplicated  cases  of  perturbation  presented  by  the  mutual  action  of 
the  planets,  will  be  greatly  simplified  and  facilitated  by  the  previous 
exposition  of  the  theories  of  the  moon  and  the  Jovian  system.  The 
inequalities  developed  in  each  of  these,  are  reproduced  in  very 
slightly  modified  forms,  in  the  case  of  the  planets.  Thus  the  ter- 
restrial disturbed  by  the  major  planets,  present  a  class  of  perturba- 
tions similar  to  those  of  the  moon  disturbed  by  the  sun.  In  both 
cases  the  disturbing  is  exterior  to  the  disturbed  body ;  in  both,  tho 
mass  of  the  disturbing  is  incomparably  greater  than  that  of  the 

*  We  are  indebted  for  the  subBtance  of  some  parts  of  this  chapter  to  the 
short  but  exccUoDt  truct  on  Gravitation  by  Professor  Airy,  to  which  wt 
refer  readers  who  may  desire  further  details. 


ASTROXOMT. 

in  both,  tbc  iJistance  of  ibe  diBtnrbing  from  ibe  ccvlnl 

cars  a  large  ratio  to  tbal  of  tba  dUlarbi-d  boily ;  and  if  in 

ar  theory  the  maaa  of  tbc  dixturbing  bodj  be  much  larger 

in  the  nisc  of  the  plaocta,  its  disiancea  from  the  disturbed  and 

wal  bodies,  bearing  also  a  much  larger  niiio  to  the  distance  of 

w  bodies  from  each  other,  the  iateasitj  of  its  distnrbiog  force  ia 

jdued  and  broagbt  into  closer  analogy  with  the  raises  referred  to. 

The  ineqnalitieB  incidental  to  the  three  inner  satellites  of  Jupiter, 

iKoding  on  the  near  commcasurab:'''"  of  their  period^,  have  also 

iterpurte  among  the  perturbations  of  the  planets,  some  of  ths 

i  remarkable  of  the  planetary  inequjililies  arising  from  tbe  cir- 

jgtance  of  the  periods  being  very  nearly  in  the  ratio  of  whole 

nbers,  as  will  presently  appear. 

ID  fine,  other  ineqnaliliea  produced  by  the  gravitation  of  planet 
1  planet,  are  analogous  to  those  found  to  prevail  between  the  outer 
clliies  of  Jupiter. 

'1246.   rerlurbaliont  of  the  terrexirinl  hy  the  mnjof  plnnets. — If 

suppose  any  one  of  the  terrestrial  to  be  disturbed  by  any  one  of 

le  major  planets,  it  will  be  easy  to  show  that  the  points  at  which 

e  disturbed  placet  and  tho  sua  are  e<|QidL''taat  from  the  distarbing 

"  "e,  tbe  taogpnliul  component  of  the 

in  nil  tasob  very  near  i!ie  poiots  of 

Let  8,Ji'j.  856,  be  tho  place  of  the 
sun,  M  the  disturbing  planet,  qq'  the 
places  of  the  disturbed  planet  at  quad- 
rature, and   PiP*,  its  places   when  at 
distances  from  M  equal  to  SM.      I^et 
^  the  arc  qv„  or  the  angle  QSP„  be  ei- 
^   pressed  by  a,  SP,  by  r  and   SM  by  r*, 
P,'  and   draw   Mm   perpendicular  to  sP/. 
It  is  evidcDt,  then,  that  tbe  angle  SMm 
=  a,  and  cuusc^iuently 


Now,  if  the  values  of  r 


nd  /ii 


of  tbc  coses  of  the  terrestrial  and 
major  planets  be  subsiiluled,  we  shall 
find  that  the  extreme  values  of  > 
will  he,  for  Mara  disturbed  by  Jupiter, 
Fijf.  BM  a  =  7°  21',  and  for  Mercury  disturbed 

by   Neptune,  a  =  0°  W,  and  for  all 
Other  coses  it  will  hu"^'<'  intermediate  values. 

It  follows,  therefore  i..''*^  '°  ^^^  "^^^  '"^'^  referred  to,  tbe  points 
Pi  I'jare  never  so  much  us  S"'."**'"*^''^  •"'■o™  the  points  of  quadrature. 


PLANETARY  PERTURBATIONS.  621 

By  tbo  application  of  the  same  process  of  investigation  as  that 
already  adopted  in  the  case  of  the  lunar  theory,  it  will  be  found 
that  the  points  P„  P3,  p'3  and  p'„  will  have  positions  very  nearly  tho 
same  as  those  assigned  to  them  in  tho  case  of  the  moon.* 

It  follows,  therefore,  that  the  several  vanishing  points  of  the 
components  of  the  disturbing  force,  on  the  position  of  which  the 
successive  phases  of  the  perturbations  so  mainly  depend,  arc  dis- 
tributed around  the  synodic  orbit  of  the  terrestrial  planets  as  dis- 
turbed by  yie  major  planets  in  a  manner  similar  in  all  respects,  to 
the  corresponding  points  in  the  lunar  theory  and  periodical  inequali- 
ties, are  accordingly  developed  in  a  like  order  and  of  a  like  character, 
differing  only  in  their  limiting  magnitudes  and  the  lengths  of  their 
periods. 

Thus  the  disturbed  orbit  is  less  curved  at  0  and  o,  and  more  so 
at  P2Q  and  p'aQ',  than  elsewhere,  so  as  to  acquire  an  oval  form, 
placed  with  relation  to  the  line  G  0  similarly  to  that  of  the  moon, 

is  196).  Its  curvature  at  0  is  more  flattened  than  at  o,  (3198). 
nequalities  affecting  the  place  of  the  planet  in  approaching  to  and 
departing  from  sjzygies,  result  from  this,  similar  to  tho  moon's  vari- 
ation, parallactic  inequality,  and  annual  equation. 

The  line  of  apsides  is  affected  with  a  motion  alternately  progres- 
sive and  regressive,  but  on  the  whole  progressive  (3215).  The 
disturbed  orbit  is  rendered  a  little  more  eccentric,  when  this  line  is 
in  quadrature  than  when  it  is  in  syzygies.  The  effect  of  the  dis- 
turbing force  on  the  whole  is,  as  in  the  case  of  the  moon,  to  diminish 
the  effective  central  attraction,  and  therefore  to  enlarge  in  a  slight 
degree  the  orbit;  and  this  effect  is,  of  course,  somewhat  greater 
when  the  disturbing  planet  is  near  perihelion,  while  the  disturbed 
planet  is  near  aphelion. 

It  must,  nevertheless,  be  observed,  that  these  and  other  like  peri- 
odical inequalities  arising  from  similar  causes,  are  not  only  smaller 
incomparably  in  magnitude,  taken  within  their  extreme  limits,  and 
slower  in  their  rate  of  development,  than  in  the  case  of  the  lunar 
perturbations,  but  that  their  absolute  limits  are  so  extremely  narrow, 
that  it  is  only  those  which  are  duo  to  the  predominant  mass  and 
greater  proximity  of  Jupiter,  which  are  productive  of  effects  great 
eoough  to  be  appreciable  by  common  observations. 

3247.  Cases  in  which  the  disturbing  is  in  closer  proxim it//  with 
the  disturbed  planet.  —  In  such  cases  the  same  close  analogy  to  the 
lunar  inequalities  does  not  prevail.  Nevertheless,  even  when  the 
disturbing  planet,  being  exterior  to  the  disturbed,  lies  in  compara- 
tively close  proximity  with  it,  several  of  the  inequalities  manifested 
in  the  lunar  motions,  may  still  be  recognised  in  a  modified  form. 
The  vanishing  points  of  the  components  are  somewhat  differently 
distributed  in  relation  to  the  lines  of  syzygy  and  quadrature.  The 
points  Vf,  v^g  of  equidistance  from  the  disturbing  body  recede  from 


ASTBOKOMT. 

.  approach  the  point  o  of  aoDJanctJOQ,  xki  the  iu- 
jijis  of  the  radial  componenla  P,  i^,  approach  CDnjanetion 
h  i/*  approach  opposition  o.  The  liisturbing  force,  however, 
oaa  a  teDduDoj  to  dituiuish  the  carvature  of  the  orbit  dcv  c 
t,  and  to  increase  it  near  P,  aod  r',.  The  general  effect  is,  as 
«,  to  diminish  tho  effective  central  nttractioii]  and  conscqueailj; 
^rafi  tho  orbit  of  the  disturbed  planet. 

Ca»e  in  tchich  Che  dUlvrbivg  i'»  tcilhiit  fhe  orbit  of  Ott 

net. — In  thci  general  effect  of  tha  disturbJDg 

traced  withe  .  bj  the  method  ezpkiDed  in 

Be  cases  tne  g  Jcat  of  the  disturbing  force  a 

^mc  effective  ce:  tiuction,  and  conseijncnlly  to 

luish  me  maenitudc  of  the  urtiit  of  the  disturbed  placet. 

249.   I^turbation  affnled  hy  tJie  position  n/  the  apuiJe*  and 

•I  in  relation  to  the  line  of  conjunction.  —  In  the  general  in»es- 

tion  of  the  planetary  perturbations  it  ia  necessary  to  obserre, 

tho  effect  produced  by  the  disturbing  force  in  each  ajnodic 

ilutioD  viU  necessarily  depend  on  the  position  of  the  line  of 

j'gies  in  rektioii  to  the  lines  of  nodes  ana  apsides,  and  will  tvj 

h  that  posidoD. 

If  the  urhila  of  the  diafurhiog  and  dislurhcJ  planpis  were  both 
circles,  and  in  a  common  plane,  tbc  effect  produced  by  the  disturbing 
force  in  eacli  synodio  rcrolution,  and  in  each  synodic  position  of  the 
planets,  would  be  absolutely  tbc  same,  irbatever  be  the  direction  of 
the  line  of  eyzy^es;  for  in  that  case  the  distances  of  m  and  p  from 
Bfji'js.  Sit',  858,  being  always  the  same,  the  distance  M  p  between 


the  disturbing  and  disturbed  bodies,  which  corresponds  to  any 
angular  distuuce  M  s  p  of  one  from  the  other  as  seeu  from  the  central 
bod^,  would  be  always  the  same,  and  the  angles  at  which  M  P  is 


PLANETAET  PSSTUBBATIONS.  628 

inclined  to  the  lines  m  a  and  p  8  would  be  alwajs  the  same.  All 
the  conditions,  therefore,  which  can  affect  the  inteosity  tnd  direction 
of  tlie  distiiTbing  force,  would  be  absolutely  identical ;  and  it  follows 
eonMqnentlj  that,  no  matter  what  ma;  be  the  direetions  of  the 
Uses  of  ayiygy  and  qnadrature,  the  disturbieg  force  during  each 
■ynodio  rerolution  would  pass  through  precisely  the  same  changes 
M  intensity  and  direction,  and  consequently  produce  precisely  the 
same  effects  upon  the  orbit  of  tbc  disturbed  placet. 

If,  howBTer,  the  orbits,  being  still  in  a  common  plane,  be  either 
or  both  of  tbcm  ellipses,  the  same  identity  of  effects  of  the  din- 
tnrbing  force  during  &  synodic  revolution  will  no  longer  prevail. 

Let  it  first  be  supposed  that  the  orbit  of  the  disturbing  planet  h, 

St.  .Sb9,  860,  is  circular;  and  that  of  the  disturbed,  elliptical. 
t  p  be  the  point  of  peribelioo,  and  a  that  of  aphelion,  p*  and  a* 
being  the  places  of  h  correepo tiding  to  these  poiuts ;  and  let  m,  » 
be  the  points  at  right  angles  toj>,  n>'  and  m'  being  the  correspooduig 
poeitioaB  of  H. 


TTpon  comparing  the  varying  distance  of  H,  whether  it  bo  outside 
the  orbit  of  p,  as  represented  in  _/ig.  859,  or  within  it,  as  represented 
in  Jiff.  860,  it  will  be  evident  that  the  effects  of  the  disturbing  force, 
during  k  synodic  revolution,  will  be  subject  to  a  variation  with  tbo 
nrring  angle  formed  by  the  radius  vector  m  a  of  the  disturbine 
planet  with  the  direction  pa  ot  the  perihelion  of  the  disturbed 
planet.  Thus,  when  M,  being  outside  p'e  orbit,  is  at  o',  it  is 
evident  that  its  distance  from  p,  in  any  proposed  synodic  position, 
will  be  much  less  than  its  distance  from  p  in  the  same  synodic 
padtion  when  H  is  at  />';  and  consequently  tbo  effect  of  the  dis- 


ASTROSOMT. 

■tUog  force  during  n  Ejiiodic  rcTolulioo  trhcn  u  is  fit  a',  u  iiiuc\i 
re*tt>r  ttinn  vt)icn  M  U  ul  j/;  ami  ibi?  •mine  muy  Ih.-  niil  of  tnj  two 
^mitc  ]>uBiliouB,  Nucb  &8  m  and  m',  or  m"  and  a"',  ichieb  thsfr 
taili'itig  ])lnDet  can  aseumc. 

It  is  obyious,  the  like  obacnrstinns  sro  appiicaUe  to  Uie  Om 
I  !Ttprc>><'iitG<l  iajrij.  8G0,  in  wbicli  M  m  within  tbc  orbit  of  P. 

Dut  not  only  are  the  cQ'c<;ts  uf  the  ilisturbiog  fctnti  iiStmth 
thuir  uiuguil.ude  according  ag  tie  radius  vcetor  uf  M  lakn  <BAni 
l^eitions  nith  relation  to  the  lino  p  s,  bat  tbcy  are  aUo  diAvfot  fi 
their  dircoiion.  Tbe  pontion  of  the  vanishing  poinEs  of  tbswt- 
ponecta  of  the  disturbing  foree,  and  the  distribution  of  lis  n 
iLrongh  which  ibej  are  allemntelj  poeilive  and  negiCive  ttttti  Aa 
orbit  of  tbc  dtaturbcd  bod;,  depend  aolclj  on  the  directioQ  cf  tlx 
lines  of  a^xyg?  acd  qundrature ;  but  tbe  effects  whicb  then  cod- 
pooonta  prodooe  upon  the  diBcrcnt  elcmcnta  of  tbe  elliptic  orbit  J 
I  s,  depend  upon  the  position  of  those  Ecreral  arcs  vitb  retatiiia  to 
f  ■  wt  line  of  apsides.  la  some  posilJooa  tbc  effect  of  the  distaiiNB| 
fbree  in  a  complete  aj'nodjc  reTolntioD,  will  be  to  Bugroent,  ia  othen 
to  diminish,  one  or  other  clement;  end  in  positiaos  io  wbich  ika 
same  elements  are  augmented  or  diroinisbcd,  thej  will  be  angmeatid 
or  diminished  in  dilL'reDt  degrees,  accordiog  to  the  angle  wbicb  it 
line  of  coDJuDctioQ  (that  is,  the  line  passing  through  r  and  N  nbeo 
seen  in  tlio  earns  direction  from  p)  forms  with  tbc  lioej)S,00B- 
ncctiug  B  with  tbe  perihelion  of  the  dbturbed  orbit. 

To  eimplif}'  this  explanation,  we  have  here  supposed  that  the  orU 
of  tbe  disturbing  bmlj  is  circniar,  while  that  of  the  disturbed  ii 
elliplieHl;  but  It  will  be  apparent,  that  like  observations,  mirfofii 
mvUniffis,  will  be  applicable  if,  reversing  tbia  supposition,  w 
BupposB  the  orbit  of  P  to  be  circular,  and  that  of  M  elliptical. 

In  fine,  if  both  orbits  be  eupposcd  to  bo  elliplical,  a  further  win 
of  variation  will  alTocI  the  disturbing  force;  fur  in  that  ease,  lb 
distance  between  M  nod  P,  and  the  relative  dirfctions  of  the  liaoi 
MP,  MS,  and  r s  will  varj,  ns  well  on  account  of  tbe  ellipticit;  d 
m'b  orbit  as  thut  of  r.  The  oficcis  of  this  force  on  each  of  th« 
elements  will  be  sobjcet  to  eonstant  variation,  depending  on  iIm 
uigles  which  the  line  of  conjunction  forms  with  the  lines  dr:Lwn  fnu 
B  to  the  points  of  perihelion  of  the  two  orbits. 

This  will  be  very  obvious  bj  comparing  the  various  poaitiniii 
irhicb  the  line  of  conjnnctions  &  P*  P  of  two  such  planets,  muioillj 
disturbing,  may  ansune,  trith  relation  to  tbc  lines  of  upsides  a  tf 
and  a' Bp',  Es  represented  in_^^,  801. 

The  orbita  in  the  preceding  illustration  have  been  supposed  la 
be  in  a  common  platic.  If  the;  be  not  so,  but  are  inclined  at  anf 
angle  to  eaeb  oI^pt,  i«iWhet  cause  of  variation  in  tbe  effects  of  th> 
conipouciits  of  ttc  ii6\MvVivi%  tovnt,  4.\bw5^  ■iic  ^^iwivc  TevolutioBi 
in  introduced-,  nndWe  aQ^iteeSccI:  "A  wiK!a ^iros -aY"^ "'^'ik.  ' 


PLANETABT  PERTURBATION'S.  625 

during  each  sncli  reTOlutioD, 

will  TBTj  with  the  Rogle  at 

I  which  the  line  of  conjuncUon 

I  is  iDcliQed    to    the    line   of 

I  Dodea. 

It  will,  therefore,  be  appa- 
I  rent  that,  in  each  poutioa 
which  the  line  of  conjunction 
nay  assume  with  relation  aa 
irell  to  the  line  of  apeidea  aa 
■Ji  the  line  of  nodes,  tlie  dia- 
:urbing  force  will,  in  each 
syDodic  revolution,  produce  a 
certain  change,  either  by  pro- 
F)g.  SSI.  grcssion  or  regression,  by  In- 

crease or  diminution  in  the  ele- 
meota  aeTcrally  of  the  disturbed  orbit,  the  magnitudo  of  which  will 
depend  OD  such  position,  so  33  to  be  always  tbe  same  for  the  same  por- 
tion, but  genernlly  different  fnr  different  positions;  and  when  such 
poditions  are  in  extreme  opposition,  the  effects  of  tho  elements  aeve- 
rally  are  ofien  also  contrary  in  tbeir  character,  so  as  mutuatly  to 
jesiroy  or  compensate  each  other  either  whoUy  or  partially,  the  pro- 
gression or  iuorvasc  resulting  from  the  effect  of  the  disturbiog  force 
ID  one  position  being  compensated,  wholly  or  partially,  by  an  equal 
w  nearly  equal  regression  or  decrease  iu  the  opposite  position  of  the 
line  of  conjunction. 

It  follows  from  this  that,  if  the  motions  of  two  plaueta  were  so 
related  that  the  line  of  conjunction  should  always  have  the  same 
position  with  relation  to  the  lines  of  apsides  and  nodes,  the  effect  of 
the  di^jturbing  force  on  each  of  the  elements,  in  each  synodic  revo- 
lution, would  be  always  the  same ;  and  tho  consequence  would  be 
that,  after  the  lapse  of  a  considerable  number  of  such  revolutions, 
the  changes  produced  in  each  revolution  accumulating,  an  alteration 
Id  the  form  and  position  of  the  disturbed  orbit  would  be  produced 
M)  great  as  completely  to  disturb  the  physical  conditions  of  the  planet 
ind  derange  the  harmony  and  order  of  tho  system. 

But  even  though  the  place  of  the  line  of  conjunction  should  not 
be  rigorously  the  same  after  each  successive  synodic  revolution,  if 
nevertheless  it  be  subject  only  to  a  small  change  of  position,  it  is 
evident  that  the  change  in  the  character  and  magnitude  of  the  effects 
nf  the  disturbing  force  on  the  elements  will  be  proportionally  small ; 
and  that,  therefore,  such  effects  will  continue  t^  accumalate  and  to 
lagment  the  variation  of  each  of  the  elements  of  the  disturbed 
orbit  in  the  same  direction,  until  by  the  long  continuance  of  the  slow 
etwnge  of  poaition  of  the  line  of  conjunction,  that  line  .at  length 
ihifia  ita  direction  so  as  to  take  np  a  position  in  ittu^h  t.  cn&^xn^ 
III.  53 


ABTRDSOUT. 


tt  will  bo  pmduced  Tipon  tbe  eltneDts.     Tb« 

litttr  will  llirn  rhnngd ;  nli^t  wu  prpviaiu^y  iocmse 

kert'i£«,  anil  vite  <ir>d;  and  this  nill   eonfitiuo   UDtll 

,  frtill  slowly  EbiftiDg  iis  posilion,  kgam  r^samcs  tm 
I  direclion  fivourublc  to  Ujc  fortner  change  of  the  elemetiU. 

In  ibia  roiniipr  iue<)Q[illtie3  mn;  be  prodocvd,  of  wliich  the  ptrinl 
;ln>y  bu  of  pcaX  length,  but  whiob,  uevertbeless,  dependiog  cem- 
^iiU;  on  the  directba  of  the  lioe  of  oonjuoction,  and  therefiiK  an 
ike  eonfi^nition  of  the  dtGtnrbing  and  disturbed  pUni.-tB,  tire  iffil 
ffrriodie,  &nd  not  ireultir  ntristiODs.  Since,  however,  the  twuaso! 
of  the  line  of  cnujuocllon  on  which  th«j  depend,  are,  in  aB  Ik 
cBUii  of  this  cliM  preeented  in  the  sttlai  system,  eitKOielj  eIa*, 
and  DonKqu(intlf  tba  pr^rinds  of  thcEO  incfiualitics  are  incompinUf 
more  prolnctcd  ihnn  those  which  anee  from  tbe  VBipog  tjodit 
'POBitionii  (if  the  dixttirbed  and  disturbing  planets,  thcj  bin  beA 
I'Oeuoainatcd  by  astronomers  as  the  " lony  iuf^iatiiin ;"  lai  it 
'  diacovery  of  gome  of  them  by  theory,  before  their  detection  bj  * 
1  one  among  the  manjtriumphs  of  phjMW- 


lathcm: 


3250.  Method  of  determining  the  change  of  direction  of  tkeSm 
of  conjunrtion.  — From  all  that  hss  been  just  eiplnlned  it  will )» 
apparent,  how  much  importance  must  attach  to  the  problea  B 
determine  the  change  of  position  of  ibe  line  of  conjunction  of  a] 
two  planela  after  each  synodic  revolution. 

I^t  P  be  tbe  pcriodio  time  of  the  interior,  and  i^  thai  of  ih 
esferior;  and  let  T  express  the  synodic  period  or  the  inUfnl 
between  tno  succe^ivo  eoiijunctjons.  It  uppeiuD  from  what  hii 
been  explained  in  ('2577),  that 


1 


1 


1 


ud  consequently. 


In  the  timo  T,  the  interior  planet  describca  360°,  besides  ofn- 
taking  tbe  exterior  planet,  and  therefore  describes,  in  additios  b 
S60°,  tbe  angle  nhich  the  exterior  planet  describes  in  tbe  tiniB 
■nd  since,  at  the  beginning  of  tbe  time  T,  tbe  two  planets  are  in  a 
junction,  and  ugain  in  conjunction  at  tbe  end  of  that  time,  the  aa^ 
loroied  by  the  direction  of  tbe  line  of  conjunction  at  tbe  end  of  tkt' 
time  T,  with  its  direction  at  the  beginning  of  the  time  T,  measa 
in  the  direction  oS  \W  ^\%\ui\,'6  Aaoiinn,  will  be  the  angle  wbkk 
exterior  pUnet  Aescri^iEs  TOftie'a-m*T-    \««.i^vii.\i^,e.\j».^    gigp 
tbe  angle*  wbicb  iVa  eitervw  ■j^wio'i.  iwRmSna  to.  S^t  ^Jai^^ 


PLANETARY  PERTURBATIONS.  627 

18       .    (2568),  the  angle  t?  which  it  describes  in  the  time  T,  will  bo 


1/         p'  —  p 

This  is,  then,  the  angle,  measured  in  the  direction  of  the  planet's 
motion,  through  which  the  line  of  conjunction  advances  in  each 
Evnodic  revolution. 

3251.  Condition  under  which  the  direction  of  the  line  of  can" 
junction  is  invariable.  —  If  the  line  of  conjunction  has  always  the 
same  direction,  it  is  evident  that  in  a  synodic  revolution  both  planets 
must  have  made  a  complete  number  of  revolutions,  and  conse- 
quently the  angle  t  must  cither  be  3G0^  or  some  exact  multiple  of 
360°.  If  4.  =  300°  we  shall  have  p  =  i>'  — p  (2548),  and,  there- 
fore, p^  =  2  p.  In  that  case,  while  the  exterior  planet  makes  a 
single  revolution,  the  interior  makes  two ;  so  that,  after  each  revo- 
lution of  the  exterior  planet,  the  two  planets  come  into  conjunction 
always  at  the  same  point.  In  this  case  it  is  evident  also,  that  the 
synodic  time  is  equal  to  the  periodic  time  of  the  exterior  planet. 

If  ♦  =  2  X  360°,  we  shall  have  P  =  2  p'  —  2  p,  and,  therefore, 

3  P  =  2  P^.  In  that  case,  while  the  exterior  planet  makes  two 
complete  revolutions,  the  interior  makes  exactly  three,  and  the 
synodic  period  is  equal  to  twice  the  periodic  time  of  the  exterior 
planet 

If  ^  =  3  X  360°,  we  shall  have  p=3p'  —  3p,  and,  therefore, 

4  p  =  3  p'.  In  that  case,  therefore,  the  conjunctions  are  reproduced 
at  the  same  point,  after  every  three  complete  revolutions  of  the 
exterior  planet. 

In  general,  if  t  =  n  x  360°,  p  =  nXP'  —  nXP,  and,  there- 
fore, (n4-l)XP  =  wXp',  and  the  conjunctions  are  reproduced 
constantly  at  the  same  point,  after  n  revolutions  of  the  exterior,  and 
n  +  1  revolutions  of  the  interior  planet. 

The  general  condition  on  which  the  line  of  conjunctions  shall 
have  one  invariable  position,  therefore,  is  that  the  periodic  times  of 
the  two  planets  shall  be  such  as  can  be  exactly  expressed  by  two 
whole  numbers,  of  which  the  greater  exceeds  the  less  by  1,  such  as  1 
and  2,  2  and  3,  3  and  4,  &c. 

3252.  To  determine  the  condition  vnder  which  the  line  of  con- 
junrtiftn  shall  have  a  limited  nvmher  (f  invariable  positions. — 
Although  the  conjunctions  may  not  be  always  reproduced  at  the 
same  point,  they  may  take  place  invariably  at  two,  three,  or  more 
fixed  points. 

If  ^  =  180°,  they  will  take  place  invarial)ly  at  two  points  which 
are  diametrically  opposed  to  each  other.  In  that  case,  we  shall  have 
2  p  =  i/  —  V  {J>25U~),  and,  therefore,  p'  =  3  p  and  x  =  }  P'.  To 
eomprehend  the  motions  of  the  planets  in  this  case^  Ut  ^  %.^4  \ 


iSTROKOMT. 

(Jig-  862)  be  tlieir  pcwtioiis  >t  uiy 
propoeed  i>oiiju notion.  The  nn^lu 
tflotiou  of  I  being  throe  litnos  tbtt 
of  K,  nhilc  the  latter  mores  from  s 
to  k'  tbrpugh  a  ecmic^rcumferencc, 
I  moves  tbrough  lliKe  Eemicircaiu- 
fereacca,  and,  lliercfore,  through  the 
whole  tireutuferonce  1 1'  i,  aod  after 
that  thr<)ui;b  the  semtdmamferenco 
1 1',  overtnktDg  the  csterior  ptutct 
at  I*,  wbcre,  tbcreforo,  the  oest  cdd- 
jnDotinn  takes  plaj:e.  Id  libe  mnti- 
ner,  the  succeeding  conjuDclioD  will 
1''^'  '''-'  tuke  place  nt  e  i  x,  aod  the  next  at 

s  i'  £*,  Bad   BO  OD,   DO    conjuiictiDO 
beiDg  possible  except  in  tbese  two  lines. 

If  f  =  mo",  or  a  ibirJ  part  of  the  circumference,  the  cODJono- 

^oua  will    be    reproduced    coutiauolly  io    tbree  fixed  directioai, 

1 '  ^viding  the  oircumfereoco  iuUj  tbree  equal  parts.      la  this  cau, 

V  3p  =  y' — p,  and,  therefore,  p'  =  4p, 

mid  T  =  J  !■'.      To  explain   the  motinn 

in  tbis  case,  let  s  I  E  {Jig.  863,)  be  the 

position  of  the  plauels  at  any  proposed 

conjunction.        Let     K     move    fornatd 

1   tbrough  120°  to  e'.     The  angnlai  mo- 

t    1  ^'\  1        ''""  "^  *  being  four  times  more  rspid 


tbro 


2b  4  X  l-iO-t 

Irill  malic  a  c 


ve  in  the  h 

.360= +120°; 
luplele  revolu- 
ill,  therefore, 


tion  and  120°  more.      Itw 
overtake  the  exlcrior  plar 
Fig.  6B3.  120°  in  advance  of  the  last  conjunction. 

In  the  same  manner,  it  may  be  shown 
that  the  nest  conjunction  will  take  place  in  the  line  8  i"  e",  120° 
Id  advauce  of  s  i'  e'.  Tbc  following  conjunclion  will,  in  the  game 
way,  take  place  in  the  line  S I  E,  120°  in  advance  of  S  l"  e".  Thus 
each  scries  of  three  coujunclions  will  take  place  in  the  lines  B  I  E, 
8  i'  id,  and  s  i"  e",  farming  with  each  other  angles  of  120° ;  and  no 
conjunctions  cau,  under  the  proposed  conditioD,  take  place  in  any 
other  line. 

If  t=90'',  it  may  be  ehown  by  precisely  the  same  reasoning 
that  p'^Sp  and  t^Jp',  and  that  the  eonjuDctioDs  will  inva- 
riably take  place  in  four  fixed  directions,  at  right  angles  to  each 
other. 

Ik  general,  in  order  that  the  conjunctions  shall  be  reproduced 


PLANBTART  PERTURBATIONS.  629 

in  mnj  proposed  number  n  of  fixed  direotions,  it  will  be  necessary 
that  the  period  F^  shall  be  exactly  n  -f  1  times  the  period  p.  In 
that  case  the  synodic  time  T  will  be  n  times  p';  and  the  fixed  direc- 
tions in  which  the  conjunctions  will  succeed  each  other,  will  divide 
the  circumference  into  equal  arcs  or  angles,  the  magnitude  of  which 

will  be . 

n 

3253.  EfftxU  of  the  duturhxng  force  in  case*  of  commenturahle 

period*.  —  It  follows  from  what  has  been  explained  (3249),  that  in 

BQch  cases  the  effects  of  the  disturbing  force  would  accumulate 

indefinitely,  without  compensation  or  with  imperfect  compensation, 

through   an   indefinite  succession  of  synodic  revolutions.     If,  for 

example,  f^=  2  p,  and  therefore  the  conjunctions  would  always  take 

place  in  the  same  line,  the  line  of  conjunctions  being  always  inclined 

to  the  line  of  ap>ides  at  the  same  angle,  the  effect  of  the  disturbing 

force  on  the  several  element-^,  in  a  synodic  revolution  would  be  always 

exactly  the  same,  and  would,  therefore,  accumulate  indefinitely  from 

revolution  to  revolution. 

If  1^=  3  p,  the  lines  of  conjunction  would  have  three,  and  only 
three,  different  positions  in  relation  to  the  line  of  apsides;  and 
although  the  effects  of  the  disturbing  force  in  a  synodic  revolution 
in  these  three  positions  would  be  different,  and  some  of  them  would 
necessarily  have  contrary  signs,  and  would  produce,  therefore, 
more  or  less  compensation,  such  compensation  would  be  imperfect ; 
and  after  each  series  of  three  conjunctions,  a  residual  inequality 
would  remain,  affecting  each  of  the  elements  which,  as  before,  would 
accumulate  indefinitely  during  an  indefinite  succession  of  synodic 
revolutions. 

In  the  same  manner,  if  p'  were  any  other  exact  multiple  of  p, 
the  series  of  conjunctions  which  would  take  place  in  the  directions 
of  the  fixed  lines  dividing  the  circumference  into  equal  parts 
would  still  be  imperfectly  compensatory,  and  residual  quantities 
would,  as  before,  remain  uncfii&ced,  which  would  accumulate  indefi- 
nitely. 

In  order  that  the  conjunctions  should  take  place  always  in  cer- 
tain fixed  directions,  it  is  not  necessary  that  the  periodic  time  of  the 
exterior  planet  should  be  an  exact  multiple  of  that  of  the  interior. 
The  same  will  happen,  if  any  exact  multiple  of  one  of  the  periods 
be  exactly  equal  to  an  exact  multiple  of  the  other,  or  in  other  words, 
if  the  periods  be  commensurable.  Thus,  if  2  p'=  5  p,  it  is  evident 
that,  counting  from  the  epoch  of  any  one  conjunction,  another  will 
arrive  in  exactly  the  same  place  after  every  two  complete  revolutions 
of  E,  and  every  five  of  i.  But,  between  these  others  will  take  place 
at  fixed  intermediate  positions,  for  we  should  have 

53* 


ABTRONOMT. 


P-  _  P       5—2 


0=  X  J  =  240^ 

I  case,  the  lines  of  coDJuDct'tan  would  be  dbtribnted  ia  tbe 

r»*nnnr  us  nheti   F*  =  4  P,   but   the  ooajancdooB  trould  not 

1  y  the  game  msoner.     Aflar  the  conjuDction  wliicU 

I'  '  "     Too),  would  succeed  that  whict 

IV  li  ..  Uie  third  of  the  series  woald  lake 

10  B  iTth,  or  the  Erst  of  the  next  seiiM, 

the  im..  c  . 

;  this  method  of  reaEODiDg,  it  will  be  easilj  seen  that, 

■ui  cases  in  which  the  periods  of  the  two  planets  would  be  id  the 

f.t  ratio  of  two  whole  Dumbers  m  aod  n,  the  conjunctions  woaU 

riahiy  succeed  each  other  ia  certain  fixed  lioes.     \\'e  shoulJ,  in 


and  siucc  ni  and  n  arc  the  whole  oumbers,  this  would  give  tbe  mag- 
nitude of  the  angles  into  which  the  fixed  directions  of  the  lines  of 
conjunction  would  divide  360°. 

It  is  evident  that,  although  complete  compensation  could  not  tab 
place  between  the  efleets  of  the  disturbing  force  upon  the  elements, 
BO  long  as  the  line  of  conjunction  is  limited  to  Gxed  directions,  their 
approach  to  compensation  is  closer  and  closer  the  more  multiplied 
are  the  directions  which  the  line  of  conjunction  can  assume. 

3254.  Planets  pr'-Kr-nl  no  ease  of  cnmmemvTnlh  pmod»,  hvl 
tome  neurit/  to.  —  By  reference  to  the  table  of  periodic  times  of  the 
planets  (2984),  it  will  be  seen  no  case  is  presented  in  the  solar 
Byslem,  in  which  the  periods  of  two  planets  are  exactly  commensn- 
rsbte;  but  as  several  cases  are  found  in  which  there  is  an  approach, 
more  or  less  close,  to  that  condition,  it  will  be  convenient  to  in- 
vestigate the  effects  which  in  general,  the  disturbing  force  would 
produce  in  their  approiimale  commensurabilitv. 

When  (ho  perinds  are  nearly  commensurable,  the  successive 
positions  of  the  line  of  conjunction  will  necessarily  be  before  or 
behind  the  positions  which  it  would  assume  in  the  case  of  eiact 
commcnsurability  by  a  certain  angular  dii^lance,  which  will  be  less 
or  greater  according  as  the  periods  dcpiirt  less  or  more  from  exact 
«nmmensurability. 


PLANETART  PEBrTURBATIONS.  631 

Sni^pose,  for  example,  that  in  the  case  of  exact  commensarability 
the  positions  of  the  Hoes  of  coDJunction  after  each  series  of  three 
sjBodio  revolutions  were  s  i  E,  8 1'  e',  and  s  i"  e",  as  represented  in 
Jig.  863,  and  snppose  that  the  deviation  of  the  periods  from  exact 
oommensurability  is  such  that  the  second  conjunction,  instead  of 
taking  place  at  is!,  shall  take  place  at  a'.  If  a"  e''  =  2  a'  e',  the 
third  conjunction  will  take  place  at  a";  and  if  Ea'"  =  Sif  a',  the 
next  conjunction  will  take  place  at  a'",  and  so  on. 

If,  then,  the  distance  a'  e'  be  very  small,  which  it  will  be  if  the 
periods  are  very  nearly  commensurable,  the  lines  of  conjunction, 
though  not  rigorously  in  fixed  directions  will,  for  a  considerable 
number  of  successive  synodic  revolutions,  crowd  about  those  fixed 
directions  which  they  would  have  rigorously  assumed  if  the  oom- 
mensurability had  been  exact,  and  during  that  interval,  which, 
when  the  synodic  time  is  of  much  length,  will  be  of  great  duration, 
nearly  the  same  inequality  will  be  produced  by  the  want  of  com- 
pensation in  the  effects  of  the  disturbing  force  as  if  the  directions 
of  the  line  of  conjunction  were  fixed. 

But,  however  small  the  advance  a'  e'  of  the  line  of  conjunction 
in  each  synodic  revolution  may  be,  its  continued  accumulation 
through  a  long  succession  of  synodic  revolutions  will  carry  that  line 
at  length  round  the  whole  circumference,  causing  it  in  slow  but 
regular  and  inevitable  succession  to  take  all  directions  with  relation 
to  the  lines  of  apsides  of  the  two  orbits.  When  it  has  made  half  a 
revolution,  or  revolved  through  180^,  it  will  have  precisely  the 
opposite  position  with  relation  to  those  lines,  and  the  disturbing 
force  will  produce  contrary  effects  upon  the  elements  of  the  dis- 
turbed orbit;  and  while  the  line  of  conjunction  revolves  through 
the  other  half  revolution,  the  disturbing  force,  for  like  reasons,  pro- 
daoes  a  series  of  effects  on  the  elements  which  are  the  opposite  to 
those  it  produced  during  the  first  half  revolution. 

3255.  Lonff  inequalities.  —  Hence,  obviously  arise  a  group  of 
inequalities,  affecting  the  elements  severally  of  the  disturbed  orbit, 
the  periods  of  which  will  correspond  with  the  revolution  of  the  line 
of  conjunction. 

What  has  been  said  of  the  varying  position  of  the  line  of  con- 
junction in  relation  to  the  line  of  apsides,  will  affect  the  inequalities 
of  the  major  axis,  the  motions  of  the  apsides,  and  the  eccentricity. 
The  varying  position  of  the  same  line  with  relation  to  the  line  of 
nodes,  will  in  like  manner  affect  the  motion  of  that  line  and  the 
variation  of  the  inclination. 

Having  thus  explained  in  general  the  principle  which  determines 
the  successive  phases  of  the  long  inequalities  of  the  planets, 
we  shall  now  briefly  notice  some  of  the  most  remarkable  of  these 
phenomena. 


tg  ineqtialiti/  of  JupUtr  and  Saturn.  —  Bj  (S984) 
It  will  ba  seen  that  tho  periodic  times  of  Satnra  ui 
nre 

r>  =  10760-21M,     p  =  4332-5848, 
ooaaequently, 

-  =  2  48325  =  -— 0-01675, 

fill  it  appenra  that  five  times  tlie  period  of  Jupiter  exceeds 
t  of  Satum  by  a  small  &aclbD.     Now,  if  2  p*  irere  eucclj 
ftp,  tbe  cDDJunctioDs  would  invariably  take  plao«  in  tbtce 
^  of  120",  (3263).     But  since 


y-P 


=  242-7% 


Hows  tbat  ID  the  serira  of  throe  Guecessive  oonjonctiani  to 

h  tbe  line  would  assame  the  tLrnH)  dirootiona  at  angles  of  I^°, 

,iie  periods  wore   exactly  commensurable,  it  advanoes  bejftod 

)e  diriictionB  sueoessively  by  the  angles,  2*7°,  2-7"  X  2  =  5'4', 

.  2'7  X  3  =  8-1°,  HO  that,  after  making  a  siogle  reTolation  in 

ee  Bjnodic  pcriodit,  it  odvimees  8  1°  Iwyond   its  first  posilino; 

and  as  it  will  continue  to  advance  at  the  same  rate,  in  eveij  three 

synodic  periods  it  will  make  a  complete  revolution  is 

360      ,,  ,, 
j^-  =  44-44  X.  T. 

Bat  the  synodic  period  ia 


and,  therefore,  the  time  of  a  complete  revolatioo  of  the  line  of  con- 
junction will  be 

dmjt  J«n. 

7253-3x44-44  =  322600  =  883-2; 
an  interval  which  is  equal  to  29*96  revolutions  of  Saturn  and  lo 
74'405  revolutions  of  Jopiter.* 

3267.  Period  of  thi,  inequalilif  ahovl  880  i/rar».  —  It  follow*, 
therefore,  from  what  has  been  explained,  that  the  line  of  conjunc- 
tion of  these  planets  revolving  from  a  given  direclion  to  one  diame- 
Wcally  opposite  in  about  440  years,  and  then  completing  its  revolu- 
tion, and  returning  to  its  original  direction  in  the  next  440  years,  a 

•  The  Astronomer  Hojnl,  in  his  tract  on  OraTitntion,  gi»M  855  jnn 
tor  this  ititenal,  but  obierres  that  the  numbers  are  not  qaite  eiaet.  thf 
ratio  of  SB  to  72,  which  h«  takes  as  that  of  the  periodic  tiueB,  not  beiiif 
quite  ac '- 


PLANETART  PERTURBATIONS.  683 

■ems  of  inequalities  will  be  prodaoed  upon  the  elements  of  the  two 
orbits,  which  will  go  on  increasing  or  decreasing  for  a  period  of  440 
jeam,  and  will  undergo  the  contrary  variation^  decreasing  or  in- 
creasing during  the  succeeding  440  years. 

As  already  observed,  however,  it  must  not  be  assumed,  in  this 
or  any  like  case,  that  the  compensation  produced  by  the  contrary 
effects  in  the  two  intervals  is  necessarily  complete,  and  that  the  in- 
crease effaces  completely  the  decrease,  or  vice  versd.  Such  a  perfect 
equilibrium  between  the  effects  of  the  perturbations  rarely  takes 
place. 

8258.  Its  effect  upon  tJie  major  axis  and  periods,  —  One  of  the 
long  inequalities  resulting  from  this  relation  between  the  mean 
motions  of  the  planets,  affects  the  major  axes  of  their  orbits,  and 
consequently  their  periodic  times.  The  major  axis  of  one  orbit 
increases,  and  that  of  the  other  decreases,  continually  for  440  years, 
and  during  the  next  440  years  the  former  decreases  and  the  latter 
increases.  The  consequence  of  this  is  that  the  mean  motion  of 
one  planet  continually  increases,  and  that  of  the  other  continually 
decreases,  during  periods  of  440  years.  Although  the  changes 
produced  upon  the  axes  from  this  cause  are  so  minute  as  to  be 
flcarcely  appreciable,  that  of  Saturn's  orbit  amounting  when  great- 
est to  only  the  1350th,  and  that  of  Jupiter's  to  the  8550th  part 
of  its  length,  the  effects  produced  upon  the  motions  of  the  planets 
are  very  considerable,  the  place  of  Saturn  being  affected  to  the 
extent  of  48',  and  that  of  Jupiter  to  21'.  The  greatest  inequality 
of  any  other  planet  does  not  affect  its  place  to  a  greater  extent  than 
8' ;  and  those  which  are  within  Jupiter's  orbit  are  much  less  affected, 
being  never  removed  from  their  mean  place  by  so  much  as  half  a 
minute. 

3259.  Its  effects  vpon  the  eccentricities.  —  It  appears  that,  during 
the  interval  in  which  the  line  of  conjunction  moves  through  120°, 
the  eccentricity  of  each  of  the  two  orbits  increases,  attains  a  max- 
imum magnitude,  and  then  decreases.  The  effect  produced  upon 
the  planet's  distance  from  the  sun  by  the  change  of  eccentticity  is 
much  more  considerable  than  the  effect  produced  by  the  change  in 
the  magnitude  of  the  major  axis.  In  the  case  of  Jupiter  it  amounts 
to  the  r230th  part  of  the  entire  distance,  and  in  the  case  of  Saturn 
to  the  314th  part. 

32G0.  Effect  on  the  direction  of  the  apsides.  —  The  effect  upon 
the  motion  of  the  apsides  is  subject  to  a  like  period.  A  progressive 
motion  is  imparted  to  them  for  440  years,  and  a  regressive  motion 
for  the  next  440  years.  Between  this  motion  of  the  apsides  and 
the  variation  of  the  eccentricity  of  each  orbit,  there  is  a  necessary 
relation ;  the  eccentricity  of  each  orbit  having  its  mean  value,  when 
the  progressive  or  regressive  motion  of  the  apsides  has  attained  Vfek 


.i  wbcD  the  ecccnlrid 

lies  arrive  at  their  n 

long  inequality  of  Jupiter  and  Satuni  is  a  plieDomcnon  of 

leniblc  historical  celebrity  and  iuterest,  owing  to  the  apparail 

ilarity  nhiob  it  explained,  buvisg  been  observed  long  beiorg 

cause  WHE  diEcovercd,  and  bsTing  given  great  perplexity  to  ai- 

aomers.     Its  cause  was  dewoDBtrated  and  the  whole  character 

aw  of  the  phenomeooD  explained  by  Laplace,  Id  17^5. 

61.   Long  ineqtialiti/  of  V'tna*. — Sest  to  that  which  has  been 

■T.  noticed,  the  most  remarkable  inccjuulity  of  this  class  is  the 

inequality  of  Venue,  tirising  frou  the  neur  commensuTabilily 

_e  periodB  of  that  planet  and  the  Kurtb.     If  p*  and  P  express 

leie  periods,  wo  tJiall  have  (2£»^4,) 

y       305256       ,  „„,,       33       „„-,., 

I,  ISpexoeedaSp'by  0-004P,  thatia,b7the250tiiputrfp. 
^'o  determina  the  nlae  of  f,  we  have 

f  =  360"  X  g^^  =  575-630  ^  5790  _  o-47'. 

But  if  8  P*  wore  exactly  equal  to  13  r,  each  EoeccBtfive  conjunetion 
would  tike  place  570=  io  advance  of  the  last ;  and  since  576°  = 
3  X  180°  +  36°,  it  follows  that  in  this  case  the  line  of  each  euc- 
eessive  conjunction  would  be  3tt°  in  advance  of  that  point  diametri 
oaily  oppoaitfi  to  the  last  eoojunotion.  By  following  this  out  it  will 
be  seen,  that  five  successive  conjunctions  would  t-ikc  place  in  lines, 
dividing  the  whole  circumference  into  five  equal  angles  of  "li". 
But  in  consequence  of  S  i**  being  a  little  greater  than  13  r,  the  line 
of  each  6uccc!!sive  conjunction  will  fall  047°  behind  the  place  it 
would  occupy  if  the  periods  were  exactly  commensurable.  By  the 
continued  accumulation  of  this  deviation,  the  line  of  conjunetion 
will  take  successively  all  positions  round  the  circumference,  shifting 
its  direction  through  0-47°  in  each  synodic  period.  To  determine 
the  time  in  whieh  it  will  make  a  complete  revolution,  it  is  only 
necessary  to  divide  72°  by  0-47,  and  multiply  the  quotient  by  the 
Bjnodio  period.     This  gives 


72  X  584 
0-47       ' 


S94G2  =  244  O.' 


This  inequality,  the  discovery  of  which  is  due  to  the  genins  and 
research  of  die  Astronomer  Royal,  nntwithslanding  tbe  long  interval 
of  its  accumulation,  does  not  esceed,  pvon  at  its  ronximum,  a.  few 
seconds ;  and  affords  a  striking  eiample  of  ibe  degree  of  precision 

*  Accovdittg  to  tte  Aatronomcr  Royal,  239  years. 


PLANETARY  PEBTUBBATIONS.  635 

to  which  onr  knowledge  of  the  planetary  motions  has  been  carried 
bj  the  application  of  the  principles  of  the  theory  of  gravitation. 

326*2.  Other  lotig  inequalities,  —  There  are  several  other  in- 
equalities of  this  class,  incidental  to  the  other  planets,  which  need 
only  be  indicated  here,  their  investigation  and  exposition  being 
precisely  similar  to  these  already  explained.  Thus  in  the  case  of 
Mercury  and  the  Earth 

p'      365-256       .,^       ,       ^,^ 

so  that  the  one  period  is  but  a  little  more  than  four  times  the  other. 
This  produces  an  inequality  whose  period  is  about  seven  years. 
In  the  case  of  Venus  and  Mercury  we  have 

p'      224-701       ^,^       5      ^^, 
P  =  -87  969  =  ^''  =  2  +  '-''' 

In  the  case  of  Mars  and  Venus 

In  the  case  of  Uranus  and  Saturn 

^      30687      ^^^       ^       ^^, 

-  =  TH^^i^  =  2-85  =  3  —  0-15. 
P       10/09 

In  the  case  of  the  Earth  and  Mars 

p'      686-979 


p  "~  365-256 


=  1-88  =  2  — 012. 


In  each  of  these  cases  long  inequalities  are  produced,  the  periods 
of  which  may  be  determined  by  the  method  already  explained. 

8263.  Long  xneqtuilities  of  the  nodes  and  inclination.  —  The 
Ttriation  of  the  motion  of  the  line  of  nodes  and  of  the  magnitude 
of  the  inclination,  consequent  upon  the  changes  of  position  of  the 
line  of  conjunction,  in  all  cases  of  near  commensurability  of  the 
periods,  are  so  exactly  similar  to  the  changes  already  explained,  of 
the  line  of  apsides  and  the  eccentricity,  that  it  is  only  necessary  here 
to  observe  that,  mutatis  mutandis^  all  that  has  been  explained  of 
the  one  is  applicable  to  the  other. 

3264.  Secular  inequalities,  —  The  inequalities  noticed  in  the 
preceding  paragraphs,  have  been  exclusively  those  whose  periods  are 
determined  by  the  variation  of  the  relative  positions  of  the  dis- 
torbing  and  disturbed  planets,  or  by  what  has  been  called  their  con- 
figuration ;  and  which  are  denominated  periodical  inequalities,  not 
because  all  other  inequalities  are  not  also  periodical,  but  because  the 
periods  of  the  former  are  of  much  more  limited  lengthy  and  exo^'^ 


ASTRONOMY. 

Df  the  Jong  ta^qvaJitiea,  suoli  as  may  1»  in  general  com- 
luiii  tlic  limits  of  DstroiiDmienl  records.     Tbc  other  cliue  of 
iities  are  thote  which  ore  from  the  [?ODltnaul  accmnulatian  of 
eaidual   phenomena,  which  remsin  uncompensated  after  llie 
irbing  and  disturhed  bodies  have  passed  through  all  their  phases 
-oD figuration,  and  rcoommonce  to  pass  through  a  like  eerier  of 
Mve  positious ;  these  are  the  secular  inequalitiks. 
265.   Sfcular  conttanry  of  die  major  oxen. —  No  result  of  the 
-trches  of  mathemutieians        nhj'sical  astronomj  has  excited  »i 
so  just  ao  admiratio       '  the  discoverj  of  the  fact  thut, 
the  major  axes  of  the  s  of  the  planets  are  subject  to 

I       lindical  Tariations,  whion  cause  iheir  periodic  timet  and 
n  motions  to  oscillate  within  narrow  limits  round  certwn  mean 
es,  j^et  that  the  mean  values  of  these  axes  are,  in  the  long  run, 
rousjj  invariable  and  euhject  to  not  the  slightest  r»rintion  from 
to  age,  and  cannot  ho  subject  to  any,  so  long  as  the  gukr  sjstein 
ot  inierfvred  with  by  any  agencies,  save  those  which  have  ]Jaj 
mg  the  budici,  great  and  small,  which  compose  it. 
I'he  importaaee  of  this  theorem,  and  the  interest  with  which  iti 
nplele  demonstration  must  be  regarded,  will  be  understood  when 
it   ia   cuntidercd   iLmI,   upon    (lie   niiignitude  of  tlic   niNJnr  mis  of 
the  orbit  of  a  planet  depends  the  apparent  motion  of  the  enn  as 
Keen  from  the  planet,  and  the  average  supply  of  light  and  warmth 
received,  in  a  given  time  from  that  luminary.     Any  continued  and 
Bccumulalcd  change  in  the  major  mis,  bueh  as  would  necessarily 
result  from  a  secular  inequality  aflecting  it,  would  not  only  subvert 
the  plij'iiieul  conditions  to  whiuh  the  organization  of  the  races  whieh 
Inhabit  the  plunets  are  adapted,  but  would  destroy  the  great  land- 
marks of  chroDology,  and  deprive  the  heavenly  bodies  of  some  of 
their  most  imporiunt  uses. 

A  wise  provision  in  the  physical  structure  and  laws  of  the  systeoi 
has,  however,  rendered  such  derangements  impossible,  by  making 
all  the  periodical  perturbations  to  which  the  major  axes  of  the 
planetary  orbits  are  subject,  rigorously  compensatory. 

First.  The  effects  of  the  radial  component  of  the  disturbing  force 
of  one  planet  eierted  upon  another  after  they  have  passed  through 
all  possible  configurations  are  rigorously  compensatory. 

If  the  disturbing  planet  bo  exterior,  the  radial  component  being 
alternately  positive  and  negative,  will  on  the  whole  produce  a  nega- 
tive effeet,  the  aggregate  of  its  negative  actions  exceeding  those  of 
Its  positive.  It  will,  therefore,  on  the  whole  diminish  the  average 
effective  central  attraction.  In  like  manner,  if  the  disturbing 
planet  be  interior  to  the  disturbed,  its  results  on  the  whole  will  be 
to  augment  the  average  effective  central  attraction.  In  the  one  cape, 
ilie  mean  distance  or  major  axis  which  corresponds  to  the  periodic 
time  by  the  harmou\c  \wn  ^'vW  \it  ^jtialer,  and  in  the  other  case  les?, 


PLANETART  PERTURBATIONS.  6ST 

than  it  would  be  in  the  absence  of  the  disturbing  force ;  bnt  in 
both  cases,  so  long  as  the  mean  effective  central  attraction  remains 
the  same,  the  mean  valoe  of  the  major  axis  of  the  orbit  will  be  in- 
Tariable. 

If  we  take  an  interval  of  time  so  great  that  each  of  the  planets 
will  have  assumed,  with  relation  to  the  other,  every  possible  rela- 
tive position,  it  will  follow  that  the  mean  value  of  the  radial  com- 
ponent of  the  disturbing  force  corresponding  to  any  proposed  point, 
p,  of  the  orlHt  of  the  disturbed  planet,  during  such  interval,  will  be 
foand  by  taking  a  mean  of  the  radial  components  of  all  the  disturb- 
ing foroes  exerted  by  the  disturbing  planet  in  all  the  points  M  of 
its  orbit  upon  the  disturbed  planet  at  the  proposed  point ;  for  at  one 
time  or  other  in  the  assumed  inter\'al,  provided  it  be  sufiBcicntly 
great,  the  disturbing  planet  must  have  been  found  at  each  of  the 
points  of  its  orbit,  the  disturbing  planet  being  at  the  same  moment 
at  p.  If,  then,  we  imagine  the  radial  components  of  the  disturb- 
ing force  exerted  by  the  planet  M,  at  each  of  the  points  of  its  orbit 
upon  the  disturbed  planet  at  the  point  p,  and  if  we  take  the  mean 
of  all  these  components  by  dividing  their  sums  by  their  number, 
the  mean  will  be  the  mean  value  of  the  radial  component  of  all 
the  disturbing  forces  exerted  by  the  disturbing  planet  upon  the  dis- 
turbed planet,  when  the  latter  was  found  at  the  point  p  during  the 
assumed  interval.  Now,  it  is  quite  evident  that  this  mean  value 
must  always  be  the  same. 

In  the  same  manner,  the  mean  value  of  the  radial  component  for 
every  other  position  of  the  disturbed  planet  may  be  found,  and  it 
will  be  apparent  that  the  mean  effect  of  the  disturbing  force  esti- 
mated in  the  direction  of  the  radius  vector  at  each  point  of  the 
orbit  of  the  disturbed  planet,  is  always  the  same,  and  consequently 
the  effect  produced  by  this  component  on  the  major  axis  is  always 
the  same.  So  far,  therefore,  as  relates  to  this  component  of  the 
distorbing  force,  the  mean  value  of  the  major  axis  taken  in  an  in- 
terval of  time  BO  great  that  the  two  planets  will  have  assumed  with 
relation  to  each  other  every  possible  position  in  it,  is  subject  to  no 
ultimate  variation. 

Secondly,  The  effects  of  the  tangential  components  are  most 
esaily  explained,  by  considering  the  whole  attractive  foroes  which 
the  disturbing  planet  exerts  upon  the  sun  and  upon  the  disturbed 
planet  It  will  be  remembered,  that  the  disturbing  force  exerted 
by  M  on  P,  is  the  resultant  of  the  attractive  force  exerted  by  M  on  p 
and  a  force  exerted  on  P,  equal  and  opposite  to  the  attractive  force 
which  M  exerts  on  s.  Now,  if  wo  take  M  successively  at  every 
point  of  its  orbit,  and  find  its  attractive  force  on  s,  it  will  be  appa- 
rent that  the  resultant  of  all  these  foroes  directed  from  s  towards  M| 
will  be  in  equilibrium,  and  therefore,  compensatory.     It  followfj 


e  4 


ASTRONOMY. 

it  tho  forces  equal  and  opposite  (o 

<u  ii:^t  OD  P,  muaC  aUo  be  oompeDsitUny. 

inins,  tborefore.  only  to  uiveBlIgile  the  total  eflech  of  I^i 

biuu  OQ  p,  ia  aU   the  posiltoos  which   the   two  bodies  eaa 

sappoacd  to  be  at  an;  given  point  of  its  orbit,  BPd  let  t 
—  every  point  of  I'U  orbit.      These  ore  positions  vhi^  ira 
ivel?  ■esumed  in  the  motions  of  the  two  bodies ;  but  tbejt 
IS  which  at  amu:  uu  .„»  aasumed  inti^rvnl  the;  muit 

-•'  ioterral  be  asm  '  Eufficient  length  ;  and  as  our 

;  ia  to  obtain  t^'  «  effect  of  ^e  forces  during 

ral,  the  ordo  the}'  are  exerted  is  innnate- 

P  bo  thus  e.uj.(Ai  ninke  a  complete  revolution 

a,  -idns  its  position,  t  follovr,  from  a  general  pria- 

of  ies,  that,  when  it  re  to  ila  primitive  place,  afUr 

(jletiu^   _    revolution,   it  wiL  e    OKOclly   the    same   orWtil 

city  as  when  it  sliirted  froi  i  place.      It   follows,  therefore, 

the  effects  of  the  tangent!"  poocnt  of  m's  attraclion  in  ao- 

ating  it  during  its  revo  ^ust  have  been  precisoly  Mnil 

uie  effects  of  the  same  oc  ^cnt  in  retardiog  it.  But  it  im 
uccn  shown  (3154.)  that  every  such  acceleration  producM  an  in- 
crease, and  every  such  retardation  a.  diiniijutioti,  of  the  major  aria 
of  the  orbit.  It  follows,  therefore,  that  in  such  a  rcvolntian,  the 
increments  and  decrcnicnts  of  the  major  axis  would  be  equal,  and  ft 
complete  compenBaCion  would  be  effected. 

Now,  the  same  will  be  true  for  every  position  whatever  which  M 
can  as5unie  in  its  orhit,  and  it  will  therefore  follow,  that  if,  while  M 
[KUiscs  from  point  to  point  of  its  orbit,  with  an  interniittiog  motion, 
p  Biiikcs  a  complete  revolution  during  the  time  it  stops  at  each 

Soint,  the  result  of  the  total  action  of  all  the  disturbing  forces 
eveloped  during  such  a  revolution  of  M  on  the  major  axis  of  p's 
orbit,  would  be  absolutely  compensatory,  and  consequently  the 
major  aii»  after  such  a  revolution  will  have  exactly  the  same  mag- 
nitude it  had  at  its  commencement. 

Now,  it  is  true  that  such  ia  not  the  way  in  which  the  two  bodies 
H  and  i>  do  actually  move.  The  disturbing  planet  M  does  not  stop 
at  each  point  of  its  path  while  the  disturbed  planet  p  makes  a  revo- 
lution, and  they  consequently  do  not  assume  the  various  eonfigura- 
ticna  in  the  order  here  assigned  to  them.  The  two  planets  move 
and  continue  to  move  simultaneously;  hut  they  do  assume  these 
Tarious  configurations,  although  they  take  place  in  a  different  order 
of  succession.  Siuce,  however,  that  order  does  not  affect  the  valuL'S 
of  their  aggregates,  and  since  the  sura  of  all  the  positive  effects  and 
the  sum  of  ail  the  negative  effects  will  still  be  the  same  in  what- 
ever oriler  they  may  take  place,  the  same  perfect  oompensation  will 


PLANETART  PERTUBBATIONS.  689 

be  Tealised  in  tlie  aotaal  motions  which  have  been  here  shown  to 
take  place  in  the  supposed  motions. 

It  will  doubtless  be  objected  to  this  reasoning,  that  we  have  sup- 
posed each  planet  to  make  its  revolution  in  an  orbit  of  fixed  mag- 
nitude and  form,  without  allowing  for  the  displacement  which  the 
disturbing  force  itself  must  inevitably  produce  during  each  revolu- 
tioUi  which^  though  very  small^  is  not  quite  inappreciable.  This, 
however,  has  been  taken  into  the  account  in  some  mathematical 
researches,  and  it  does  not  appear  to  affect  the  conclusion. 

What  is  true  in  this  reasoning  of  the  effect  of  the  disturbing 
force  of  any  one  planet  upon  another,  will  be  equally  true  of  all 
the  planets,  primary  and  secondary,  on  that  other ;  and  it  may, 
therefore,  be  inferred,  in  general,  that  the  major  axes  of  the 
planetary  orbits  are  not  subject  to  any  secular  variation,  and  that 
in  the  course  of  ages  the  periods  and  mean  moUons,  which  by  the 
harmonic  law  depend  on  the  major  axis,  can  never  suffer  any  per- 
manent change. 

3266.  Secular  variation  of  the  apsides.  —  It  has  been  shown 
that  the  change  of  position  of  the  apsides  in  a  synodic  revolution, 
depends  on  the  position  of  the  line  of  conjunction  with  relation  to 
the  perihelion  of  the  disturbed  orbit,  but  in  an  interval  of  time  so 
long  as  to  allow  the  line  of  conjunction  to  assume  all  possible  posi- 
tions, all  possible  effects  will  be  produced  upon  the  apsides.  The 
magnitude  of  these  effects  will  vary  with  the  varying  distance  of 
the  disturbing  planet  from  the  disturbed  orbit.  The  greatest  effect 
will  obviously  be  produced  at  those  parts  of  the  disturbed  which 
are  nearest  to  the  disturbing  orbit;  and  in  taking  a  mean  of  all 
the  variations  of  the  apsides  during  the  entire  interval  these  effects 
will  predominate,  so  that  it  may  be  assumed  that  the  final  residual 
effect  upon  the  apsides,  will  bo  identical  in  its  character  with  the 
effect  produced  in  those  conjunctions  which  take  place  at  the  points 
where  the  two  orbits  are  nearest  to  each  other. 

The  position  of  these  points  will  evidently  depend  upon  the  rela- 
tive magnitude  of  the  two  major  axes,  their  relative  position,  and 
the  eccentricities  of  the  two  orbits. 

If  that  half  of  the  disturbed  orbit,  in  the  middle  of  which  aphe- 
lion is  placed,  be  nearer  than  the  other  half  to  the  orbit  of  the 
disturbing  planet,  the  secular  motion  of  the  apsides  will  be  pro- 
gressive ;  if  it  be  more  remote,  the  motion  will  be  regressive.  If 
the  position  of  the  orbits  be  such  that  both  halves  are  equidistant 
from  the  orbit  of  the  disturbing  planet,  there  will  be  no  secular 
variation  of  the  apsides. 

The  secular  motion  of  tho  apsides  will  continue  to  have  the 
same  direction,  until  their  change  of  relative  position  shall  alter 
the  cond^ioos  and  render  them  stationary,  or  reverse  the  direction 
of  the  motion. 


itlar  variation  of  the  tceentridtg. — The  BoeaUr  efM 

.iiuruing  force  upon  ibe  eoccotricit;  of  the  diatarbed  orbit, 

r  [[iBCof  the  apsides,  Kiuiilur  in  character  to  the  effect  product 

se  poiais  of  tha  disturbed  orbit,  vbich  are  ncmrest  to  ttie  di«- 

iig  orbit.     Tbe   eeocDlrioitj  will  accordingly,  on    the  whole, 

Dr  iacrcnse  or  dt.'crciae,  or  suffer  no  cbaoge,  according  to  ibe 

tioD  of  tbe  peribelioD  of  tbe  disturbed  orbit  at  those  poinU 

re  Ihe  two  orbits  are  in  greal«et  prozimitj,  and  it  will  contione 

affected  io  Ibe  same  manner,  n"*'l  the  conditioDB  are  changed 

le  secular  change  of  tbe  apsides. 

le  place  where  tbe  two  orlnta  arc  io  closest  proximitj,  both 

are  in  general  moving  cither  frooi  aphelion  to  perihelion,  or 

"jutrery,  m  that  one  eccentricity  is  increasing  and  the  other  de- 

e  secular  variation  of  tbe  eccentrioitics,  if  it  cootitmcd  to  tkke 

^  in  the  same  way,  either  always  increasing  or  always  decreasingi 

Id,  after  a  period  of  time  of  great  lengtli,  but  still  detinile,  so 

ge  as  to  derange  in  a  serious  degree  the  economy  of  the  systeni, 

to  expose  tbe  planets  to  Guob  viciasilades  of  lempcratore  ai 

.id  be  inoompacible  with  their  well-being,  not  to  lucniioD  other 

_-se8  of  derangement  which  would  atlcod  such  changes.     It  h 

foutid,  howoViT,  by  pursuing  the   inquiry,  and  Iraciug  the  changes 

in  long  periods  iuctdentsl  to  the  eccentricity,  that,  slow  and  long 

continued  as  these  are,  they  are  still  periodic,  and  ultimately  com- 

peosatory.     After  varying  in  one  way,  either  by  continual  increase 

or  continual  diminution,  for  many  thousand  years,  each  eccentricity 

will  at  a  certain  epoch  cease  to  vary,  and  will  then  begin  to  undergo 

a  contrary  variation,  dccreasiog  if  it   had  before   increased,   and 

increasing  if  it  had  before  decreased ;  and  tbis  will  continue  for 

periods  of  like  length  until  it  attain  another  limit  at  which  it  will 

become  stutiooary,  and  so  on  without  end. 

3:208.  Sf':Hhir  VII  rial  ion  of  III  f  norhs. — The  same  mode  of  ezpl*- 
nation  as  was  adopted  in  ibo  case  of  tbe  other  elements,  wiU  serve 
to  explaiu  the  sccuhir  variation  of  the  nodes  and  inclinations.  It 
bus  been  sbonn  that  llie  coitipoiiunts  of  the  disturbing  force,  which 
are  enjual,  parallel,  and  opposite  to  the  pbnel's  attraction  on  tbo 
BUD,  taken  in  every  point  of  its  orbit,  are  exactly  compensatory, 
and  may  therefore  in  tliis  fttfe  be  neglected.  If,  then,  the  forces 
exerted  by  the  disturbing  plunct  M,  at  all  points  of  its  orbit  upon  P, 
at  any  one  point  of  its  orbit  he  taken,  it  is  easy  to  see  that  llicir  re- 
sultant will  be  a  force  which  will  tend  to  draw  P  from  the  plane  of 
its  own  orbit  towards  the  plane  of  m's  orbit.  This  will  be  apparent 
from  the  consideralinn  that  the  total  effect  of  m's  attraction  will  be 
nmtiar  in  character  to  its  effeot  where  most  intense,  that  is,  at  tbe 
points  where  the  two  orbits  are  in  closest  proximity.     Jf  follows, 


PLANETARY  PERTURBATIONS.  641 

therefore,  that  the  nodes  of  p's  orbit  must  secularly  regress  upon 
m'b  orbit. 

It  is  necessary,  nevertbcless,  to  bear  in  mind  that  this  secular 
regression  on  the  orbit  of  the  disturbing  planet  docs  not  infer  its 
regression  on  other  places.  A  regression  on  one  place  may  cause  a 
progression  of  the  nodes  of  the  same  orbit  with  another  plane. 

3269.  Secular  variation  of  the  inclination. — If  the  orbits  of  both 
planets  were  absolutely  circular,  the  periodical  inequalities  of  the 
inclination  would  be  exactly  compensatory,  and  there  would,  there- 
fore, be  no  secular  variation  of  that  element ;  for  in  such  case  at 
points  equally  distant  from  the  point  which  is  most  remote  from  M, 
M  exerts  equal  disturbing  forces  on  the  inclination,  one  tending  to 
increa.se  it,  and  the  other  to  decrease  it. 

But  if  the  orbits  be  elliptic,  a  certain  point  can  be  determined 
where  the  effect  of  the  orthogonal  component  of  the  attracting  force 
of  M  on  p  is  greater  than  at  any  other  point,  and  the  total  effect 
produced  on  the  inclination  by  M  taken  in  every  part  of  its  orbit,  on 
P  taken  in  every  part  of  its  orbit,  in  all  positions  of  the  line  of  con- 
jnnction  with  relation  to  the  line  of  nodes,  will  be  similar  in  charac- 
ter to  this  maximum  effect ;  and  such  will  be  the  character  of  the 
eecular  variation  of  the  inclination. 

The  observations,  however,  which  have  been  made  (3267),  re- 
specting the  limits  within  which  the  secular  variation  of  the  eccen- 
tricities are  confined,  are  equally  applicable  to  the  inclinations. 
These  also,  though  they  may  severally  increase  continually  (subject 
to  their  periodical  oscillations),  for  thousands  of  years,  will  necess- 
arily decrease  continually  for  periods  of  like  duration,  and  the  limits 
within  which  this  secular  oscillation  is  confined  are  in  all  cases 
extremely  narrow. 

3270.  Laplace* s  theorems  of  the  relations  hetioeen  the  eccentricities 
and  inclinations  of  the  planetary  orbits. — The  researches  of  Laplace 
have  led  to  the  discovery  of  a  beautiful  mathematical  relation  which 
prevails  between  the  eccentricities  and  inclinations  of  the  planetary 
orbits,  which  may  be  easily  comprehended  without  any  profound 
mathematical  knowledge,  although  its  demonstration  does  not  admit 
of  exposition  on  principles  sufficiently  elementary  to  allow  of  its  in- 
troduction here. 

THEOREM. 

"If  thx  numbers  which  express  the  square  of  the  eccentri- 
city AND  THE  square  ROOT  OF  THE  SEMI-AXIS  MAJOR  OF  EACH  OF  THE 
rLAKET.VRr  ORBITS  BE  MULTIPLIED  TOGETHER,  AND  THEIR  PRODUCT  BE 
XCLTIPLIED  BT  THE  NUMBER  WHICI^  EXPRESSES  THE  MASS  OF  THE 
PLANET,  THE  SUM  OF  ALL  SUCH  PRODUCTS  FOR  ALL  THE  PLANETS  WILL 
ALWATS  BE  THE  SAME,  NOTWITHSTANDING  THE  SECULAR  VARIATION  OF 
THE    KCCENTRICITT.'' 

This  celebrated  theorem  may  be  conveniently  and  very  concisely 

54* 


ASTROSOMT. 

lically  as  follows :  Let  a  express  the  mean  vilne 

.^,  .i._jw.'  &xifl.     Let  m  express  tbc  mass  of  tLe  pkii«l,  and 

m!Qtrioitj )  let  all  the  axes  aod  all  the  raa^Ksea  be  L-ipresspd 

lation  to  tbe  same  unit.     If,  then,  the  gymUol  2  be  used  to 

j  tbe  result  of  the  addition  of  the  preoediDg  products  taken 

IV  planeta  aeverullj,  wc  shall  have 

X  (m  X  v/"^  X  O  =  C, 
be  foand  that  tbis  sum  c  nerer  has  varied  nnd  Dever 

maDuer  the  relation  of  the  inclination  is  exprmxd 
g 

THEOREM. 

THK     riCMBBBS   ITBICR     KXFRKSB    IBK    EQITARE     OF    1 


If  I  express  the  inclination,  this  theorem  may  in  like  manner  be 
expressed  thus, 

and  it  will  he  found  that  c'  never  has  and  never  will  vary. 

It  was  shown  in  a  paper  by  ihe  author  of  this  volume,  read 
before  the  Astronomical  Sociely,  that  if  the  present  position  of  tbe 
plane  of  the  ecliptic  be  taken  as  the  fised  plane  of  reference,  tbe 
values  of  these  sums  will  be 

c  =  OOO000S27fl4I 
(/ =^000000314170. 

3271-  Conservative  injluence  erroneous}!/ asrribfd  to  these  Aro- 
rems.  —  These  theorems  have  been  represented  by  astronomical 
writers  generally  as  affording  a  complete  security  against  any  undue 
secular  increase  of  the  eccentricities  or  inclinaiions  of  the  planetary 
orbits.* 

It  has  been  shown,  however,  in  the  memoir  already  referred  to, 
by  the  author  of  this  volume,  that,  except  so  far  as  relates  to  the 
major  planets,  these  theorems  have  no  such  conservative  infinence, 
and  that  the  eccentricities  and  inclinations  of  the  terrestrial  planets, 
for  anything  contained  in  these  formula;,  might  increase  to  au 
extent  which  would  utterly  derange  the  economy  of  the  system. 

•  See.  for  eiample,  llcrscliel.  Oullints  of  Astronomj,  ed.  18-19,  p.  405, 
«2;  Omnt,  History  of  fl   *  ...-.--    ,r. 


SPHEROIDAL  PERTURBATIONS.  648 

CHAP.  XXIV. 

THEORY   OF   SPHEROIDAL  PERTURBATIONS. 

3272.  Attraction  of  planets  would  be  central  if  their /orms  were 
exactly  itpherical. — In  the  preceding  inyestigadons  of  the  effects  of 
the  reciprocal  atlractioDS  of  the  bodies  com  posing  the  solar  system, 
the  attraction  exerted  bj  each  of  these  upon  the  others^  is  considered 
to  emanate  from  its  centre  in  all  directions  around  it,  as  laminous 
xajs  would  from  a  radiant  point.  This  would  be  strictly  true  if  the 
gravitating  bodies  were  all  spherical;  since  it  is  a  property  of  a 
sphere  that  the  matter  composing  it,  supposing  it  to  be  either  uni- 
formly dense,  or  to  have  a  density  varying  according  to  some  fixed 
law  depending  on  the  distance  from  tlic  centre  of  the  mass,  exercises 
on  all  distant  bHlies  exactly  the  same  attraction  as  if  its  entire  mass 
were  concentrated  at  its  centre. 

But  if  the  attnicting  body  be  not  spherical,  this  will  not  be  true; 
and  accordingly  the  attraction  exerted  by  any  such  body,  must  be 
investigated  with  especial  reference  to  its  form. 

3273.  Disturbing  forces  consequeyit  on  spheroidal  forms.  —  Now, 
although  the  planets  generally,  including  the  earth,  are  very  nearly j 
they  are  not  exactly^  spherical,  as  has  been  already  explained.  The 
ellipticity  of  these  spheroids,  though  too  inconsiderable  to  produce 
any  sensible  effect  upon  their  mutual  attractions,  or  to  require  to  be 
taken  into  account  in  any  analysis  of  their  perturbations,  is  never- 
theless sufficient  to  produce  very  sensible  effects  on  the  mutual  at- 
tractions of  the  spheroidal  planets  and  their  satellites,  and  even  upon 
the  phenomena  resulting  from  the  central  attraction  of  the  sun 
exerted  upon  them. 

These  effects  are  manifested  in  the  motions  of  the  planets  them- 
selves by  periodical  changes  in  the  position  of  their  axes  of  rotation, 
and  in  their  satellites  by  similar  changes  in  the  elements  of  their 
orbits. 

It  is  these  effects  that  we  denominate  spheroidal  inequali- 
ties ;  the  name  indicating  their  physical  cause. 

3274.  Effects  which  woidd  be  produced  if  a  satellite  were  at- 
tached to  the  surface  of  tlie  earth  at  the  equator.  —  If  the  earth 
were  attended  by  a  second  satellite,  revolving  close  to  its  surface 
and  in  the  plane  of  its  equator,  its  periodic  time  would  be  less  than 
that  of  the  moon,  in  a  ratio  which  is  easily  ascertained  by  the  har- 
monic law.  Let  m  express  the  moon's  period,  /  its  distance,  p  the 
period  of  such  a  satellite  as  is  here  supposed,  and  r  its  distance  from 
the  earth's  centre      We  should  then  have 


ASTROSl>JJT. 

jG  suppq^d  Efttcllite  is  close  to  tbo  surface,  its  distuioe    > 
.  ^,-eQtrc  is  the  c^tlL's  scuii-diametcr  ;  aad  since  the  maoa't 
Id  is  sixty  scmi-diamctcrs  of  the  eartL,  ve  shill  have 

'1-  2-. 

ance  m  =  C55-73  Lours  (2470),  it  fol!ws  lliat  p  =  3613 

■  satellite  would  be  subject  to  the  disturbing  action  of  the 

1  would  proi3uce  in  its  orbit  inequalities  similar  in  kind  to, 

t  in  magnitude  from,  those  produced  bj  the  sun's  dis- 

i  on  the  moon's  orbit.    Its  nodes,  tliat  is,  the  equinoctial 

ta  ^.iiiuiuuch  as  its  orbit  is  by  the  supposition  the  plana  of  the 

kir),  would  receive  a  slow  regressive  malioD ;  and  its  iucliaa- 

tbat  is,  the  obliquity  of  the  ecliptic,  would  be  subject  to  a  vari- 

ffbose  period  would  depend  on  tbat  of  the  successive  rctujDi 

»  sun  to  the  same  equinoctial  point. 

s  salellil*  would  also  be  subject  to  the  disturbing  nction  of 
_.oon,  which  would  afiect  it  in  a  maancr  nearly  similar;  since, 
^hat  case,  also,  the  disturbing  body  would  be  exterior  ta  tbe  dis- 
hed.    It  would  import  to  tlie  line  of  nodes  of  the  Buppceed 
Balellito,  tliat  is.  to  the  intorsocli™   of  tlie  plane  of  il^  orbit  with 
the  plane  of  the  earth's  equator,  a  retrograde  motion  upon  the 
former  plane;  and  since  that  plane  is  ioclloed-at  a  very  sm^dl  angle 
to  the  plane  of  the  ecliptic,  this  would  produce  a  like  retrograde 
motion  of  the  equiuoctial  points  upon  the  ecliptic. 

A  variation  of  the  inclination  of  the  plane  of  the  equator  to  tbat 
of  the  moon's  orbit,  and,  therefore,  to  the  plane  of  the  ecliptic, 
would  also  he  produced,  the  period  of  which  would  depend  oq  the 
moon's  motion. 

But  the  moon's  orbit  would  also  be  disturbed  by  the  attraction 
of  the  supposed  satellite.  A  regressive  motion  would  be  imparted 
to  the  line  in  wbteh  the  plane  of  its  orbit  intersects  that  of  the 
equator,  and  a  periodical  variation  of  inclination  would  likewise  be 
produced,  depending  on  the  period  of  the  supposed  satellite. 

Let  us  now  tmngine  tbat  the  supposed  satellite,  instead  of  re- 
volving in  3-G13  hours,  moves  with  a  mucti  slower  motion,  and 
revolves  in  23  hours  dud  56  miuutoa,  the  time  of  the  earth's  rota- 
tion. The  inequalities  which  it  suScrs  and  which  it  produces,  will 
then  be  changed  only  in  their  magnitudes  and  periods,  but  will 
rclam  the  same  general  character.  But  the  supposed  satellite  now 
having  the  same  motion  precisely  as  the  surface  of  the  earth  close 
to  which  it  is  placed,  may  be  imagined  to  adhere  to  that  surface,  so 
as  to  form,  iu  fact,  a  part  of  the  earth,  without  iu  any  way  deranging 
the  conclusions  which  have  been  deduced  above. 
S275.  Lii-e  ffffcfs  woiUd  he  produced  by  an)/  number  of  inch 


SPHEROIDAL  PBBTURBATIONS.  645 

tatelliteSy  or  what  would  he  equioalentj  hy  the  spheroidal  form,  — 
Bat  the  same  obflervations  would  be  equally  applicable  to  any  num- 
ber of  satellites  similarly  placed  and  similarly  mcrving,  which  might, 
therefore,  be  imagined  to  be  successively  attached  to  the  surface  of 
the  globe  at  aud  near  the  equator,  until  such  a  protuberance  would 
be  formed  upon  it,  as  would  in  effect  convert  it  into  the  form  of  an 
oblate  spheroid,  such  as  the  form  of  the  earth  b  known  to  be. 

It  is,  however,  to  be  further  considered,  that  the  effects  of  the 
disturbing  forces  which  thus  act  upon  this  protuberant  matter,  are 
necessarily  modified  by  the  inertia  of  the  spherical  mass  within  it^ 
to  which  it  18  imagined  to  be  attached.  The  protuberant  mass 
which  alone  is  acted  on  by  the  disturbing  forces,  cannot  obey  any 
action  of  these  forces,  without  dragging  with  it  this  vast  spherical 
mass  to  which  it  is  united.  The  motions  and  changes  of  motion, 
therefore,  which  it  receives,  will  be  rendered  slower  in  proportion  to 
the  mass  with  which  such  motions  must  be  shared. 

These  observations  are  obviously  applicable  equally  to  any  of  the 
other  planets,  which  being  attended  by  satellites  have  the  spheroidal 
form.  This,  as  has  been  already  explained,  is  the  case  with  Jupiter 
and  Saturn,  and  would  probably  be  found  to  prevail  equally  in  the 
oases  of  the  other  major  planets. 

8276.  Preceuion  of  the  equinoxes.  —  Since,  therefore,  we  may 
consider  the  spheroidal  protuberance  around  the  terrestrial  equator 
as  a  satelli^  attached  to  the  earth,  it  will  follow  that  the  general 
effect  of  the  sun's  disturbing  force  acting  upon  it,  will  be  to  impart 
to  its  nodes,  that  is,  to  the  equinoctial  points,  a  retrograde  motion, 
will  be  much  slower  than  that  which  they  would  receive  from  the 
same  cause,  if  this  protuberant  matter  were  not  compelled  to  carry 
with  it  the  mass  of  the  earth  contained  within  it. 

The  moon  exercises  a  like  disturbing  force  which  produces  a  like 
regression  of  the  nodes  of  the  equator  on  the  moon's  orbit ;  and 
that  orbit  being  inclined  at  a  small  angle  to  the  ecliptic,  this  is 
attended  with  a  like  regression  of  the  equinoctial  points. 

The  mean  annual  regression  of  the  equinoctial  points  upon  the 
plane  of  the  ecliptic  arising  from  these  causes,  is  50  1". 

8277.  The  sun  returns  to  the  equinoctial  point  before  completing 
its  revolution.  —  Since  the  equinoctial  points  thus  move  backwards 
on  the  ecliptic,  it  follows  that  the  sun,  after  it  has  in  its  annual 
coarse  passed  round  the  ecliptic,  will  arrive  at  either  equinoctial 
point  before  it  has  made  a  complete  revolution.  The  equinoctial 
point  being  50*1''  behind  the  position  it  had  when  the  sun  started 
from  it,  the  sun  will  return  to  it  after  having  moved  through  50*1" 
less  than  a  complete  revolution.  But  since  the  mean  hourly  appa- 
rent motion  of  the  sun  is  147-8"  (2458),  it  follows  that  the  centre 
of  the  sun  will  return  to  its  equinoctial  point, 


ASTROKOMT. 


^omplctiDg  its  rcTolation. 

i.  Equinoctial  and  mdrrval  year.  —  Hence  is  explained  tiia 
,  which  sppeare  in  (29S4),  Table  II.,  that  while  the  aideM«l 
:,  or  actual  revolution  of  the  earth  roniid  the  sun,  is 

10-S8, 
'  tevoluyon,  or  the  time  between  two  sncces^ve  equi- 


365242255  =  365     5    48    50-4, 
alter  being  le«  than  the  former  by  20°-  20' . 
le  euccemiTe  returns  of  the  sun  to  the  same  eqainoctial  point 
,,  therefore,  always  precede  its  return  to  the  Game  point  of  the 
tjo,  by  20--  20'  of  time,  and  by  50  1"  of  spnce. 
.279.  Period  o/ preeation. — To  determine  the  period  in  wfaieli 
Ao  equinoctial  points  moFing  bsclcwsnts  constantly  at  this  mran 
rate  wovld  moke  a  cnniplete  rcvnlulion  cf  llie  ccliplic,  it   is  only 
necessary  to  find  how  often  5U-1"  must  be  repeated  to  make  np 
860°,  or,  what  is  the  same,  to  divide  the  number  of  seconds  in  360" 
by  501.     This  gives 

'  —  =  2o868  years. 

3280.  lis  effect  upon  the  loiigiluiteo/cekstial  o'yVf/ji.  —  Although 
this  motion,  e^Iow  as  it  is,  is  easily  detected  from  year  to  year  by 
modem  instruments,  it  was  not  until  the  sixteenth  century  rhat  its 
precise  nilc  was  appertained.  Small  as  is  its  annual  amount,  its 
accumulation,  conliuucd  from  year  to  year  for  a  long  period  of  time, 
causes  a  groat  displacement  of  all  the  objects  in  the  heavend,  in  re- 
lation to  the  equinoctial  points  from  which  longitudes  and  right 
ascensions  arc  nica.iun^d.  In  "I'C  years,  the  equinoxes  retrograde 
1°,  ami  tlicrcforc,  in  that  time,  the  longitudes  of  all  celestial  ohjeoU 
of  fixed  piiiiilinn,  such  as  the  stars,  have  their  longitudes  augmented 

.  1°.  Since  the  formation  of  the  earliest  eatalognea  in  which  the 
positions  of  the  fixed  stars  were  registered,  the  retrogression  of  the 
equinoctial  points  has  amnuntcd  to  30°,  so  that  the  present  longi- 
tudes of  all  the  ohjecis  consigned  to  these  catalogues,  is  30°  greater 
than  those  which  are  there  assigned  to  them. 

3281.  Pi-eicigim,  ■i/cqiiiii'.j-es  prod'iccs  a  roltUlun  of  the  pole  of 
the  rqiialor  i-oiind  t/ml  of  the  ctUptic.  —  If  two  diameters  of  the 
celestial  sphere  be  imagined  to  be  drawn,  one  perpendicular  to  the 
plaDc  of  the  equator  Md  the  other  to  that  of  the  eclipljc,  the  angle 


SPHEBOIBAL  PERTURBATIONS.  647 

iDcIuded  between  them  will  obyiously  be  eqnal  to  the  angle  under 
the  equator  and  ecliptic ;  and  since  the  extremities  of  these  diame- 
ters are  the  poles  of  the  equator  and  ecliptic,  it  follows  that  the  arc 
of  the  heavens  included  between  these  poles  is  equal  to  the  obliquity 
of  the  ecliptic. 

But  since  a  plane  passing  through  these  diameters  is  at  right 
angles  both  to  the  equator  and  ecliptic,  the  line  of  equinoxes  or  the 
intersection  of  the  planes  of  the  equator  and  ecliptic,  will  be  at  right 
angles  to  that  plane.  If,  therefore,  the  equinoctial  points  revolve 
round  the  ecliptic  in  a  retrograde  direction,  it  follows  that  the  plane 
passing  through  the  diameters  above  mentioned,  and  through  the 
poles  of  the  two  circles  to  which  the  line  joining  these  points  is  at 
right  angles,  will  revolve  with  a  like  motion,  round  that  diameter 
of  the  sphere  which  is  at  right  angles  to  the  plane  of  the  ecliptic, 
and  which  therefore  terminates  in  its  poles.  But  since  the  pole  of 
the  celestial  equator  is  upon  this  circle  at  a  distance  from  the  pole 
of  the  ecliptic  equal  to  the  obliquity  of  the  ecliptic,  it  follows  that 
the  pole  of  the  equator  will  be  carried  round  the  pole  of  the  ecliptic, 
in  a  lesser  circle  parallel  to  the  plane  of  the  ecliptic,  with  a  retro- 
grade motion  exactly  equal  to  that  of  the  equinoctial  points. 

3282.  Distance  of  jpole  of  equator  from  pole  of  ecliptic  varies 
with  the  obliquiti/. — And  since  the  distance  of  the  pole  of  the  equa- 
tor from  that  of  the  ecliptic  must  always  be  exactly  equal  to  the 
obliquity  of  the  ecliptic,  it  follows  that  every  change  which  may 
take  place  from  whatever  cause,  in  the  position  of  the  plane  of  the 
equator,  whether  the  change  affect  the  angle  at  which  it  is  inclined 
to  the  ecliptic,  or  the  position  of  the  equinoctial  points,  must  be 
attended  with  a  corresponding  change,  either  in  the  apparent  dis- 
tance of  the  pole  of  the  equator  from  that  of  the  ecliptic,  or  in  the 
rate  or  direction  of  the  motion  of  the  latter  round  the  former. 

3283.  PoU  star  varies  from  aye  to  age, — As  the  pole  of  the 
•qoator  is  carried  with  this  slow  motion  round  the  pole  of  the 
ecliptic,  its  position  for  all  popular,  and  even  for  some  scientific, 
purposes  is  usually  indicated  by  the  nearest  conspicuous  star,  for  it 
rarely  happens  that  any  such  star  is  found  to  coincide  with  its  exact 
place.  Such  star  is  the  pole  star,  for  the  time  being;  and  it  is 
clear  from  this  motion  of  the  pole,  that  the  polo  star  must  necessarily 
change  from  age  to  age. 

The  present  polar  star  is  a  star  of  the  second  magnitude  in  the 
constellation  called  the  '*  Lesser  Bear,''  and  its  present  distance 
from  the  exact  position  of  the  pole  is  1°  24'. 

The  motion  of  the  pole  as  above  described,  however,  is  such  that 
this  distance  is  gradually  diminishing,  and  will  continue  to  diminish 
until  it  is  reduced  to  about  half  a  degree ;  after  which  it  will  in- 
crease,  and  after  the  lapse  of  a  long  period  of  time,  the  pole  will 


ASTHONOMT. 

star,  and  it  will  ceaso  to  bear  the  name,  or  Mm 

I,  01  t  pole  star. 

,  TOTTnrr  and  ftilnre  }>ote  rfnrs.  —  If  upon   any  staiMoap  a 

i«  *n — '  round  (he  polo  of  the  ecliptic  at  a  distaooe  from  it 

^     '  rrle  will  pa^s  through  ait  positions  which  the  poI« 

ill  hare  in  time  to  come,  or  has  had  in  tinie  put; 

be  easily  seen  which  arc  the  conspicnoiu  etara  io 

•«  Qcij  hood  it  vill  pass  in  sfteT  ages,  and  near  which  it 

'•vfi  —       -•  — 1,  and  which  will  become  in  future,  or  have 

">"*,  —  pole  star  of  the  age. 

■8  from  the  present  time,  for  example,  it  will  be 

le  will  pass  withio  a  few  degrees  of  the  itu  of  the 

luae  in  the  constellation  of  "Lyra,"  called  a  hyrte. 

tig  back  in  the  same  manner  the  position  of  the  pole 

ig  [lie  Btare,  it  is  found  that  at  an  epoch  3970,  or  nearly  4000 

I,  bufure  the  present  time,  the    pole  waa  55°  15'  behind  in 

ut  jioaitioa  in  longitude;  and  at  this  time  the  nearer  bnght 

to  it  was  the  star  y,  in  the  conBtellatioo  of  ''  Draco."     T&e 

ncc  of  this  atAr,  at  that  time,  from  the  pole  mnst  hnrv  been 

i4'  26". 

32«5.  Rnnnrlohl'  rh-cimft'inrermmM'il  irifh  the  f^-omid!.— 
In  the  researches  which  have  been  made  in  Egypt,  a  somewhat  rc> 
markubJc  circumstance  haa  been  discovered,  having  relation  to  thb 
subject. 

Of  the  nine  pyramids  which  still  remain  standing  at  Obtteb,  vx 
have  openings  presenl*;d  to  the  north,  leading  to  straight  passages 
which  dcaccnJ  at  an  inclination  varying  from  26°  to  27",  the  axes 
of  the  pnsBages  bi'iiig  in  all  cases  io  the  plane  of  the  meridian  of  the 
pyramid.  Two  pyramids,  still  staoJiog  at  Aboasseir,  have  similar 
openings  leading  to  passages  having  similar  directions. 


!  imagine  an  observer  stationed  at  the  bottom  of 
of  tticsc  passages,  aud  looking  out  along  its  axis  as  be  would 
through  the  lube  of  a  telescope,  his  view  will  be  directed  to  a  pfrint 


J 

upon  the  northern  meridian  of  the  place  of  the  pyramid  at  a 
tude  of  between  26°  and  27°,  corresponding  with  the  slope  of  the 
passage.  This  is  precisely  the  altitude  at  which  the  star  y  Braconis 
must  hare  passed  the  meridian  below  the  pole,  at  the  date  of  3970 
years  before  the  present  time,  alloiFing  for  the  difference  of  position 
of  the  pole  according  to  the  principle  affecting  the  precession  of  the 
equinoies  esplaioed  above.  Now,  the  dale  of  the  construction  of 
the  pyramids  corresponds  almost  eiactly  with  thb  epoch;  and  it 
cannot  be  doubled,  that  the  peculiar  direction  given  to  these  passages 
must  have  had  reference  to  the  position  of  y  Draconis,  the  pole  star 
of  that  age. 

8286.  Nutation.  —  The  regression,  described  above,  of  the  equi- 
noctial points  u-pon  the  ecliptic,  must  bo  understood  as  their  mean 


SPHEROIDAL  PERTURBATIONS.  648 

change  of  place  prodaced  by  the  disturbiDg  fbroea  of  the  nm  tad 
moon  npon  the  protnberant  matter  of  the  equator  in  long  periods - 
of  time.  Bat  this  regression  is  not  prodaced  at  a  nnifbrm  rate. 
The  distorbing  forces  Taiy  in  their  action  according  to  the  general 
principles  abreadj  explained,  with  the  angles  formra  by  linea  drawn 
from  the  snn  and  moon  to  the  centre  of  me  earth  with  the  plane  of 
the  equator.  So  &r  as  relates  to  the  snn,  this  variation  in  its  effect 
goes  throoffh  all  its  changes  within  a  year.  In  the  ease  of  the 
moon,  it  will  obvioasly  vary  from  month  to  month  and  from  year 
to  year,  with  the  change  of  position  of  the  moon's  nodes;  and  as 
these  nodes  haye  a  regressive  motion  making  a  complete  revolntion 
in  abont  nineteen  years,  the  variation  of  the  effect  of  the  moon's 
distorbing  force  will  pass  throngh  all  its  changes  within  that  period. 
The  regressive  motion  imparted  to  the  equinoctial  points,  and  also 
to  the  pole  of  the  equator  in  moving  round  the  pole  of  the  eoliptioy 
as  already  described,  by  the  sun  and  moon,  is  therefore  sntject  to 
mn  alternate  iucrease  and  decrease,  whose  period  is  a  year  tor  the 
son,  and  nineteen  years  for  the  moon. 

But  these  are  not  the  ouly  effects  produced  npon  the  position  of 
the  pole  of  the  equator  by  the  disturbing  action  of  the  moon  and 
ann.  According  to  what  has  been  explained  in  general  of  the  effects 
of  the  orthogonal  component  of  the  disturbing  force,  it  will  be  easily 
understood  that  the  protuberant  matter  of  the  equator  being  re- 
garded as  a  satellite  disturbed  by  the  sun  and  moon,  the  inclination 
of  the  plane  of  the  equator  to  the  ecliptic  will  be  subject  to  a  varia- 
tion proceeding  from  the  disturbing  force  of  the  sun,  whose  period 
will  DC  a  year ;  and  its  inclination  to  the  plane  of  the  moon's  orbit 
will  be  subject  to  a  like  variation,  whose  period  is  about  nineteen 
jeara.  These  changes  of  the  inclination  of  the  plane  of  the  equator 
to  that  of  the  ecliptic  and  the  moon's  orbit  will  be  attended  with  a 
correaponding  motion  of  the  polo  of  the  equator  to  and  from  the  pole 
of  the  ecliptic. 

This  alternate  spproach  and  recess  of  the  pole  of  the  equator  to 
and  from  the  pole  of  the  ecliptic,  combined  with  the  alternate 
increase  and  decrease  of  its  regressive  motion,  is  called  the  Nutation; 
that  part  of  it  due  to  the  sun  being  called  the  solar  nutation;  and 
that  due  to  the  moon,  the  lunar  nutation. 

The  solar  nutation  is  an  inequality  of  so  small  amount  as  alto- 
gether to  escape  observation,  and  therefore  must  be  looked  upon  to 
have  a  merely  theoretical  existence. 

It  is  otherwise,  however,  with  the  lunar  nutation.  By  die 
alternate  increase  and  decrease  of  the  regressive  motion  of  the  pole, 
combined  with  its  alternate  approach  and  recess  to  and  from  the 
pole  of  the  ecliptic,  the  pole  is  moved  in  such  a  manner  that,  if  it 
were  affected  only  by  the  disturbing  force  of  the  moon,  it  would 
describe  an  ellipse  such  as  A  bod,  fig,  864;  the  maysc  axsaa  t£ 

m.  55 


ASTEOSOMT. 

nbich  would  be  in  the  *]ircetion  a  s  nf  At 

pole  of  the  ecliptic,  and  wnnld  niessnre  lib", 
while  the  tniDor  axis  would  be  it  right  angUt 
to  this  direction,  and  would  mcBSun;  13.74". 
But  while  the  pole  of  the  equator  describe! 
this  ellipse  compietiDg  its  revolntioa  in  olat- 
t«en  jeani,  it  is  carried  by  the  cominaa 
notion  of  preceaaion,  in  a  retrograde  di;e»- 
tion,  ag  already  described,  at  the  i 
bOl"  in  each  year,  and  will,  ihereforr,  in 
nineteen  years  he  carried  throtigh  15-5'  ii 
motion  round  the  pole  of  the  equator.  S 
by  combining  this  motion  with  the  elliptio 
motion  already  doscribed,  it  will  be  euiljr 
Eeen  that  the  polo  of  the  equator  would,  is 
revolving  round  the  pole  of  the  ecliptic,  »J- 
tcnialely  approaching  to  it  and  receding  froB 
it  through  9-25",  describe  an  undulating  lioa 
Gucfa  as  is  represented  in  ^.  8G5,  '  ' 
represeota  llie  pole  of  the  ecltptio. 

rig.  664.  3287.    Equation  of  tht  eqiiinoxa.  —  Siooe 

the  regression  of  the  equinoxes  does  ni 
place  at  a  aniform  rate,  but  is  Euhjcct  to  variations,  alternaielj 
lncre4«ing  and  decreasing  during  every  nineteen  years,  its  true  pluw 


will  di&er  from  its 


If  we  conceive  a 


niform  motion  at  the  r»te  of 
50°  1",  the  place  of  sach  pciot 
would  be  the  mean  place  of  tb« 
equinoctial  point.  The  tme  pUst 
would  vary  from  this,  preceding  it 
when  the  disturbing  force  augmenti 
the  rate  at  which  the  equinocciti 
point  moves,  and  falling  behind  it 

V\  )     when  it  decreases  that  rate. 

'\^  /  The  distance  between  the 

and  imaginary  equinoctial  points  is 

called  the  equation  of  the  equxnoxt*. 

The  mean  place  of  the  equinox 

Fig.  esj.  for  any  proposed  time  is  given  E>j 

tables;   and    the   equation    of  tlie 

equinoxes  for  the  proposed  time  gives  the  quantity  to  be  a ' "  ' 

to,  or  subtrocled  from,  the  mean  place,  to  find  the  true  place. 

3288.   Proportion  of  the  mean  preceaion  due  to  the  diiturbiiy 
forctt  of  0\t  moon  and  mn.  —  If  the  entire  amount  of  the  mean 


SPHEROIDAL  PERTURBATIONS.  651 

precession  in  a  givcD  time  be  expressed  by  7,  the  part  dne  to  the 
moon  will  be  5,  and  that  due  to  the  sun  will  be  2. 

3280.  Like  effects  produced  in  the  case  of  other  planets.  —  These 
disturbing  effects  produced  upon  the  plane  of  the  planet's  equator, 
are  not  confined  to  the  case  of  the  earth.  All  the  planets  which  have 
the  spheroidal  form,  are  subject  to  similar  effects  from  the  sun's 
attraction  on  their  equatorial  protuberance,  the  magnitude  of  these 
effects  being,  however,  less  as  the  distance  from  the  sun  is  increased. 
In  the  case  of  the  major  planets,  the  sun's  disturbing  action  on  tho 
planet's  equator,  proceeding  from  this  cause,  will  be  altogether 
insensible. 

The  disturbing  forces  of  the  satellites  exerted  upon  the  plane  of 
the  equator,  in  the  cases  of  the  major  planets,  however,  must  be 
coDsidenble  in  magnitude,  especially  so  far  as  relates  to  the  inner 
satellites,  and  very  complicated  in  its  character,  the  precession  and 
natation  of  each  of  the  satellites  separately  being  combined  in 
affecting  the  actual  position  of  the  pole  of  the  planet. 

Since,  however,  these  phenomena  are  necessarily  local,  and  mani- 
fested only  to  observers  on  the  planet,  they  offer  merely  speculative 
interest  to  the  terrestrial  astronomer. 

8290.  Effects  of  spheroidal  perturbation  on  the  motions  of  the 
moon  generaiiy  minute.  —  The  protuberant  matter  of  the  terrestrial 
spheroid  disturbs  the  lunar  orbit,  in  the  same  manner  as  would  a 
satellito  placed  at  the  surface  of  the  earth  and  in  the  plane  of  the 
eqoaUir.  From  what  has  been  explained  of  the  general  effects  when 
the  distorbinff  body  is  within  the  disturbed  orbit,  it  will  follow  that 
the  terrestrial  spheroid  must  impart  a  progressive  motion  to  the 
moon's  apsides,  and  a  regressive  motion  to  the  nodes.  These  in- 
aqnalities  have,  however,  a  theoretical  existence  only,  being  so 
minute,  compared  with  the  progression  of  the  apsides  and  regression 
off  the  nodes  due  to  the  disturbing  force  of  the  sun,  that  they  do  not 
prod  ace  any  observable  change  iu  these  motions. 

8291.  Spheroidal  inequality  of  the  inclination  of  the  moon's 
orbti  observable.  —  A  case,  however,  exists,  in  which  the  disturbing 
force  of  the  terrestrial  spheroid  does  produce  sensible  effects  on  the 
lunar  orbit. 

It  has  been  already  shown,  that  the  moon's  nodes  move  round 
the  ecliptic  with  a  retrograde  motion,  in  about  nineteen  years. 
Twice  in  this  period  they  miLst,  therefore,  coincide  with  the  equi- 
noctial points ;  and  when  they  do  so,  the  line  of  nodes  must  coincide 
with  the  inclination  of  the  planes  of  the  equator  and  ecliptic.  In 
one  of  the  two  positions  which  they  thus  assume,  the  plane  of  the 
moon's  orbit  must  lie  between  the  planes  of  the  ecliptic  and  equator 
as  represented  in  Jif/,  806,  where  acdc'a'  represents  the  equator, 
acd^a'  the  ecliptic,  and  ac/d^/'a'  the  moon's  orbit.  In  tho 
other  posidon  the  moon's  orbit  will  make  a  greater  angle  with  thA 


ASTRONOMY. 


tqiutor  than  Uie  ecliptio  does,  and  will  lie  above  the  ecliptie,u 
tepicscnteil  at  A.bDb'  a'. 


Now,  if  no  distorbing  force  acUd  Dpon  the  ]>lane  of  the  loooa'i 
•rbit,  ita  obliquity  to  tbe  plaue  of  the  ecliptic  woald  remaia  inn- 
liable;  and,  iLerefore,  in  bolh  pasitioca  here  repreaected,  the  »af^ 
U  would  make  wiih  tbe  ecliptic  would  be  the  same,  that  ia  to  u;, 
6°  8'  48",  which  ia  the  mean  inclination  of  Lhe  moon's  orbit. 

But,  if  it  be  admitted  that  tbe  bpberoidal  protnbersnoe  of  the 
MTtb  acts,  aa  it  baa  been  ahow  o  to  do,  as  a  Hatellitc  would  sitnale 
in  Ihe  plane  of  the  equator,  thia  ntlraction  would  libewiae  tend  la 
draw  llie  tuoon  towards  that  plane,  and  it  would  act  more  energvti- 
callj  when  the  jilane  of  the  moon's  orbit  niakps  a  iess,  than  when 
it  make*  a  greater,  augle  with  the  equator-  Thni  th«  ipbenidal 
perturbationa  of  the  oKtih  will  act  more  onergeticallj  in  ilirtiiliiw 
the  plane  of  the  moon's  orbit,  when  it  has  the  poalioa  a  dl>i  A, 
than  wbeo  it  has  the  poution  a  6  d  &' a'.  The  oonee 
be  that  the  angle  farmed  bj  ADci  with  acd  would 
greater  than  the  angle  formed  hj  Abo  with  A e D. 

Another  eonseqaence,  of  still  greater  practical  importmca  in  pn^ 
docing  an  inequality,  which  wotJd  be  still  more  easily  ol«eiTibi(t 
will  follow  ftom  thia.  The  greater  energy  of  the  dhiUirlHitg  font 
when  the  mcoo'i  orbit  has  the  poeitioii  Ado  than  wlien  it  has  the 
poeition  A  6  D,  will  impart  to  the  moon  a  more  rapid  angular  motiM 
when  it  passes  through  the  point  of  the  orbit  represented  by  ArfB^ 
than  when  it  paases  through  that  point  of  the  orbit  indiciled  by 
A  6  s ;  that  is  lo  say,  the  apparent  motion  of  the  moon  will  be  ncn 
rapid  than  its  mean  motion,  when  the  orbit  has  the  former  pontiaB, 
and  lees  rapid  when  the  orbit  has  the  latter  posilicm.  Now,  a  msU 
TariatioD  of  the  moon's  apparent  motion  is  mom  easily  ebaerfed 
than  a  small  vatialion  of  the  inclination  of  its  orbit  in  the  eeliptie. 

Theae  effects  of  the  disturbing  feme  ot  the  spheruda]  protnbenaee 
of  the  earth  hare  aooordJugly  been  obeerved. 

It  has  been  found  that  iht  angle  formed  by  A(2d  with  Acsii 
greater,  and  the  angle  formed  by  Afio  with  acd  le«,  than  the 
mean  inclination  of  the  moon's  orbit  to  the  eoliptie;  and  while  the 
aooB'a  orUt  haa  the  position  A  do  ita  apparent  motioa  i>  greater, 


SPHEROIDAL  PERTURBATIONS.  658 

and  -while  it  has  the  apparent  position  a  5  d  its  apparent  motion  b 
less,  than  ita  mean  motion.  This  difference  is  found  to  produce  a 
Tariation  of  the  moon's  place  in  its  orbit  or  of  its  longitude  amounting 
to  8",  by  which  it  gets  in  advance  of  its  mean  place  when  the  orbit 
has  the  position  xdD,  and  lags  behind  it  when  the  orbit  has  the 
position  A  &  D. 

Since  the  interval  between  the  epochs  at  which  the  moon's  orbit 
has  the  two  positions  indicated  in  the  figure,  is  one  half  the  period 
of  the  regression  of  the  nodes,  that  is  about  nine  years  and  a  half, 
it  follows  that  the  moon's  inclination  to  the  ecliptic  gradually  in- 
creases duriuff  that  interval  of  nine  years  and  a  half,  from  its  posi- 
tion A  if  D  to  Its  position  a  &  d,  and  that,  during  the  next  nine  years 
and  a  half,  it  gradually  decreases  from  its  position  A  2>  D  to  its  posi- 
tion AdD;  therefore,  it  follows  that  the  moon's  angular  motion  is 
continually  greater  than  its  mean  value  during  nine  years  and  a 
half,  and  continually  less  during  the  next  nine  years  and  a  half. 

Now,  this  inequality  in  its  exact  quantity  depends  altogether  upon 
the  obUteness  of  the  terrestrial  spheroid,  or,  what  is  the  same,  on 
the  ratio  of  the  equinoctial,  to  the  polar  diameter  of  the  earth.  If 
thia  ratio  were  greater  than  301  to  300,  its  actual  value,  the  ine- 
qnality  of  the  moon's  motion  consequent  upon  it  would  be  greater, 
luad  accordingly  its  apparent  place  would  be  more  than  8"  in  advance 
of  the  true  place  in  the  one  interval  of  nine  years  and  a  half,  and 
kn  so  in  the  succeeding  nine  years  and  a  half;  and,  on  the  con- 
traryi  if  the  ratio  of  the  equatorial  to  the  polar  diameter  were  less 
than  801  to  800,  the  variation  of  the  moon's  apparent  motion  would 
be  lees  than  8".  Thus  it  appears,  that  this  minute  inequality  of 
the  moon's  motion,  developed  in  the  protracted  periods  of  nineteen 
jear8|  supplies  a  measure  of  the  spheroidal  form  of  the  earth,  the 
nanlt  of  which  completely  verifies  the  other  methods  already  ex- 
plained, of  determining  the  ellipticity  of  the  terrestrial  spheroid. 

8292.  Spheroidal  inequalities  of  the  Jovian  tystem.  —  The  ob- 
lateness  of  Jupiter,  still  greater  than  that  of  the  earth,  produces 
inequalities  of  the  motion  of  the  satellites,  similar  to  those  produced 
by  the  spheroidal  protuberance  of  the  earth  upon  the  moon,  but 
greater  in  degree  and  more  rapid  in  their  development,  in  proportion 
to  the  greater  ellipticity  of  the  planet  and  the  greater  proportional 
proximity  of  the  satellites.  Thus,  a  progressive  motion  is  imparted 
to  the  apsides,  and  a  regressive  motion  to  the  nodes  of  each  of  the 
aatellites ;  and  these  motions  are  so  much  the  more  considerable  the 
nearer  the  satellite  is  to  the  planet.  The  effect  of  this  spheroidal 
perturbation  on  the  inner  satellites  is  so  predominant,  that  the  mo- 
tion of  these  satellites  is  nearly  the  same  as  it  would  be  if  no  other 
disturbing  force  whatever  affected  them. 

It  will  be  obvious  that  a  very  complicated  system  of  inequalities 
nraat  thus  be  produced  upon  the  satellites  of  Jupiter,  inasmuch  aa 

65* 


ASTROSOMT. 

tnnf  effeot  of  the  spheroidal  protuberanoe  of  Oit  planet 

elements  of  eaob  of  the  orbits,  is  neceGsarily  mixed  np 

.ae  distorbine  effects  of  the  tatellites  upon  each  other. 

93.   Spheroidal  inr^uaHlia  of  the  Sntumian  gyafem.  —  The 

rbini^  forces  produced  by  the  spheroidal  form  of  Saturn,  tre  in 

a  similar  to  thoec  developed  id  iho  Jovian  gysteta.     The 

^e  ring  is  near);  the  same  as  if  the  oblsteness  of  the 

'.  w«re  sngraented,  —  with  this  difference,  however,  that  the 

it  being  attached  to  the  pir  oot  clogged  with  the  inertia 

t  spherical  mass  within  aging  npon  it,  as  is  the  case 

■nheroidal  protuberanc         ^ne  planet 

'"»iiM  of  this,  the  I  «!  efcota  of  the  ring  and  the 

'■berance  of  the  is  to  impart  a  Terj  npid 

n  to  the  Bpsit  a  regressive  motion  to  the 

i«  of  the  severs'  '         ites.     These  effects  must  he 
iBij  grcBi  the  inner,  ti  the  more  remote  satellites. 

1  theory  (  perturhsti  liiis  system  is  rendered  veiy 

1,  owing  K  fiict,  tha  "an,  in  oonaequcnce  of  its  re- 

ess  ana  ol   uie  small  vitii  le  which  the  whole  system 

.luds  at  it,  can  produce  no  se.  lertiirbation.     The  sRtelliteB 

mn,  however,  been  so  imperfectly  ooeervwi  that  no  data  have  been 
obtained,  by  which  the  results  of  the  theoretical  reasoniog  respect- 
ing the  spheroidal  perlQrbationa  can  be  verified  with  regud  to  any 
of  the  aabellites,  except  the  sixth.  This,  has,  howerer,  baea  Mb> 
mitted  to  an  elaborate  series  of  obeerTations  by  Vrotamor  Boaid, 
who  has  ascertained  the  nUe  of  progression  of  its  apsides,  and  tfa« 
regrosaion  of  its  nodes. 

By  oaloolaling  what  the  progrsssion  and  regretdon  wotild  (w, 
which  would  arise  fimm  a  given  mass  assigned  to  the  ring,  and  eon- 
puing  the  results  of  snob  calonlatioa  with  the  aotnal  progremtm  of 
the  apsides  and  regresuon  of  the  nodes,  he  found  that  &t»  Mtod 
inequalities  are  such  as  wonid  be  prodncad,  if  the  mass  of  tia  nng 
unonnted  to  the  118th  part  of  the  entire  mass  of  the  i^aoet  In 
this  approximative  calculation,  however,  the  whole  ineqoali^  inci- 
dent to  the  nodes  and  apsides  of  the  mxth  satellite,  is  aseribed  lo 
the  disturbing  foroe  of  the  ring.  It  is  evident,  therefore,  that  the 
Talue  of  the  mass  of  the  ring,  thna  obtained,  most  be  more  than  its 
true  value. 

It  appears,  therefore,  that  while  the  entire  mass  of  this  ensnlar 
append^,  stopendons  as  it  is,  is  less  than  the  118th  part  of  the 
mass  of  the  planet,  the  mass  of  the  moon  amounts  to  so  tnndi  as 
the  80th  part  of  the  mass  of  the  earth.  It  follows,  therefim,  that 
relatively  the  entire  mass  of  Saturn's  ring  is  less  than  that  (tf  tha 
moon,  in  the  proportion  of  2  to  3. 


FIXKD  8TAB8.  665 


CHAP.  XXV. 

THX  nZlD  STARS. — STSLLAB  PABALI4AX  AMD  DISTANOS. 

82M.  Creation  not  ctrcufMcrtbed  hy  the  tolar  $y$tem.  The  re- 
cion  of  spaoOi  yast  as  it  is,  which  is  oceapied  by  the  sokr  systenii 
forms  but  s  small  portion  of  that  part  of  the  material  nniTerBe  to 
whioh  eeieiitific  inqoirj  and  research  haTO  been  extended.  The 
inaoisitiTe  Rpirit  of  man  has  not  rested  content  within  such  limits. 
Takinff  its  stand  at  the  extremities  of  the  system^  and  throwing  its 
searching  glance  toward  the  interminable  realms  of  space  which  ex- 
tend beyond  them,  it  still  asks — ^What  lies  there  1  Has  the  Infinite 
eireamsoribed  the  exercise  of  his  creative  power  within  these  pre- 
cincts—  and  has  He  left  the  unfathomable  depths  of  space  that 
stretdi  beyond  them,  a  wide  solitude  1  Has  He  whose  dwelling  is 
immensity,  and  whose  presence  is  eveiywhere  and  eternal,  remained 
inaetiTe  Uiroughout  regions  compared  with  which  the  solar  system 
shrinks  into  a  point  ? 

Bran  thon^  scientifio  research  should  haye  left  us  without  defi> 
Bite  information  on  these  questions,  the  light  which  has  been  shed 
on  the  Dirine  character,  as  well  by  reason  as  by  reyelation,  would 
ksvB  filled  us  with  the  assurance  that  there  is  no  part  of  space,  ho#- 
tfor  remote,  which  must  not  teem  with  evidences  of  exalted  power, 
inexhaustible  wisdom,  and  untiring  goodness. 

But  science  has  not  so  deserted  us.  It  has,  on  the  eontrary, 
sai^4ied  us  with  much  interesting  information  respecting  regions  of 
the  universe,  the  extent  of  which  is  so  great  that  even  the  whole 
dtoMBsioiis  of  the  sdar  system  supply  no  modulus  sufficiently  great 
So  enable  us  to  express  their  magnitude. 

8295.  The  $olar  tyitem  mrrounded  by  a  vast  hut  limited  void.^- 
We  tare  furnished  with  a  variety  of  evidence,  establishing  incontes- 
SiUy  the  fiiet,  that  around  the  solar  system,  to  a  vast  distance  on 
fliveiy  aide,  there  exists  an  unoccupied  space ;  that  the  solar  system 
■lands  alone  in  the  midst  of  a  vast  solitude.  It  has  been  shown, 
that  the  mutual  gravitation  of  bodies  placed  in  the  neighbourhood 
of  eaeh  other,  is  betrayed  by  its  effects  upon  their  motions.  If, 
therefore,  there  exist  beyond  the  limits  of  the  solar  system,  and 
within  a  distance  not  so  great  as  to  render  the  attraction  of  gravita- 
tion imperceptible,  any  mass  of  matter,  such  as  another  sun  like  our 
own,  such  a  inass  would  undoubtedly  exercise  a  disturbing  force 
npon  the  various  bodies  of  the  system.  It  would  cause  each  of 
them  to  move  in  a  manner  different  from  that  in  which  it  would 
have  moved  if  no  such  body  existed. 

Thus  it  appears  that,  even  thoogh  a  mass  of  matter  in  our 


ASTRONOMY. 

hood  nbotild  escape  direct  otserrstion,  its  presence  would  ■ 

ibly  betrayed  by  the  effecta  which  its  gravitation  would 

iM  upon  tbo  pianots.     No  sach  effects,  however,  sra  diacorer- 

The  pianeta  move  as  they  would  moTO  if  the  solar  sysCem 

indcpeudeQt  of  any  external  disturbing  attraction,     thtst 

ma  are  such,  aod  euch  only,  as  can  be  accounted  for  by  the 

'"lion  of  the  sun  and  the  reciprocal  attra'^tion  of  the  other 

a  of  the  system.     The  inference  from  this  is,  that  there  do«s 

*       ■■      '      '        eighbourhood  of  tho  boIm 

^ita  auch  a  maas  to  exerciiw 

nence ;  and  that  if  any  body 

rsc,  it  must  be  placed  at  a 

pitode  of  onr  system  will 


B  of 


id  the  itirrovmlin/}  void.  — 
Jen,  on  any  clear  night,  t* 
the  conotless  mnltitndc  of 
ring  what  a  companticel; 
me  of  the  solar  syecein,  and 
r  one  time,  we  ftre  natnnllj 
e  these  vast  nuni- 


loy  mass  D 
"-'tliin  any  disu 

liaoovcrable  distu 
iMir  sun  exists  ic 
D  it,  that  the  * 

lOtt  int,  compared 

rit.    S/ie  »uiTi  mail  be  pic-- 
let  of  tenn'ble  parallax. 
mplate  the  firmament,  an< 
B  that  sparkle  upon   it,  r 
Dtiaiber  are  comprised  am 
of  thcEO  bow  few  are  visibL 
unpeljed  ta  the  inquiry,  Where  in 
bers  of  o\>jeet3  placed  'i 

Very  little  reflection  and  reasoning,  applied  to  the  conndnation 
ti  our  own  position  and  to  the  appeannoe  of  the  heavens,  will  ood- 
Tinoe  us  that  the  objects  that  chiefly  appear  on  the  finnament, 
most  be  at  almost  immeasureable  distauceB.  The  earth  in  iti 
annual  course  round  the  sun  moves  in  a  circle,  the  diameter  of 
which  is  about  200  millions  of  miles.  We,  who  observe  th« 
heavens,  are  transported  upon  it  ronnd  that  vast  cirole.  The  statimi 
ftom  which  we  observe  the  univerve  at  one  period  of  the  year  ia, 
then,  200  millions  of  miles  from  the  station  from  which  we  view  it 
Bt  another. 

Now  it  is  a  fact,  within  the  familiar  experience  of  every  one,  that 
the  relative  position  of  objects  will  depend  npon  the  point  froia 
which  they  are  viewed.  If  we  stand  npon  the  bank  of  a  rirer, 
along  the  margin  of  which  a  multitude  of  ships  are  stationed,  and 
view  the  masts  of  the  vessels,  they  will  have  among  each  other  a 
certain  relative  arrangement  If  we  change  our  position,  however, 
through  the  space  of  a  few  hnodred  yards,  the  relative  position  of 
these  masts  will  not  be  the  same  as  before.  Two  which  before  lay 
in  line  will  now  be  seen  separate;  and  two  which  before  were  sepa- 
laled  are  now  brought  into  line.  Two,  one  of  which  was  to  the 
right  of  the  other,  are  now  reversed  j  that  which  was  to  the  right, 
b  at  the  left,  and  vice  vertA ;  nor  are  these  changes  produced  by 
any  change  of  position  of  the  ships  themaelvea,  for  they  are  moored 
io  ftationsrj  poutiona.     The  changes  of  appaaimnoo  are  the  reaall 


THB  FIXED  STABS.  657 

of  <wr  aum  change  of  pontion ;  and  the  sreater  that  ehaoge  of 
position  18,  the  greater  will  be  the  relative  change  of  these  ap]>ear- 
anoes.  Let  na  suppose,  however,  that  we  are  moved  to  a  much 
greater  distance  from  the  shipping ;  any  change  in  our  position  will 
produce  much  less  effect  upon  the  relative  position  of  the  masts ; 
perhaps  it  will  require  a  very  considerable  chance  to  produce  a  pei^ 
oeivable  effect  upon  them.  In  fine,  in  proportion  as  our  distance 
from  the  masts  is  increased,  so  in  proportion  will  it  require  a  greater 
ehange  in  onr  own  position  to  produce  the  same  apparent  change  in 
tlieir  position. 

Tims  it  is  with  all  visible  objects.  When  a  multitude  of  station- 
ary objects  are  yiewed  at  a  distance,  their  relative  position  will 
depend  upon  the  position  of  the  observer;  and  if  the  station  of  the 
observer  be  changed,  a  change  in  the  relative  position  of  the  objects 
must  be  expected;  and  if  no  perceptible  change  is  produced,  it 
must  be  inferred  that  the  distance  of  the  objects  is  incomparably 
greater  than  the  chance  of  position  of  the  observer. 

Let  us  now  apply  these  reflections  to  the  case  of  the  earth  and 
the  stars.  The  stars  are  analogous  to  the  masts  of  the  ships,  and 
the  earth  is  the  station  on  which  the  observer  is  placed.  It  might 
baye  been  expected  that  the  mscnitude  of  the  globe,  being  eight 
thousand  miles  in  diameter,  would  produce  a  ehange  of  position  of 
the  observer  sufficient  to  cause  a  change  in  the  relative  position  of 
the  stars,  but  we  find  that  such  is  not  the  case.  The  stars,  viewed 
from  opposite  sides  of  the  globe,  present  exactly  the  same  appear- 
ance; we  must,  therefore,  infer  that  the  diameter  of  the  earth  is 
abedutely  nothing  compared  to  their  distance. 

But  the  astronomer  has  still  a  much  larger  modulus  to  fall  back 
upon.  He  reflects,  as  has  been  already  ob^rved,  that  he  is  enabled 
to  view  the  stars  from  two  stations  separated  from  each  other,  not 
hj  8000  miles,  the  diameter  of  the  earth,  but  by  200  millions  of 
miles,  that  of  the  earth's  orbit.  He,  therefore,  views  the  heavens 
on  the  1st  of  January,  and  views  them  again  on  the  1st  of  July, 
the  earth  having  in  the  meanwhile  passed  to  the  opposite  side  of  its 
orbit,  yet  he  finds,  to  bis  amazement,  that  the  aspect  is  the  same. 
He  thinks  that  this  cannot  be  —  that  so  great  a  change  of  position 
in  himself  cannot  fail  to  make  some  change  in  the  apparent  position 
of  the  stars ;  —  that,  although  their  general  aspect  is  the  same,  yet 
when  submitted  to  exact  examination  a  change  must  assuredly  be 
detected.  He  accordingly  resorts  to  the  use  of  instruments  of  ob- 
servation capable  of  measuring  the  relative  positions  of  the  stars 
with  the  last  conceivable  precision,  and  he  is  more  ^han  ever  con- 
founded by  the  fact  that  still  no  discoverable  change  of  position  is 
found. 

For  a  long  period  of  time  this  result  seemed  inexplicable,  and 
accordingly  it  formed  the  greatest  difficulty  with  astronomers,  in 


^9 


Q&Bi  ASTKOKOMT. 

kdniittiog  the  snnual  motion  of  the  ctrth.  Tlio  allenialM 
was  this;  it  was  neccGEorj,  either  to  fall  havk  upOD  UieH 
rjticia,  in  which  the  earth  was  Btatiooity,  or  to  anppow  I 
immense  change  of  position  of  the  earth  in  the  connw  of  b>fl 
oould  produce  no  discOTcnble  change  of  appearance  in  the  ri 
fact  which  involves  the  inference  that  the  diameter  of  tbp  « 
orbit  must  be  *,  mere  point  compared  with  the  distance  of  the  DCarart 
ptara.  Such  an  idea  appeared  eo  inadmisEihlc  that  for  a  long  period 
of  time  man;  preferred  to  embrace  the  Ptoiemaio  bTpotliuw,  btMt 
BS  it  was  with  difficulticfl  and  contradictions. 

Improved  means  of  instrumental  observation  and  niioroni«taMl 
measurement,  united  wilb  the  leal  and  skill  of  obecrvcra,  liavs  >l 
length  surmounted  these  difficulties ;  and  the  parallax,  small 
indeed  hut  atill  capable  of  measurement,  of  several  Klars  bas  been 


!3290.  Anjival paraUnz.  —  PaTathcllc  itUipx.  —  To  render  these 
results  and  the  processes  by  which  tbej  have  been  attained  ialel- 
ligiblc,  wo  must  resume  the  esplanatioo  of  the  general  effects  of 
unoal  parallax,  already  brie6y  given  (3442). 
The  visual  ray  by  which  a  star  is  seen,  and  which  is  its  apparent 
direction,  is  carried  by  (lie  annual  nintion  of  the  earth  round  th^ 
Burface  of  a  cone,  of  which  ilic  oarlb's  orbit  I'which  we  may  here 
consider  as  a  circle)  is  the  base  and  of  which  the  star  is  the  apex. 
The  line  drawn  from  the  centre  of  the  earth's  orbit  to  the  star, 
vhich  is  its  true  or  heliocentrio  direction,  is  the  axis  of  this  cone; 
&nd  consequently,  the  parallax  of  the  star  is  the  angle  under  tha 
Utter  line,  and  the  visual  ray  by  the  motion  of  which  the  snrfiuM  U 
the  cone  is  formed. 

The  same  optical  effect  would  be  produced  by  transfeniog  the 
OThital  motion  of  the  earth  to  the  star,  the  observer  being  supposed 
to  be  stationary  and  placed  at  the  centre  of  tbe  earth's  orbil^  and 
this  BuppoutioD  will  render  all  the  parallactJo  phenomena  much 
more  easily  comprehended.  Let  tbe  star,  then,  be  imagined  to 
move  in  a  circle  equal  and  parallel  to  tbe  earth's  orbit,  the  oentn 
of  the  circle  being  the  true  place  of  the  star.  The  place  of  (he  star 
in  this  circle  of  parallax  must  always  be  diametrically  opposite  lo 
the  corrcBponding  place  of  the  earth  in  its  orbit.  The  star  so  moving 
would  suffer  exactly  the  same  apparent  displacement  as  it  would 
appear  to  suffer  if  it  were,  as  it  is,  at  rest  in  its  true  place,  the  earth 
moving  in  its  proper  orbit  round  tbe  sua. 

Let  e,  Jiff.  867,  bo  tbe  tme  place  of  the  star,  and  let  a  b  a'  B*  be 
its  circle  of  parallax,  the  plane  of  which  is  parallel  to  that  of  tbe 
ecliptic,  and  tbe  radius  of  which  is  equal  to  that  of  the  earth's  orbit 
Let  BB'  be  the  line  in  which  tbe  plane  of  this  circle  is  intersected. 
by  a  plane  through  the  sun  and  star  perpendicular  to  the  ecliptic,  or 
viiat  is  the  same,  by  the  plane  of  the  circle  of  latitude  passing 


STELLAB  PABALLAX  AND  DISTANCE.  OM 

I  throngh  the  bUt;  uid  let  Aa'  b«  the  diameter 
of  the  circle  of  pamlks  which  ja  at  right  aoglea 
to  that  plane.     When  the  longitude  of  the  sun 
ia  the  same  as  that  of  the  star,  the  apparent 
place  of  the  star  will  be  at  b',  that  eztremitj  of 
I    the  diameter  b  b*  which  is  most  remote  firom  the 
1 ;  and  when  the  longitude  of  the  bud  ex- 
ds  that  of  the  star  b;  180°,  it  will  be  at  B, 
the  extremity  of  the  same  diameter  which  it 
neareat  to  the  snn.     When  the  longitude  of  the 
min  ezceeda  that  of  the  star  by  90°,  the  apparent 
place  of  the  star  will  be  at  a',  the  eastern  ex- 
tremity  of  the   diameter  A  a';   and   when  it 
Kg.  Bsr.  exceeds  that  of  the  star  hj  270°,  it  will  be  at 

A,  the  western  extremity.  It  appears  therefore, 
tlixt  while  the  ann  makea  a  complete  revolution  of  the  ecliptic  from 
the  point  at  which  it  baa  the  longitude  of  the  star  antil  its  return 
to  the  BBme  point,  the  star  appears  to  moTe  rouod  the  circle  of  the 
parallax  Arom  B*  in  the  direction  indicated  by  the  arrows,  taking 
■acceasively  the  positions  p  and  the  angle  ^  &p  or  the  arc  ^p, 
Imng  klw&ya  equal  to  the  oifFerence  of  the  longitudes  of  the  aun  and 
■tar  measured  from  the  star  in  the  order  of  signs. 

Bat  the  plane  of  this  circle  a  b'  a'  b  beiog  parallel  to  that  of  the 
ecliptic,  wiU  be  inclined  to  the  surface  of  the  celestial  sphere,  at  an 
•ngle  equal  to  the  complement  of  the  latitude  of  the  star;  and  by 
the  common  principles  of  projection  it  will,  when  projected  optiimlly 
OD  that  surface,  become  an  ellipse,  of  which  tho  major  axia  ia  the 
projection  of  tho  diameter  a  a',  and  is  parallel  to  Qtt  eolip^  ud 
the  minor  axis  that  of  Bb',  and  which  is  perpendicnlar  to  the 
eetiptic,  and  therefore  coincident  with  the  circle  of  ladtnde  of 
the  star.  The  diameter  a  a'  being  parallel  to  the  sar&ce  on  which 
it  is  projected,  is  not  altered  in  apparent  magnitnde  by  projection  ; 
Imt  die  diameter  b  b*  is  dimioiahed  by  projection,  in  the  ratio  of  tht 
dot  of  the  star's  latitude  to  1. 

In  the  figure,  thia  ellipse  is  represented  abore  the  circle  of 

It  will  be  apparent  that,  when  the  star  is  prctjected  on  B  or  B*, 
ite  longitude  ia  not  a&ected  by  parallax,  but  its  latitude  is  increased 
by  8  B  at  b,  and  diminished  by  b  b*  at  b'.  In  like  manner,  when 
the  atar  is  seen  at  A  or  a',  its  latitude  ia  not  afiected  by  parallax ; 
bnt  its  longitude  is  iucreased  by  e  a'  at  a',  and  dimioisowl  by  8  A 
•t  A. 

When  the  star  is  seen  at  any  of  the  intermediate  pdnta  p  of  the 
puxllactio  ellipse,  it  ia  affected  by  parallax  both  in  latitude  and 
longitadB,  e  n  beiog  the  paralUz  in  longitude,  and  p  n  the  p^H'T 
In  Utitui^ 


VW  A8TR0S0UT. 

By  tie  mere  inspection  of  tbc  figure  it  will  1»«  sppucat,  ttsl  iKe 
paralbj  in  loDgiiyde  b  n  is  not  affected  b;  projvclJOD,  being  tha 
nme  in  the  {>arollBctic  circle  as  in  the  ellipse ;  bal  that  tli«  parallax 
in  Istilude  p  n  is  reduced  in  the  ratio  of  the  am  of  the  sta/e  lati- 
tude to  1. 

It  is  eaay,  and  in  Bome  rc!<pectfi  clearer,  to  czprots  iLeve  ntUtinos 
in  the  Bjmbols  of  nrithmelic.  Let  w  be  the  excess  of  ibo  (no's 
longitude  above  that  of  the  Blnr,  let  a  be  the  sngle  which  tix  redim 
of  the  circle  of  parallax  subtends  at  the  earth,  and  let  &  be  Ibe 
latitude  of  tbc  etar.  The  angle  b'  sp  in  the  panlUcdo  oirolo  will 
then  be  u,  and  tbc  parallax  in  longitude  a  n  trill  be  «  X  un, «. 
Ttie  pBrailui  iu  latitude  nbicb  is  ^n  in  the  parallactic  ellipH  nil 
be  «  >:  COS.  u  X  ain.  ),. 

When  the  star  is  at  b  or  b',  pos.  u  =  I,  and  s  b'=  u  X  sin.  x,  lod 
when  it  is  at  A  or  a',  etn.  u=^l,  and  6  A=t>. 

8298.  Eiitntria'tff  of  jiaratlactic  tllipu  Jrpevdt  on  ttar'i  hti- 
bitlf.  —  The  ecceoiriciiy  of  the  parallactic  ellipse  increNscs  m  the 
Btar'a  latitude  deereaaes.  If  th«  star  be  at  the  pole  of  the  ediplk, 
tbe  plane  of  the  cirole  of  parallax  being  parallel  to  the  aor&ce  of 
the  ogI  Btial  ^here  it  is  not  altered  by  projection ;  and  the  appannt 
mo     n    f    h  8  in  B  circle,  of  which  the  centre  is  tbc  true 

pla  f  h  aa  and  of  which  the  raJius  is  the  star's  panlisi. 
Wh  n  th  la  ude  of  the  star  is  less  than  90°,  the  oblif|uity  of  the 
plane  of  he  irole  of  parallax  to  the  visual  direction  gives  aa  ellip- 
Idail  form  to  ite  projection,  which  becomes  more 
and  more  elongated  the  nearer  the  etar  is  to  the 
eoliptio.  When  the  star  is  in  the  ecliptic,  the 
cirole  of  parallax  is  viewed  edgeways,  and  the 
par&llaotio  ellipse  is  flattened  into  its  major 
axis.  The  ator  ia  this  position  oscillates  cut 
and  west  of  its  true  place  to  a  distance  eqod  to 
the  parallax. 

la/iff.  868  the  forma  of  the  parallactic  ellipsa 
are  represented  as  they  vary  in  eccentricitj 
from  a  perfect  circle  at  the  pole  of  the  ecliptio 
to  a  lino  equal  to  twice  tho  parallax  in  the 
ecliptic  itself. 

3299.  DifficuUs  of  determining  Outpara&a 
ariieifrotn  lU  minute  n mount.  —  It  might  be 
supposed,  that  where  the  character  and  laws  of 
the  phenomena  are  ao  clearly  onderslood,  th« 
discovery  of  their  existence  could  present  no 
great  difficulty.  Nevertheless,  nothing  in  the 
whole  range  of  aatronomical  research  has  more 
baffled  the  eSbrts  of  observers  than  this  question 
ni  IV  Y^w^^is-s       This  has  arisen  altogether 


8TBLLAB  PARALLAX  AND  DISTANCE.  661 

horn  tbe  extreme  minateness  of  its  magDitnde.  It  is  quite  certain 
thftt  the  quantity  we  have  designated  by  «  in  the  preceding  pan^ 
grapbS}  does  not  amonnt  to  so  much  as  1"  in  the  case  of  any  of  the 
aomerooB  stars  which  have  been  as  yet  submitted  to  the  course  of 
obflervmtiofi  which  is  necessary  to  discover  the  parallax.  Now,  since 
in  the  determination  of  the  exact  urauographical  position  of  a  star 
geooentrically  and  heliocentrically  considered,  there  are  a  multitude 
of  disturbing  effects  to  be  taken  into  account  and  eliminated,  such 
■■  precession,  nutation,  aberration,  refraction,  and  others,  besides 
the  proper  motion  of  the  star,  which  will  be  explained  hereafter ; 
and  since  besides  the  errors  of  observation,  the  quantities  of  these 
are  subject  to  more  or  less  uncertainty,  it  will  astonish  no  one  to  be 
told  that  they  may  entail  upon  the  final  result  of  the  calculation,  an 
error  of  V ;  and  if  they  do,  it  is  vain  to  expect  to  discover  such  a 
residual  phenomenon  as  parallax,  the  entire  amount  of  which  is  less 
than  V. 

8300.  JBbw  the  distance  is  inferred  from  the  parallax — paral- 
Iodic  unit — If  in  any  case  the  parallax  or  the  quantity  which  in 
the  preceding  paragraphs  has  been  expressed  by  «,  and  which  is 
the  semi-axis  major  of  the  parallactic  ellipse,  could  be  determined, 
the  distance  of  the  stars  could  be  immediately  inferred.  For,  if  this 
Talue  of  «r  be  expressed  in  seconds  or  in  decimals  of  a  second,  and 
if  &  express  the  semidiameter  of  the  earth's  orbit,  and  D  the  distance 
of  the  staTi  we  shall  have 

206265 
D  =  B  X . 

H  therefore,  «r  =  1"  the  distance  of  the  star  would  be  206265 
times  the  distance  of  the  sun,  and  since  it  may  be  considered  satis- 
ftotorily  proved  that  no  star  which  has  ever  yet  been  brought  under 
observation  has  a  parallax  greater  than  this,  it  may  be  affirmed  that 
the  nearest  star  in  the  universe  to  the  solar  system  is  at  a  distance 
ai  least  206265  times  greater  than  that  of  the  sun. 

Let  us  consider  more  attentively  the  import  of  this  conclusion. 
The  distance  of  the  sun  expressed  in  round  numbers  (which  are 
sufficient  for  our  present  purpose)  is  95  millions  of  miles.  If  this 
be  multiplied  by  206265,  we  shall  obtain — not  indeed  the  distance 
of  the  nearest  of  the  fixed  stars — ^but  the  minor  limit  of  that  dis- 
tanoe,  that  is  to  sav,  a  distance  within  which  the  star  cannot  lie. 
This  limit  expressed  in  miles  is 

D  =  206265  X  95,000,000  =  19,595,175,000,000  mUes, 

or  nearly  twenty  trillions  of  miles, 

8301.  Motion  of  light  supplies  a  convenient  unit  for  the 
ateUar  distance, — In  the  contemplation  of  such  numbers  the 
inaagination  is  lost,  and  no  other  clear  conception  remains,  ez- 
QSpt  of  the  mere  arithmetical  expression  of  the  result  of  the 

III  56 


I  A6IBON01I7. 

I  MnpnUlion.     Aitronomera  theonelTcs,  UiCtuloined  M  liay  tn 

I  ^  deal  with  etupetidoiia  Dumbers,  are  compelled  to  seek  for  unit* 

1  .V  proporliooate  magDitiide  la  bring  the  aritliDietical  expreagion  of 

I'^e  qunatities  witbin  moderate  litnits.     The  motioD  of  ligbl  fxtp- 

^  Bliei  one  of  the  most  conveiiieDt  oioduli  for  this  purpose,  and  ba«, 

VJ  oommon  conseDt,  been  adopted  aa  the  unit  io  &U  computkdoiu 

Vhoae  object  is  to  guagc  tbc  uoivcrse.     Wc  have  sbowo  that  light 

movei  at  the  rate  of  192000  miles  per  second.     If,  then,  the  dis- 

tance  D  above  oomputed  be  divided  by  192000,  the  qnotieat  wiU 

be  the  time,  expressed  id  seconds,  which  light  takes  to  move  oyer 

that  distance.     But  since  even  this  will  be  an  unirioldj  number,  it 

nay  be  reduced  to  minutes,  hours,  days,  or  ereti  to  years. 

In  thia  muuner  ve  find  that,  if  any  star  have  a  parallax  of  1",  it 
toUBt  be  at  such  a  distance  from  our  sjf^tem  that  light  would  uke 
S-235  years,  or  three  years  und  eighty-five  days,  to  come  from  it  W 
the  earth. 

If  the  Hipace  through  which  light  moves  in  ayear  be  taken,  tber^ 
fore,  as  the  unit  of  stellar  distance,  and  b  be  the  parallax  expitawd 
in  seconds  or  decimals  of  a  second,  we  shall  hare 


3302.  Methodt  of  oicertaining  Ike  parallax,  and  coiiif^uaillj 
the  dUlance.  —  It  will  easily  be  imagined  that  astronomers  hare 
diligently  directed  their  obaervations  to  the  discovery  of  sonw 
change  of  apparent  position,  however  small,  produced  upon  the 
stars  by  the  earth's  motion.  As  the  stars  most  likely  to  be  aSeeted 
by  the  motion  of  the  earth  are  those  which  are  nearest  to  the  system, 
uid  therefore  probubly  which  are  brightest  and  largest,  it  has  been 
to  such  chiefly  that  this  kind  of  observntioa  has  been  directed ;  aod 
tince  it  was  cirtain  thai,  if  any  observable  effect  be  produced  bj 
the  eiirth'fi  motiiiu  jit  iill,  it  must  be  eitrcracly  small,  the  nicest  and 
moBl  delicate  means  of  obserfation  were  those  alone  from  whidi  ihs 
ducorery  oonld  be  expected. 

One  of  the  eorlitr  expedients  adopted  for  the  solation  of  thia  pro- 
blem was  the  erection  of  a  telescope,  of  great  length  and  power,  io 
B  position  permanently  fixed,  attached,  for  example,  to  the  side  of 
k  pier  of  solid  masonry  erected  upon  a  foundation  of  rock.  Thli 
instrument  was  screwed  into  snob  a  position  that  particular  eton, 
u  they  crossed  the  meridian,  would  necessarily  pass  within  its  field 
nf  view.  Miorometrio  wires  were,  in  the  nsual  manner,  ptaoed  in  ito 
eye-piece,  so  that  the  exact  point  at  which  the  stars  passed  tb« 
tnendisn  each  night,  could  be  observed  and  recorded  with  the 
neatest  precision.  The  instrument  being  thus  fixed  and  immorahle, 
ua  transits  of  the  stars  were  noted  each  night,  and  the  exact  |dao« 
wlisn  they  passed  tbe  meridiwreooided.    Xbu  kind  of  obMrntiaa. 


STELLAR  PABALLAZ  AND  DISTANOB.  668 

vat  wrried  cm  throagh  the  year ;  and  if  the  earth's  change  of  posi- 
tioDi  by  reason  of  its  annoal  motion,  should  produce  any  effect  upon 
the  apparent  position  of  the  stars,  it  was  anticipated  that  such  effect 
would  be  discovered  by  these  means.  After,  however,  making  all 
allowanoo  for  the  usual  causes  which  affect  the  apparent  position  of 
the  stars,  no  change  of  pontion  was  discovered  which  could  be 
tflrined  to  the  earu's  motion. 

8308.  ProfenoT  HendenovCt  discovery  of  the  paraUax  of  m 
OaUawru — Notwithstanding  the  numerous  difficulties  which  beset 
the  solution  of  this  problem,  by  means  of  observations  made  with 
ilia  ordinary  instruments,  I^rofessor  Henderson,  during  his  resi- 
dence as  astronomer  at  the  Royal  Observatory  at  the  Cape  of  Good 
Hope,  succeeded  in  making  a  series  of  observations  upon  the  star 
designated  a  in  the  constellation  of  the  Centaur,  which,  being  after- 
wards submitted  by  him  to  the  proper  reductions,  gave  a  parallax 
of  l'^  Subsequent  observations  made  by  his  successor,  Mr.  Maclear, 
at  the  same  observatory,  partly  with  the  same  instrument,  and 
partly  with  an  improved  and  more  efficient  one  of  the  same  class, 
have  fully  confirmed  this  result,  giving  0*9128,  or  |f  ths  of  a  second 
as  the  parallax. 

It  is  worthy  of  remark,  that  this  conclusion  of  Messrs.  Henderson 
and  Maclear  is  confirmed,  in  a  remarkable  manner,  by  the  hct  that 
like  observations  and  computations  applied  to  other  stars  in  the 
ficinity  of  a  Centauri,  and  therefore  subject  to  like  annual  causes 
of  apparent  displacement,  such  as  the  mean  annual  variation  of 
temperature,  gave  no  simUar  result,  showing  thus  that  the  displace- 
■Mot  found  in  the  case  of  a  Centauri  could  only  be  ascribed  to 
parallax. 

Since  the  limits  of  error  of  this  species  of  observation  affecting 
the  final  result  cannot  exceed  the  tentii  of  a  second,  it  may  then  be 
assumed  as  proved,  that  the  parallax  of  a  Centauri  is  I'',  and  conse- 
qacvitly  that  its  distance  from  the  solar  system  is  such  that  light 
Bwst  take  8*235  years  to  move  over  it. 

8304.  Differential  method.  —  In  the  practical  application  of  the 
weoeding  and  all  similar  methods  of  ascertaining  the  stellar  parat 
Uz,  it  must  not  be  imanned  that  eyery  apparent  deviation  from  a 
ixsd  position  that  may  be  observed,  is  to  be  immediately  placed  to 
the  account  of  parallax.  There  are  a  great  number  of  other  causes 
of  apparent  displacement,  which  must  first  be  allowed  for;  and  it  is 
ooly  after  eliminating  these,  and  discovering  the  quantity  and  direo- 
ticNi  of  the  residual  displacement,  that  we  are  in  a  positioii  to  pro- 
nounce upon  the  existence  and  quantity  of  the  parallax.  But  in  all 
such  calculations  the  various  quantities  to  be  thus  taken  into  ac- 
ooant  and  previously  eliminated,  are  subject  to  errors,  small  in 
magoitade  it  is  true,  but  still  great  enough  on  the  whole  to  absorb 
IIm  Mitirs  amount  of  a  residual  phenomena  so  minute  as  the  stellax 


AETKOHOUT. 

X  must  in  Mine  cases  be.     All  snoh  methods  of  obaemtioa 

1  calculation  are  therefore  liable  to  be  roodercd  abortive  bj  ili« 

ot,  that  they  are  Eutijecl  to  auurcea  of  ultimate  error,  the  araitant 

if  which  mflj  be  greater  than  the  quantity  aonght. 

Indepcndeat  of  thU  class  of  errors,  there  arc  others  which  do  cot 

s  impede  the  discovery  of  a  (juimCtty  so  excecdiDgljr  otinule  u 

1  parallax,  aod  which  have  a  very  different  origin.     All  asuo- 

[  Domical  instruments  are  exposed  to  uncertain  and  rariable  chaagu 

[  V  temperature,  which  cause  the  materials  of  which  tbey  are  ooio- 

boeed  to  undergo  equally  uncertain  and  variable  expanaons  and 

eontractions.     The  piers  of  stone-work  lo  which  they  are  attached, 

fiay,  the  very  fouudaiion  on  which  these  piera  rest,  is  Ibble  to  theM 

t^anges,  which  more  especially  affect  the  result  of  the  oampariMn 

.  9f  ol^erTatioDS  made  at  intervals  of  sis  months,  and  tber^ore  at 

oppoeito  seasons  of  the  year  when  the  effects  of  difference  of  (cm- 

ferature  are  the  most  aggravated.     "Hence,"  as  Sir  John  Her> 

Khel  observes,  "  arise  stow  oscillatory  niovements  of  esceodingly 

minute  amount,  which  levels  and  plumb-liocs  afford  but  very  inao- 

D)iral«  means  of  detecting,  and  which  beiny  also  annual  in  dieir 

tTttriod,  (after  rejecting  what  is  merely  casnal  and  momeatary,)  mix 
uemselves  intimately  with  the  matter  of  our  inqniry,"  and  give 
results  which  are  especially  liable  to  be  mist4ikea  fur  those  of  stellar 
parallas.  Refraction  itself,  besides  its  casual  and  irregular  changes, 
IS  subject  to  menu  periodical  variations  which  vary  in  different 
latitudes,  and  in  different  places  in  the  same  latitude,  acoording  t« 
nnasoertained  laws,  hut  which,  having  periods  dependent  <»  tha 
Masons,  and  therefore  annual,  most  always  be  liable  to  be  coofoandad 
with  those  of  parallax. 

It  was,  therefore,  highly  deurable  to  discover  a  method  of  d^ 
teoting  the  stellar  parallai,  which,  white  it  would  be  trae  from  tlu 
nnoertunties  attending  the  other  sources  of  displacemeot  which  an 
'minated  subject  to  a  do- 
I  tain  limit  of  error,  Bhovld 
be  independent  of  tb« 
rces  of  error  of  the  latter 
I  class.  This  object  was  at- 
I  tained  by  an  expedient  whiok 
I  we  shall  now  explain. 

Let  B,  Jig.  869,  be  a  star 
I  which  we  will  snppoM  to 
I  have  sensible  paraltax ;  and 
I  let  A  B  a'  b'  be  its  parallaotiQ 
I  ellipse.  Let  s*  be  another 
J.,    gjg  star    situate    in    the    uma 

parallel  to  the  ecliplio,  and 
wenfbro  having  the  same  la^tode,  and  w  near  to  it  u  to  b* 


8TBLLA&  PAIUILLAX  AND  DISTAVOL  0W 

kMlvded  with  s  in  the  field  of  the  telescope;  and  let  flf'  be  another 
Mloate  in  the  same  circle  of  latitude,  and  therefore  haying  the  same 
kmgitade  as  8,  and  also  so  near  to  s  as  to  be  included  in  the  field 
of  view  of  the  telescope. 

Let  us  suppose  for  the  present,  that  the  stars  sf  and  sf'  hare  no 
atDsible  parallazi  and  therefore  undergo  no  apparent  ehange  of  po* 
ittioB  throughout  the  year.  From  what  has  been  already  ezpkinedi 
It  will  be  evident  that  the  apparent  place  of  b  will  be  a',  when  the 
son's  longitude  exceeds  that  of  the  star  by  90^ ;  it  will  be  B,  when 
il  exceeds  it  by  180^ ;  a,  when  it  exceeds  it  by  270^ ;  and  b',  when 
the  min's  longitude  is  the  same  as  that  of  the  star.  The  semi-axis 
major  sa  of  the  parallactio  ellipse  u  the  actual  parallax,  or  the 
mgle  which  the  semi-diameter  of  the  earth's  orbit  subtends  at  the 
Biw.  Let  this  be  expressed  by  «.  B  B  the  semi-axis  minor  will  be 
Ibiind  by  multiplying  this  last  by  the  sine  of  the  star's  latitode,  as 
bas  been  already  explained.  Let  this  latitude  be  expressed  hjX} 
W9  shall  therefore  have 

BA  =  «,     8B  =  «X  sin. X* 

Let  b'asd,  ifA'ssdj  and  b'  s  =  a.  Since  8A=:  sa'szi^ 
WIS  shall  haye 

(hat  is,  the  true  distance  between  the  stars  b  and  if  is  half  the  sum 
of  their  apparent  distances  at  the  times  when  the  difference  be- 
tween their  longitude  and  that  of  the  sun  is  270^  and  90^,  and 
Qie  parallax  of  B  is  half  the  difference  between  the  same  apparent 
fistances. 

In  like  manner,  let  8"  ^  =  d',  b"  b  =  d',  and  s^  8  =  A,  and  we 
AsU  have 

A' =  J  (1/ -*- d'),  «  X  sin.x=J(»'  — ^'); 

Ihal  is,  the  true  distance  is  half  the  sum  of  the  apparent  distanoes 
when  the  difference  of  lonsitude  of  the  sun  and  star  is  0®  and  180^. 
md  the  parallax  is  half  the  difference  of  Uie  same  distances  diyided 
bj  the  sign  of  the  star's  latitude. 

It  is  evident,  therefore,  that  under  the  supposi^n  here  made  of 
016  absence  of  all  sensible  parallax  in  the  subsidiary  stars  s'  and 
fTf  the  aq^nal  parallax  of  the  star  8  would  be  found  by  measuring 
vith  the  micrometer  the  distance  between  the  stars  8  and  b',  at  the 
noehs  when  the  sun's  longitude  differs  from  that  of  the  star  by 
»*>  and  270^. 

In  like  manner,  the  parallax  would  be  found  by  comparing  the. 
ite  8  with  the  star  s"  at  the  epoch  when  the  difierence  between  the 
toBcitttde  of  the  sun  and  that  of  the  star  is  0^  and  180^.  - 

£  b  evident,  that  the  four  observations  here  indicated,  two  upon 
Meh  of  the  starsi  will  bs  made  at  intervals  of  three  monthS|  deter- 

66» 


I 


066  ASTROMOUT. 

nined  hj  tho  epochs  at  wbioh  the  loD^tiide  of  the  son  eieeedt 
tiut  of  the  Elar  by  0",  90",  180',  and  270'. 

The  precinoD  nith  ubich  niicromctTical  measur«meiiU  am  b« 
effected,  when  applied  to  two  o-r  mora  ohjects  which  are  iiimii!»- 
noously  present  in  the  field  of  siew  of  the  talesoope,  renders  this 
instbod  of  obxcrvation  susceptible  of  eztraordiou'y  exaetncas.  It 
is  also  attended  with  the  obvioua  adraatage  of  being  toUlly  inde- 
pendent of  bU  disturbing  CAuacs-  wbiuh,  iu  thie  cose,  equally  aSe«t 
all  the  ohjeclH  present  eiiuultaneoosly  id  the  field  of  Tiew ;  thm  *U 
the  UDcert»Dtie9  attending  the  cffeots  of  re&actioo,  aherraiioa, 
precesston,  nutatioo,  ke-,  toay  be  here  discarded,  aa  Dot  inlcrfcriag 
in  nny  vray  with  the  final  result  of  the  observations. 

3305.  Potidon  mii~romf.tf-r,  tl*  application  lo  ihit  proUrtii.-~ 
But  these  are  not  the  only  indications  of  tbd  stellar  pitralJBX  pr»- 
K&ted  by  this  method  of  observation.  An  Mmngetnent  prorided 
in  the  mierometcrs  applied  on'the  eye-piece  of  the  astro&omica!  la- 
BtrumenC,  supplies  the  observer  with  the  means,  not  only  of  niei> 
Buriog  the  apparent  distance  between  Ewo  or  more  points  which  are 
preseqt  simuttaneonsly  in  the  field  of  view,  but  also  the  directioa 
iX  the  line  joining  these  two  points  with  relation  to  •ome  fiitd 
direction,  sneb,  for  example,  as  a  parallel  or  a  perpendicular  to  the 
ecliptic,  Tbus,  when  the  star  s  is  secu  at  A,  the  direction  of  the 
lioe  joining  it  with  the  star  s',  ia  parallel  to  the  ecUptio ;  bnt  wheft 
it  is  seen  at  B,  the  line  B  s*  Joining  it  with  the  star  s*  is  inclined  to 
the  ecliptic  at  the  angle  Baa. 

The  micrometric  apparatus  jnst  indicated,  which  from  its  nse  ii 
called  the  posititm  micromeler,  enables  the  observer  to  measure  with 
the  greatest  precision  the  angle  b  a'  s,  and  in  like  manner  to  me^ 
gore  the  equal  angle  b'  s'  a  when  the  star  a  is  seen  at  the  lomr 
point  b'  of  the  parallactic  ellipse. 

The  same  apparatus  enables  the  observer  to  measure  the  angU 
A  s"  B,  which  the  line  Joining  the  stars  a  a'  when  the  sun's  Imp- 
tnde  ezoeeds  that  of  the  star  hj  90°  makes  with  a  perpendionlai  la 
4ie  ecliptic,  that  is,  the  angle  a.  a"  a,  and  in  like  manoer  ha  can 
measure  the  angle  a'  b"  B. 

Let  the  angle  B  s'  a  =  t,  and  let  the  angle  a  s"  8  =  f' ;  we  shall 
then  have 

•  X  sin.  X  =  1(D  +  (/)  ><  tan.  41, 

•  =l(D'  +  d')  X  tan.^'. 

If,  therefore,  the  angles  f  and  ^'  be  ascertained,  they  supply 
further  data  by  which  the  results  of  the  oombined  obserratioDB  may 
be  verified. 

If  the  subsidiary  stars  a'  and  eT  be  not  in  the  exact  poutioii  ben 
lasumed,  but  have  latitudes  and  longitudes  differing  more  or  less 
fiom  those  of  the  star  a,  the  question  will  be  somewhat  modified, 
bat  its  invoBti^tioa  wilt  present  no  difficulty. 


&I2LLAB  PAEALLAX  AND  DISTAHCB. 


667 


8806.  Ciue  of  tvM  itan  having  equal  parallax.  —  If  tlie  two 
Btira  Been  at  once  in  the  field  of  view  of  the  telescope  have  equal 
parallAxes,  both  beiog  sensible,  thcj  will  appear  to  describe  similar 
pcnllactic  ellipMS,  and  will  from  time  to  time  oocnpy  similar  posi- 
tions in  these  elli^eea,  nnoe  thdr  poution  will  be  detennined  by  the 
difierenoe  of  loDgito^  of  the  enn  and  the  etan.  It  foliowe  from 
tbis,  Uiat  the  lines  drawn  from  the  eentres  of  the  paraltaetio  ellipses 
to  anr  umoltaneonii  positions  of  the  stars  in  theee  elltpees,  will  be 
pandlel  and  eqoal ;  and  oosseqaentl/  the  line  joining  the  stars  will 
alwajB  be  panllel  to  the  major  axis  of  the  ellipae  au  always  equal 
to  the  true  diatanee  between  the  stats.  This  will  eanlj  be  compre- 
hended bjrefeienoe  to^.  870,  where  S  and  <  are  the  true  positions 


K«.  aro. 

of  the  stars,  and  a  b  a'  B*,  and  aha'  V ,  the  two  parallaotio  ellipses, 
and  F  and  p  simaltaneous  positions  of  tbe  stars  in  these  ellipses. 
The  semi-diameters  B  r  and  s^  being  parallel,  it  is  evident,  that  pp 
will  be  eqaal  to  B  j,  that  is  to  say,  the  apparent  distance  between 
the  stars  will  be  equal  to  the  true  distaoce  between  them  ;  and  the 
Kne  Pj),  joining  the  siinultaDcous  positiana  of  tbe  stars  will  be  oon* 
Stantly  parallel  to  tbe  line  9  «,  that  is,  to  tbe  ecliptio.  Bnt  if  tbe 
star  I  be  not,  as  here  supposed,  in  the  same  parallel  to  tbe  eeliptJo 
with  the  etar  s,  the  same  will  ncvertbeless  be  true,  the  line  joining 
the  apparent  places  of  the  two  stars  being  always  parallel  to  the 
Une  joinioe  tbeir  true  places.  It  is  evident,  therefore,  that  if  the 
two  Stars  tnua  compared  hud  exactly  equal  parallBies,  which  they 
wonld  have  if  tbey  were  at  exactly  equal  distances  from  the  solar 
system,  thb  method  of  observation  would  not  sapply  any  means  of 
determining  tbe  common  value  of  their  parullai. 

3307.  (Jate  in  wAicA  they  have  vnrqual  paraUaxea.  —  But  if 
while  the  parallax  of  the  Hubsidiury  star  is,  on  tbe  one  hand,  not 
abaolutely  insensible,  as  first  supposed,  nor,  on  the  other,  equal  to 
that  of  ^e  principal  star,  but  it  is  much  loss  than  that  of  Uie  prin- 
oipal  star,  then  the  subsidiary  star  will  appear  to  move  in  a  paral- 
ilactic  ellipse  proportionally  smaller  than  that  of  the  principal  star. 

Let  aba' b',^.  87 1)  be  the  parallactic  ellipse  of  tbe  principal 


ASTEONOMT. 


■br,  and  let  a  fi  a'  6'  be  the  panlladio  ellipse  ef  the  snbddiuy  Hu, 
Wiiioh  to  aimplifj  the  eipluiatioD  we  will  aappoae,  aa  beforo,  lo  ht 


Fig.  8T1. 

-  In  the  g&me  pinllel  to  the  eeliptio  with  the  prineipkl  et*r.  Siwt 
the  two  Stan  have  the  Mine  latitude,  their  p»ra!Uelie  elltpses  will  be 
rimilar,  and  their  minor  axes  will  oooHequeatly  bear  the  same  ratio 
to  their  major  axea,  as  represented  in  the  fisure.  The  simultaneoos 
plaoes  of  the  two  atars  in  the  parallactio  eUipsea,  will  al«o  be  such 
that  the  sstni-di»met«r  of  the  ellipaea  a  p  and  «  v  wht^  pus  throogh 

-  them,  will  alwaya  be  parallel.  B«t  Hnee,  in  this  cue,  tp  will 
always  be  less  tLun  S  p,  the  liae  Tp,  nUicli  joiua  the  siaiullaneooi 
places  of  the  stars,  will  not,  aa  ia  the  formpr  case,  be  parallel  to  S  i, 
nor  eqnal  to  it.  It  will,  od  the  cootrar?,  be  iDcliDixl  to  it  at  ii 
wigle  which  will  Tar;  with  the  poaition  of  the  atars  in  the  panllaotig 
olbpaes,  and  which  will  increase  gradnall;  from  the  points  a  a  to 
the  pcwis  B  b,  where  ila  obliquity  to  the  liee  s  «  is  greatest. 

Let  A  a,  the  apparent  distance  between  the  two  stars  when  tht 
■an'a  longitude  exceeds  that  of  the  star  bj  90°,  be  expressed  ai 
before  b;  d;  and  let  a'  a',  their  apparent  distance  when  the  ann's 
loBgitude  exceeds  that  of  the  alar  b;  270°,  be  eipressed  by  d. 
Let  the  parallax  8  a  of  the  principal  star  be  eipresaed  hja,  and  lal 
the  parallax  a  a  of  the  snlwidiai;  star  be  expressed  by  a*.  Vm 
true  distanoe,  b  i,  between  the  stars,  being  expressed  as  before  by  A, 
we  shall  have 

I  A=lCDxrf).  «-«'=K''— tO- 

'  The  reeults  are,  therefore,  absolutely  the  Bame  as  if  the  snbaidiary 
star  8  had  no  seosible  parallax,  and  the  parallax  of  the  prindpal 
star  S  were  equal  to  the  difierence  between  its  parallax  and  that  ot 
the  subsidiary  star.  If  tbe  problem  be  pursued  through  its  othv 
details,  it  will  be  found  that  the  changes  of  inclination  of  the  lins 
joining  tbe  apparent  places  of  the  two  stars  to  a  fixed  line,  eueh  H 
the  parallel  to  tbe  ecliptic,  will  abo  be  the  same  aa  they  would  bs 
if  the  subaidiarv  star  had  no  sensible  parallax,  and  tbe  prinoipsl' 
BMr  had  a  parallax  eqnal  te  tbe  difference  of  the  parallasee. 

8808.  i^arailox  of  nine  itarM  amxrtained.  —  Notwitbstandlof 


STELLAR  PARALLAX  AND  DISTANCE. 


860 


ihe  greftt  maltitude  of  stars  to  which  instraments  of  obseryation  of 
unlooked-for  perfection,  in  the  hands  of  the  most  able  and  zealous 
observers,  have  been  directed,  the  results  of  all  such  labours  have 
hitherto  been  rather  negative  than  positive.  The  means  of  obser- 
vation have  been  so  perfect,  and  their  application  so  extensive,  that 
it  may  be  considered  as  proved  by  the  absence  of  all  measureable 
displacement  consequent  upon  the  orbital  motion  of  the  earth  that, 
a  very  few  individual  stars  excepted,  the  vast  multitude  of  bodies 
which  compose  the  universe  and  which  are  nightly  seen  glittering 
in  the  firmament,  are  at  distances  from  the  solar  system  greater 
than  that  which  would  produce  an  apparent  displacement  amounting 
to  the  tenth  of  a  second.  This  limit  of  distances  is,  therefore,  ten 
parallactic  units,  or  about  two  million  times  the  space  between  the 
earth  and  sun. 

Within  this  limit,  or  very  little  beyond  it,  nine  stars  have  been 
foand  to  be  placed,  the  nearest  of  which  is  that  already  mentioned, 
of  which  Professor  Henderson  discovered  the  parallax.  Those  of 
the  others  are  due  to  the  observations  of  Messrs.  Bessel,  Struve, 
and  Peters.  In  the  following  Table  the  parallaxes  of  these  stars 
are  given  with  their  corresponding  distances  expressed  in  parallactic 
units,  and  also  in  the  larger  unit  presented  by  the  distance  through 
whioh  light  moves  in  a  year. 

TABLE. 
mne  Stan,  with  their  ascertained  Parallax  and  corresponding  Distances. 


star. 

Panllaz. 

DUtance. 

CbMrrer. 

SuB't  dut. »  1". 

Ana.  BOt  of  lif  bt>sl. 

«  OMtMri  

0i)13" 

225916 

8-51825 

Hendenon. 

in  CTml .i.tT- 

0-318 

692712 

9-29580 

BmmL 

*■*  VJi|»«* 

M  liTTB, ••••••. ••••••• 

0-261 

7902S0 

12-39400 

StraTe. 

HMnfl  .••.r.«..**f.«tT- 

0-230 

896780 

14-0650 

Hendenon. 

1880  Oroombridge 

0*220 

912660 

14-3140 

Peteri. 

C    \3mWmD  ......•.«.•«••• 

0-138 

1650800 

24-3230 

Peten. 

afguii'ui 

0-127 

1624100 

25-4725 

Peters. 

POlartorr.       r    T     -t    -T 

0-067 

8078MO 

48-2833 

Peten 

Ob|wUft» 

WM 

4484000 

78*«400 

Pttten. 

k 

W9  ABTHONOMT. 

The  psTsllsx  of  the  first  eeven  of  these  Bl»rs  may  be  Fonsdned 

[  iH  haTing  been  asccrtainei]  wilb  tolerable  cenaiotj  and  preci«OD, 

I  The  very  small  amount  of  ibat  of  the  last  two  ia  sueh  as  to  render 

ore  doubtful.     What  is  tertain,  bowcver,  in  relation  to  ILem  u, 

ihat  the  aotiial  amonat  of  their  parallax  ia  loss  than  the  tenth  of  a 

Mcond. 


CHAP.  XXVI. 
UAaNntmi  and  ltistke  of  the  sTAas. 

8309.  Orders  of  magnitude  of  the  ilari.  —  Among  tbe  multi- 
tude of  atata  dispiirsed  over  tbe  firmaioent,  «e  find  a  great  Tariet;  i 
of  aplendour.  Those  trbbb  are  the  brightest  and  largest,  aod 
wbioh  are  aaid  to  be  of  the  /irsl  magnitude,  are  fen ;  the  next  ia  | 
order  of  brightness,  nbicb  are  called  of  tbe  ucond  maffnitudr, 
«re  more  namerous;  and  aa  tbey  decrease  in  brightness  their  nam- 
ber  rapidly  increases.  I 

'r        Tbe  nnmber  of  stara  of  tbe  first  nrngaitnde  does  not  exesid    I 
(wenty-four;   the  gecoDd,  fifty ;   tbe  [bird,  two  hundred ;   and  so  en; 
tbe  number  of  the  smallest  visible  vritbout  a  telescope  being  bom 
12,000  to  15,000. 

The  stars  which  are  capable  of  beiog  seen  by  tbe  naked  eya  an 
usually  resolved  into  seven  orders  of  magnitude  —  tbe  first  b«Dg 
tbe  brightest  and  largest,  while  those  of  the  seventh  magnitude  an 
tbe  smallest  that  the  eye  can  distinctly  see. 

3310.  These  varitUes  of  magnitude  caused  chiejtif  hy  differattt 
»f  distance.  —  Are  we  to  suppose,  then,  that  this  relatiTe  bright- 
ness which  we  perceive,  really  arises  from  any  difference  of  rntrinsia 
■pLendour  between  the  objects  themselves  ?  or  does  it,  as  ii  may 
•quslly  do,  ari^e  from  their  difference  of  distance  ?  Are  tbe  atiif 
of  tbe  seventh  magnitude  so  much  less  bright  and  couspicaous  thas 
those  of  the  first  inngoilude,  because  they  are  really  smaller  orU  ' 
placed  at  the  same  distance?  or  becauee,  being  intriDsically  equal 
in  splendour  and  magnitude,  tbe  distance  of  those  of  the  seveatfa 
magnitude  is  so  much  greater  than  tbe  distance  of  those  of  liia 
£rst  magnitude,  that  they  are  dimiDished  in  their  apparent  bright- 
ness ?  VVe  know  that  by  tbe  laws  of  optics  tbe  light  received  ftom 
K  luminous  object  diminishes  in  a  very  rapid  proportion  as  tbe  dis- 
tance increases.  Thus  at  double  the  distance  it  will  be  four  tUMi 
less,  at  triple  tbe  distance  it  will  be  nine  times  lees,  at  a  hoB^rad 
times  the  distance  it  will  be  ten  thousand  times  less,  and  so  oo. 

It  ia  evident,  then,  that  the  great  variety  of  lustre  which  pt^ 
Tails  among  the  stars  may  be  indifferently  eiplaiaed,  eittMr  bf 
mppoung  tnem  <^yia\»  of  diSwent  intriiuie  brightons  uid  magu- 


MAGNITUDE  AND  LUBTRB  07  THB  STARS.  671 

liide^  placed  at  the  same  distance ;  or  objecta  geiierall j  of  die  lame 
order  of  magnitude,  placed  at  a  great  diversity  of  distances. 

Of  these  two  suppositions,  the  latter  is  infinitely  the  more  pro- 
bable and  natural ;  it  has,  therefore,  been  usually  adopted :  and  we 
aooordingly  consider  the  stars  to  derive  their  variety  of  lustre 
almost  entirely  from  their  places  in  the  universe  being  at  various 
disUnces  from  us. 

8311.  Stars  as  distant  /rom  each  other  generally  as  they  are 
Jrom  the  sun.  —  Taking  the  stars  generally  to  be  of  intrinsicallv 
equal  brightness,  various  theories  have  been  proposed  as  to  the  posi- 
tiona  which  would  explain  their  appearance ;  and  the  most  natural 
and  probable  is,  that  their  distances  from  each  other  are  generally 
equal,  or  nearly  so,  and  correspond  with  the  distance  of  our  sun 
from  the  nearest  of  them.  In  this  way  the  fact  that  a  small  num- 
ber of  stars  only  appear  of  the  first  magnitude,  and  that  the  num- 
ber increases  very  rapidly  as  the  magnitude  diminishes,  is  easily 
rendered  intelligible. 

8812.  Why  stars  increase  in  number  cu  they  decrease  in  magnu 
tmde.  —  If  we  imagine  a  person  standing  in  the  midst  of  a  wood, 
■onronnded  by  trees  on  every  side  and  at  every  distance,  those 
wbich  immediately  surround  him  will  be  few  in  number,  and  by 
proximity  will  appear  large.  The  trunks  or  stumps  of  those  which 
Monpy  a  circuit  beyond  the  former,  will  be  more  numerous,  the 
eirtait  being  wider,  and  will  appear  smaller,  because  theii  listanoe 
is  ffreater.  Beyond  these  again,  occupying  a  still  wider  circuit, 
iriu  appear  a  proportionally  augmented  number,  whose  apparent 
BagDitiule  will  again  be  diminished  by  increased  distance ;  and  thus 
Ae  trees  which  occupy  wider  and  wider  circuits  at  greater  and 
greater  distances  will  be  more  and  more  numerous,  and  will  appear 
oontinQally  smaller.  It  is  the  same  with  the  stars ;  we  are  placed 
ia  the  midst  of  an  immense  cluster  of  suns,  surrounding  us  on 
•my  side  at  inconceivable  distances.  Those  few  which  are  placed 
imiiiediately  about  our  system,  appear  bright  and  large,  and  we  call 
tbem  stars  of  the  first  magnitude.  Those  which  lie  in  the  circuit 
bqrond,  and  occupy  a  wider  range,  are  more  numerous  and  less 
bn^i;  and  we  call  them  stars  of  the  second  magnitude.  And 
tfceio  is  thus  a  progression  increasing  in  number  and  distance  and 
dbniiiishing  in  brightness,  until  wo  attain  a  distance  so  great  that 
tta  stars  are  barely  visible  to  the  naked  eye.  This  is  the  limit  of 
linon.  It  is  the  limit  of  the  range  of  the  eye  in  its  natural  oon- 
dilion ;  but  an  eye  has  been  given  us  more  potent  still,  and  of  in- 
inilely  wider  range  —  the  eye  of  the  mind.  The  telescope,  a  crea- 
ture of  the  understanding,  has  conferred  4^pon  the  bodily  eye  an 
ioinitely  augmented  range,  and,  as  we  shall  presently  see,  haa 
fluaUed  ns  to  penetrate  into  realms  of  the  universe,  which,  without 
ili  9adf  would  never  have  been  known  to  ns.    But  let  ns  panae  fbr 


I 

I 


l^TS  ASTFlO:<OMr. 

tin  prewut  and  dwell  for  a  moment  upon  lliat  nnge  of  epaoe  whieb 
WnieE  withio  the  acupe  of  natural  vision. 

3313.  Wlxit  are  ihf  Jix(d  slartf  — The  extent  of  the  etelUt 
universe  visible  to  the  naked  eye,  and  tlie  arrang^meat  of  Btan  in 
it  and  tliuir  relative  diatancce,  have  just  been  esplained.  Bat  cori- 
tieity  will  b«  awakened  tt>  discover,  not  merelj  the  position  and 
arrangemeDt  of  thoss  bodies,  hut  to  ascertain  what  ia  their  natun, 
and  what  parts  they  play  on  tlie  great  theatre  of  creation.  Are 
they  analngons  to  our  planeta  ?  Are  they  inhahited  globes,  wanned 
and  illumiDated  by  neighhounDg  tiuna T  Or,  on  the  other  hand, are 
they  tbcfflGelvcs  suns,  dispensing  light  and  life  to  Bystcma  of  tat- 
xounding  worlds  ? 

3314.  Tf'kifopei  ilonol  magnify  ihem  like  the plantti. — WW 
S  telescope  is  directed  to  a  atar,  the  effect  produced  U  striking 
different  fnim  that  which  we  find  when  it  it  applied  to  a  planet.  A 
planet,  to  the  nuked  eye,  with  one  or  two  exceptions,  appears  like  a 
oommnn  star.  The  teleecnpe,  however,  immediately  presents  it  to 
na  with  a  distinct  circular  disk  similar  to  that  which  the  tnoon  oOen 
io  the  naked  eye,  and  in  the  case  of  some  of  the  planets  a  poweiU 
"lelBBoope  will  render  them  apparently  even  larger  than  the  nuoa. 
Bnt  the  effect  is  very  different  indeed  when  the  same  instrament  ii 
directed  even  to  the  brighlest  star.  We  Cad  that  instead  of  mag- 
nifying, it  actually  diininisbca.  Tiicrc  is  an  optical  illusion  pro- 
duced when  we  behold  a  star,  which  makes  it  appear  to  us  to  h« 
Burrouodcd  with  a  radiation  which  causes  it  to  be  represented  when 
drawn  on  paper,  by  a  dot  irith  rays  diverging  on  every  aide  frotn  it. 
The  effuut  of  the  telescope  is  to  cat  off  this  radiation,  and  present 
to  ns  the  Giar  as  a  mere  lucid  point,  having  no  senaible  magnitude; 
Sor  can  aay  augmented  tclescopi-c  power  which  has  yet  been  resorted 
to,  produce  any  other  effect.  Telescopic  powers  amounting  to  eil 
{houaand  were  occasioDally  used  by  Sir  William  Herscbel,  and  Ik 
ataled  that  with  these  the  apparent  magnitude  of  tbo  stars  Beemed 
tat,  if  possible,  than  with  lower  powers. 

3315.  The  absence  of  a  di>k  proi'eA  by  Oieir  occuhafion  ly  ik  ■ 
•won.  —  We  have  other  proofs  of  the  ficl  that  the  stara  have  no 
Mnaible  disks,  among  which  may  be  mentioned  the  remarkibls 
affect  called  the  occultaljon  of  a  star  by  the  dark  edge  of  the  moon. 
When  a  moon  is  a  crescent  or  in  the  quarters,  as  it  moves  over  the 
firmament,  its  dark  edge  successively  approaches  to,  or  recedes  fnim 
the  stars.  And  from  tiroe  to  time  it  happens  that  it  passes  betweea 
the  stars  and  the  eye.  If  a  star  had  a  sensible  disk  in  this  case, 
the  edge  of  the  moon  would  gradually  cover  it,  and  the  star,  instead 
of  being  iuetantancousl;  cxtingubbed,  would  gradually  disappear. 
This  is  found  not  to  be  the  case ;  tbo  star  preserves  all  its  lustn 
Vatil  the  fflouent  it  comes  into  ooutaol  with  ths  dark  edge  of  tfa« 


MAGNITUDB  AND  LUSTRE  OF  THE  STABS.  678 

moon's  disk,  and  then  it  is  instantly  eztiDgoished,  without  the 
slightest  appearance  of  diminution  of  its  brightness. 

3316.  Meanimj  of  the  term  magnitude  as  applied  to  stars.  —  It 
may  be  a^ked  then,  if  such  be  the  case,  if  none  of  the  stars,  great 
or  small,  have  any  discoverable  magnitude  at  all,  with  what  mean- 
ing can  we  speak  of  stars  of  the  first,  second,  or  other  orders  of 
magnitude?  The  term  magnitude  thus  applied,  was  used  before 
the  iuveution  of  the  telescope,  when  the  stars,  having  been  observed 
only  with  the  naked  eye,  were  really  supposed  to  have  different 
magnitudes.  We  must  accept  the  term  now  to  express,  not  the 
comparative  magnitude,  but  the  comparative  brightness  of  the  stars. 
Thus  a  star  of  the  first  magnitude,  means  of  the  greatest  apparent 
Imghtness ;  a  star  of  the  second  magnitude,  means  that  which  has 
the  next  degree  of  splendour,  and  so  on.  But  what  are  we  to  infer 
from  this  singular  fact,  that  no  magnifying  power,  however  great, 
will  exhibit  to  us  a  star  with  any  sensible  magnitude?  must  we 
admit  that  the  optical  instrument  loses  its  magnifying  power  when 
applied  to  the  stars,  while  it  retains  it  with  every  other  visible 
object  ?  Such  a  consequence  would  be  eminently  absurd.  We  aro 
therefore  driven  to  an  inference  regarding  the  magnitude  of  stars, 
as  astonishing  and  almost  as  inconceivable  as  that  which  was  forced 
upon  us  respecting  their  distances.  We  saw  that  the  entire  mag- 
nitude of  the  annual  orbit  of  the  earth,  stupendous  as  it  is,  was 
nothing  compared  to  the  distance  of  one  of  those  bodies,  and  con- 
sequently if  that  orbit  were  filled  by  a  sun,  whose  magnitude  would 
therefore  be  infinitely  greater  than  that  of  ours,  such  a  sun  would 
not  appear  to  an  observer  at  the  nearest  star  of  greater  magnitude 
than  I'';  consequently  would  have  no  magnitude  sensible  to  the 
eye,  and  would  appear  as  a  mere  lucid  point  to  an  observer  at  the 
star !  We  are  then  prepared  for  the  inference  respecting  the  fixed 
stars  which  telescopic  observations  lead  to.  The  telescope  of  Sir 
William  Herschel,  to  which  he  applied  a  power  of  six  thousand, 
did  undoubtedly  magnify  the  stars  six  thousand  times,  but  even 
then  their  apparent  magnitude  was  inappreciable.  We  are  then  to 
infer  that  the  distance  of  these  wonderful  bodies  is  so  enormous 
compared  with  their  actual  magnitude,  that  their  apparent  diameter, 
seen  firom  our  system,  is  above  six  thousand  times  less  than  any 
which  the  eye  is  capable  of  perceiving. 

8317.  Why  stars  may  he  rendered  imperceptible  by  their  dis- 
tance,— It  appears,  therefore,  that  stars  are  rendered  sensible  to  the 
eye,  not  by  subtending  a  sensible  angle,  but  by  the  light  they  emit 
It  has  been  already  explained  (1131)  that  an  illuminated  or  lumi- 
nous object,  such,  for  example,  as  the  sun,  has  the  same  apparent 
brightness  at  all  distances,  and,  consequently,  that  the  quantity  of 
light  which  the  eye  of  an  observer  receives  from  it  being  in  the 
exact  ratio  of  the  apparent  area  of  its  visual  disk,  is  inversely  aa  tb.<^ 
III.  57 


ASIEONOMT. 

I  its  tlUlaDoe.  It  TemaiDB,  however  to  expliun  how  it  an 
after  it  ceases  to  have  a  disk  of  eensible  diameter,  it  doea 
cease  to  bo  -visible.  Tiiis  arisce  from  tLe  fWt  that  tlie  Inttiiuoai 
t  ooustituUng  tbe  imago  oa  the  retina,  is  iutriDsically  hh  bri^l 
'bcQ  that  image  has  a  large  and  sensible  magnitude.  The  eje 
loreforc  eeosible  to  tbe  light,  though  not  sensible  to  the  n»g- 
e  of  the  image  ;  and  it  continQes  U>  be  sensible  ti>  the  tight, 
bj  increase  of  distance  the  light  vhich  enters  the  pupil  and  it 
^tcd  on  the  retina,  though  r'-"  aa  intense  in  its  brilliancT  u 


small  in  its  ^aui        mat  it  is  insufficient  t 


prouuci; 


Claaijication   of  tlar*    6y   mn^niludet    arbitrary   anil 
lent.  —  Tbe  distribution  of  the  stars  viiuble  to  the  naked  c\a 
^  -T  orders  of  magnitude,  has  be«n  so  long  and  »o  generii'lj 
ivt      and  is  referred  to  so  universally  in  the  works  of  astmuo- 
J,  buvient  and  modern,  that  it  would  be  impossible  altogether  (e 
rsede  it,  and  if  possible,  such  a  change  would  be  attended  triiii 
I  ioconveuienee.     Nevertheless,  this  classification  is  open  to 
-     ij  objeetione,  and  is,  from  its  loosenesB  and  want  of  deGailenea 
v.^  preciNoD,  in  ungular  discordance  vith  the  actual  state  of  ub«- 
nomioal  science.     The  stars  whicL  abound  in  such  countless  num- 
bers on  tbe  firmanicnl,  are  of  iufinite  gradations,  from  that  of  Siring, 
the  most  gplccdid  object  of  this  cli^s,  to  the  most  faint  stars  stbich 
tbe  ^barfcf^t  and  most  practised  eye  can  distinguish  on  tbe  dark>it 
uud  de^ircst  ni^ht.     To  distribute  such  a  scries  bo   impercepliblj 
decreasing  in   splendour,  into  seven  orders  of  magnitude,  moit 
obviously  be  an  arbitrary  process,  in  which  no  two  observers  could 
possibly  agree.     There  are  no  natural  breaks  of  continuity  by  whidi 
the  stars  of  the  first  magniludc  could  be  separated  from  those  of  tbe 
secoad,  the  second  from  those  of  the  third,  and  so  oa.     Whatever 
be  the  stare  assigned  to  any  class,  the  brightest  will  be  uDdistin- 
gjuishable  from  the  faintest  of  those  of  tbe  next  superior  magoitDde, 
and  tbe  faiolest  will  be  equally  undistinguisbable  from  the  brightest 
of  the  nest  inferior  magoitudo. 

The  stars  assigned  to  any  order  of  mBguitudc  must,  in  such  i 
classification,  differ  greatly  one  from  another  in  brightness.  Thuf, 
of  the  24  or  25  stara  that  arc  usually  assigned  to  the  first  magni- 
tude in  tbe  received  classification,  Siriua,  the  brightest,  ia  abonl 
four  times  as  bright  as  a  Centauri,  which  may  bu  taken  as  the  type 
of  tbe  average  brightness  of  stars  of  this  magnitiiile. 

3319.  ImpOTtaitce  of  more  exact  aslrometric  tjpeiii'rnrs. — Whtn 
it  is  considered  that  the  exact  r^tio  of  the  apparent  lustre  of  ibo 
Btars,  combined  with  their  parallaxes  when  the  Litter  are  knowu, 
inpplios  tbe  data  by  which  the  absolute  splendDur  of  these  bodiof 
may,  as  will  presently  appear,  be  calculated;  ami  furilier,  that  ihej 
may  be  thus  brought  into  immediate  numerical  comparisoa  with  tb« 


UAOSITUDE  AND  LUSTRE  OF  TUB  STARS. 


675 


■an,  which  is  itself  oalj  on  iucliviJual  of  the  same  class  of  bodies, 
the  importance  of  tbo  expedient:]  fur  tho  mure  exact  ealimation  of 
their  relntive  lustre,  acd  a  more  prticist  has!:*  of  clussificalinD  ds  to 
■pparcDt  magnitude,  cannot  fail  to  he  fell  and  acbnowEedgi'd.  Tiie 
importance  uf  tbia  is  rendered  »till  greater  t>y  tbe  euusidcraliiin  cliut 
the  pxralliis  of  ■  very  small  number  uf  stars  being  found  to  have 
appreciable  magnitude,  the  oomparoiive  lustre  of  these  bodies  taken 
in  tbe  mass,  is  the  only  ground  apon  which  anj  estimate  of  their 
relative  dislauces  can  he  determined;  and  when  the  large  nnmber 
which  are  subject  to  observation  is  considered,  and  the  improbahilitj 
of  their  differing  greatly  in  intrinsic  magnitude  taken  coUoctivelj 
in  classes,  it  must  be  admitted  that  their  relative  apparent  bright- 
nesB  csoDOt  fiiil  to  be  >  tolerabi;  exact  exponent  of  their  comparative 
distances. 

3320.  Ailromclcr  conlricet!  and  applUJ  hff  Sir  J.  ITcrichrl.  — 
Daring  his  residence  at  tbe  Cape,  Sir  J.  Ilcrschel  contrived  an 
apparatus  for  the  more  exact  detcrminatioo  of  the  rehitive  lustre  of 
the  stars,  and  applied  it  with  great  adviintage  to  ibe  determination 
of  the  relative  brightness  of  a  considerable  number  of  these  objects. 
This  apparatus  consisted  of  a  rectangular  glass  prism,  and  a  Icna 
to  nonntcd  that  two  celestial  objects  might  he  seen  in  juxta-position, 
one  directly,  and  the  other  by  reflection  and  transmission  through 
the  prism  and  lens,  the  apparent  brightness  of  the  latter  being 
capable  of  being  varied  at  pleasure  by  tbe  observer,  so  that,  by 
proper  adjustments,  the  two  objects  thus  seen  may  be  rendered  sen- 
sibly equal  in  brightness,  ^'hen  this  is  accomplished,  the  arrange- 
Dents  of  the  apparatus  are  such,  that  by  measuring  the  distance  of 
the  eye  of  the  observer  from  the  focus  of  tbe  lens,  a  measure  mav 
be  obtained  by  which  the  comparative  lustre  of  any  objects  to  which 
the  apparatus  may  be  successively  directed  may  be  determioed. 

To  render  this  intelligible,  let  P,J>i/.  872,  represent  the  rectaognlar 
priim,  one  of  the  faces  of  which  is  placed  so  as  to  receive  a  pendl 


issing  from  &  diatant  object  3  pcrpendioalarly  upon  il. 

-js  are  Wtally  reflected  (1006,)  by  the  back  of  the  prism  at 

emerging  from  tbo  otlier  face  of  the  prtam,  are  received  upon 

lena  L,  aud  brought  to  a  focus  r,  as  if  they  came  from  the  direc- 

I  p  t.     TLc  parallel  peacil  is  thus  converted  into  &  divergent 

cil,  of  vbich  F  is  tbe  focns,  and  the  point  f  will  appear  U>  lo 

plfced  any  irliere,  as  at  e,  witbia  tbe  limits  of  the  divergent 

1  as  a  star,  tbe  apparent  brightness  of  which  will  be  more  or 

ording  as  the  eye  is  nearer  to  or  more  distant  from  v.    It 

from  tbe  principles  of  optic?,  that  tbe  apparent  brightoe« 

d  point  F  nill  be  inversely  as  the  square  of  the  iSstaiure 

eye  from  Ibis  point.     If,  Ihen,  M  express  the  opparect 

-when  the  eye  is  at  the  unit  of  distance  from  it,  M  divJW 

expreES  its  apparent  lastre  when  the  eye  ia  at  the  d» 

let  us  now  suppose  the  apparalns  so  arranged  in  its  poeition  tlial 
e  the  eye,  placed  within  the  divergent  pencil,  sees  the  focuir, 
y  also  see,  in  joxla-poeilion  with  it,  a  star  s,  whose  lustre  is  ti 
termined.  Let  the  eye  be  moved  to  or  from  f  until  the  lustre 
.ne  star  becomes  sensibly  equal  to  that  of  f.  If,  then,  the  lustre 
.  the  »t,nr  be  expressed  by  y,  we  shall  have 


Let  the  apparatus  be  then  directed  to  another  star,  nbose  loitn 
8*  is  to  be  compared  with  tbe  former,  and  lei  the  same  opemtion  hi 
repeated,  the  distance  of  the  eye  from  F  being  so  regulated  as  to 
render  iho  apparent  lustre  of  the  point  f  equal  to  that  of  ibe  second 
Biar.  The  distance  of  the  eye  from  r  being,  in  this  case  cxpres«d 
by  d',  we  shall  then  have 


and  consequently, 

s  _  !>''_ 

8'  "  !)■  ' 
that  is  to  say,  the  apparent  lustres  of  tbe  two  stars  are  in  tbe  inverw 
numerical  ratio  of  the  squares  of  the  distances  of  the  eye  frx>ia  r, 
which  would  render  tbe  apparent  lastro  of  F  equsd  to  those  of  the 
stars  respectively. 

In  the  series  of  observations  made  at  the  Cape  by  Sir  J,  Herschel, 
the  moon  was  the  object  with  which  the  stars  were  thus  compared. 
The  planet  Jupiter  would,  perhaps,  be  more  convenient;  but  am 
object  which  would  retain  an  invariable  brightness  during  ibe  shoA 
interval  necessary  for  the  comparison  of  the  stars  under  observation, 
would  Bcrre  the  purpose. 


MAGNITUDE  AND  LUSTRE  OF  THE  STARS.  677 

In  this  manner.  Sir  J.  Hcrschel  ascertained  nnmerically  the  com- 
parative brightness  of  a  considerable  nainbor  of  stars  under  the 
tourth  magnitude,  and  has  given,  in  his  '<Cape  Observations"  a 
catalogue,  exhibiting  the  relative  magnitudes  to  two  places  of 
decimals. 

8321.  Principle  on  which  the  successive  orders  of  stellar  mag- 
nitude should  he  hosed,  —  Astronomers  are  not  agreed  as  to  the 
optical  conditions  by  which  the  successive  orders  of  stellar  mag- 
nitudes should  be  fixed.  It  might  appear,  at  first  view,  that  a  star 
of  the  second  magnitude  ought  to  have  one  half  the  brightness  of 
one  of  the  first  magnitude,  that  a  star  of  the  third  magnitude  ought 
to  have  one  third  of  the  brightness,  and  so  on. 

But  such  a  proportion  would  not  be  at  all  in  accordance  with  the 
common  classification  of  magnitudes. 

The  more  generally  received  condition  has  been  a  succession  of 
magnitudes,  such  as  a  star  of  a  given  intrinsic  lustre  would  have  if 
removed  to  a  scries  of  distances  increasing  in  arithmetical  pro- 
gression. Thus,  Ftars  of  the  first  magnitude  would  be  at  the  unit 
of  the  stellar  distance ;  those  of  the  second  magnitude  would  have  a 
lustre  due  to  twice  this  distance ;  those  of  the  third  magnitude,  to 
three  times  this  distance,  and  so  on.  Now,  since  the  apparent  lustre 
of  an  object  is  in  the  proportion  of  the  inverse  square  of  the 
distance,  it  would  follow  that,  in  this  system,  the  succession  of 
brightness  would  be  as  the  numbers  1,  i,  -},  -f^,  and  so  on. 

Meanwhile,  whatever  may  be  the  principle  adopted  for  this  clas- 
lification,  the  astrometric  expedient  contrived  by  Sir  John  Herschel^ 
being  sufficient  for  the  numerical  estimation  of  the  relative  bright- 
neases  of  different  stars,  it  will  be  sufficient  to  determine  a  variety 
of  interesting  and  important  problems  respecting  the  absolute  lustre 
Mad  magnitudes  of  those  objects,  not  only  compared  with  each  other, 
bat  with  the  sun. 

3322.  Comparative  lustre  of  a  Centauri  with  that  of  the  fuU 
moon.  —  By  means  of  the  instrument  described  above,  Sir  J. 
Herschel  compared  the  full  moon  with  certain  fixed  stars,  and 
ascertained,  by  a  mean  of  eleven  observations,  that  its  lustre  bore 
to  that  of  the  star  a  Centauri,  which  he  selected  as  the  standard  star 
of  the  first  magnitude,  the  ratio  of  27408  to  1 ;  in  other  words,  he 
showed  that  a  cluster  consisting  of  27408  stars  equal  in  brightness 
to  that  of  a  Centauri  would  give  the  same  light  as  the  full  moon. 

8323.  Comparison  of  the  lustre  of  the  full  moon  with  that  of  the 
tun.  —  Dr.  Wollaston  by  certain  photometric  methods  which  are 
oonsidered  to  have  been  susceptible  of  great  precision,  compared  the 
light  of  the  sun  with  that  of  the  full  moon,  and  found  that  the  ratio 
was  801072  to  1 ;  or  in  other  words,  that  to  obtain  moon-light  as 
intense  in  its  lustre  as  sun-light,  it  would  be  necessary  that  801072 
full  moons  should  be  stationed  in  the  firmament  together. 

57* 


AStaOKOHT. 

■ism  of  the  tmi't  light  wiA  tfiaf  o/a  Cmlauri.— 
ion  of  theao  obsorvalions  bj  Hcrschel  Md  Wol- 
I  >plied  with  incuDS  of  bringiDg  into  direct  numerical 
u  'ID  and  tfae  star  a  CentaurL     Since  it  appean  thit 

[  of         mlAnri  is  2T40S  times  less  tbnn  that  of  tbe  full 
V  Sn  light  of  the  full  moon  is  801072  Umea  leas  thin 

_t  will  evidently  follow,  tbal  if  we  express  by  g  the 
ol  ,  and  bj  t  that  of  a  Oentaiiri,  we  shall  have 

B  =  27408  X  801""*^  X  » =  21955,000,000  x  «; 
is  to  EBj,  the  light  of  loo  bud  is  very  Dcarl;  22,000,000,000 
I  more  inteDse  ihaa  that  of  a  Centauri. 

)  geoeraliso  these  reenlta,  m  express  the  ratio  of  tbe  light  of 
-  fyi  moon  to  that  of  any  star,  as  delerniiDod  b;  HerMtel'i 
.■omeler,  we  sball  then  have, 

8=  801072  X  m  X  *; 
ansi^quontly, 


8010T2  X  m 
3325.    CtmtparitoR  of  the  intrinxtc  tplendour  of  (A«  tun  aiuf  a 

^Ufd  shir.  —  SiDce  all  niialo^  and  obscrvalion  lead  to  ihi;  rnn- 
dusion,  that  the  Htars,  like  the  sun,  arc  eclf-luoiiDoaa  bodies, 
although  no  telescopic  power  which  we  can  command  can  exhibit 
tbem  with  a  senaible  diak,  it  cannot  be  doubted  that  they  are,  like 
tbe  suD,  spberical  bodies.  If,  then,  i  ciprera  the  intrinsio  bright- 
neas,  or  what  is  the  same,  tbe  absoiuto  quantity  of  ligbt  emitted  b; 
a  BuperScial  unit  of  tbe  viaible  surface  of  such  a  sphere,  and  if  K 
eipreea  the  superficial  magnitude  of  the  bemiapbere  presented  to 
the  eye,  the  total  quantity  of  ligbt  emitted,  or  tolal  intrinsic  lustre, 
will  be  expressed  by  I  x  M.  But  the  apparent  lustre,  will  accotd- 
ing  to  the  common  optical  law,  decrease  as  the  square  of  the  dis- 
tance of  the  observer  increases,  and  consequently,  if  I  X  M  ezpres 

the  laetrc  at  the  unit  of  distance,  I  x  -  ,•  will  esprCKS  it  at  the  ilia- 

tance  n,  so  that  wc  ?ball  have 

I   X  M  =  L  X   I)'. 

If  the  apparent  lustre,  and  tbe  distance  uf  the  star,  therefore,  be 
both  known,  the  intrinsic  lustre,  which  depends  conjointly  upon  the 
magnitude  of  the  luminous  surface  exposed  to  view  and  its  intrinsic 
brightness,  will  be  known. 

3320.  AstromHrr  suij,ji-tltd  Iff  Dr.  Lardn'-r.—To  bring  a  fixed 
■tar  into  ininiediatc  eouipiirison  wilh  the  ^un,  and  to  obtjiin  a  mea- 
Buro  of  tbe  visual  magoitude  of  the  star,  suppnaing  it  to  have  id 
intrinsic  lustre  equal  to  that  of  tbo  sun,  would  be  easy  if  tbe  di*- 
tance  could  be  ascertained  to  which  it  would  be  necessary  to  remon 


MAGNITUDE  AND  LUSTRE  OF  THE  STABS. 


679 


ike  san,  so  that  it  shall  present  to  the  eye  the  same  apparent  lostre 
•B  the  star,  for  in  that  case  the  visual  magnitude  of  the  sun, 
which  could  he  calculated  by  means  of  its  real  magnitude  and 
distance,  would  necessarily  be  equal  to  the  visual  magnitude  of  the 
Btar.  In  this  manner,  a  visual  angle  too  small  to  be  ascertained  by 
direct  instrumental  measurement,  would  be  determined  by  indirect 
means. 

Let  cf  =  the  real  diameter  of  the  sun,  d  =  the  distance  to  which 
it  would  be  necessary  to  remove  it  from  the  observer,  so  that  it 
might  present  to  the  eye  the  same  appearance  as  a  given  star,  and 
let  t  ==  its  visual  diameter  at  that  distance.     We  should  then  have, 

^^  =  206265  X  d 

— > 

D 

and  ^  would  then  be  the  visual  angle  subtended  by  the  star,  if  the 
star  be  supposed  to  have  the  same  intrinsic  lustre  as  the  sun.  But 
if  the  star  be  supposed  to  have  a  greater  or  less  Intrinsic  lustre  than 
the  sun,  then  the  visual  magnitude  of  the  star  will  be  greater  or 
less  than  ^. 

Although  the  sun  cannot  be  removed  to  increased  distances,  the 
same  optical  effect  may  be  produced  by  the  following  expedient. 

Let  A  B  0  D  be  a  tube  like  that  of  a  telescope,  furnished  with  a 


A.                                                           ] 

B 

<i 

J 

n* 

Fig.  873. 

diaphragm  at  b  c,  so  constructed  that  by  sliding  pieces  a  circular 
aperture,  having  a  diameter  variable  at  pleasure  within  practical 
limits,  may  be  made  in  its  centre.  Let  a  sliding  tube  having  an 
eye-hole  in  a  diaphragm  at  the  end  of  it,  like  that  in  the  eye-piece 
of  a  telescope,  be  attached  to  the  other  end  A  D  of  the  tube,  so  that 
the  distance  of  the  eye-hole  from  the  variable  aperture  m  n  may  be 
▼aiied  at  pleasure  within  practical  limits.  It  is  evident,  that  the 
diameter  of  the  aperture  m  n,  and  the  distance  ^m  E  to  m  n,  being 
known,  the  visual  angle  subtended  by  m  n  at  e  will  be  determined. 
If  the  tube  thus  constructed  and  arranged  be  directed  to  the  disk 
of  the  sun,  a  circular  part  of  that  disk  having  any  desired  visual 
diameter,  can  be  made  visible  to  an  eye  placed  at  E.  This  can 
always  be  accomplished  within  limits  by  the  variation  of  the  diame* 
ter  m  fi  of  the  aperture,  and  the  variation  of  the  distance  of  B  from 


ASTBONOMY. 


1-nnderstooJ  prinwple  of  optics  (1132),  tho  cirenlit 
,  disk  risible  tLrough  the  aperlore,  has  eiacilj  the 
ppcBiance  both  in  apparoat  magnitude  anil  brightness,  as  iha 
plf  would  have  if  it  were  removed  lo  such  &  distance  from 
)  ,  tbat  it  would  stibtcud  the  same  visual  angle  u  tlul 
ifl         r  the  aperture  m  n  at  the  eyo  E. 

the  ppnratua  be  so  adjusted,  that  the  apparent  lustre  of 

^  Bun  seen  tbroagh  the  aperture,  Ghall  be  eqaal  u 

irvatioD  of  this  kind,  to  tbe 

aeas  folloir,  that  the  visual  angle 

le  apenure  k,  will  be  equal  to  the  visual 

aieDaed  by  the  star;  as  the  former  caa  be  calculated 

ine  the  real  diameter  oi  lue  aperture  aiid  its  distance  from 

^a         r  can  be  inferred. 

'. r'^'^'^'^'  application  of  this  method,  the  difficulty  ariKi 

not  being  able  to  bring  the  Inminous  poiut  seen  in  the  tube, 

immedi&te  juxtaposition  wilt  tho  sUr  with  which  it  is  com- 

__.     Tho  observer  must  rely  npon  his  judgment  nnd  memory  of 

ipparaot  brightneas  of  the  stare,  to  determino  when  Ihitt  of  tbe 

Doua  point  eeen  in  tho  tube  ie  equal  to  it 

a!i27.    Comparison  of  the  sun  and  a  CfiitouW— There  will  ba 

no  difficulty  iu   the  applicatioQ  of  this  principle  (o  all   sUrs  wboM 

Krtillax  and  relative  distance  with  reference  to  a  known  titandard, 
B  been  determined.     Take,  for  example,  tbe  case  of  a  CentaurL 
By  Hurschel'B  aBtrometric  estimate,  we  have  for  this  star, 


2I,955,OU0,00U' 
B  still  expresrang  the  light  of  the  sun. 

It  appears  by  Henderson's  obserTatioca,  that  the  parallax  of  ibii 
star  is  0!)13",  wliieh  corresponds  to  a  distance  of  2'2&9I6  semi- 
diatnctcrs  of  tbe  earth's  orbit.     We  shall  consequently  Lave 

225916'        _oQn 
'  ^  "  ~21,955,0UO,0aO-  ^'^-^- 

It  follows,  therefore,  that  this  star,  placed  where  the  sun  is,  woulil 
have  2'324  times  its  splendour  or  illuminating  power. 

Now.  this  may  ariEe  either  from  the  star  having  a  greater  suprr 
lioial  magnitude  than  the  sun  in  that  proportion,  or  if  it  have  the 
same  superficial  magnitude,  having  greater  intensity  of  light.  Bol 
wbiehever  may  be  the  ease,  it  is  certain  tbat  its  illuminating  pow« 
would  be  greater  than  that  of  the  sun,  in  the  ratio  of  2324  to  1. 

8328.  Comjiariion  of  Oie  sun  and  Sirivf.  —  SiT  John  Herwhd 
found  by  hU  oatiometric  obscrvationa,  that  the  lustre  of  tho  Dog- 


I 


MAGNITUDE  AND  LUSTRE  OF  THE  STARS.  681 

•tar  is  four  times  that  of  a  Ccntauri.  For  the  Dog-star  we  shall 
have,  therefore, 

8 

^~  5,488,750,000' 

and  since  it  appears,  by  the  observatioDs  of  Peters,  that  the  parallax 
of  this  star  is  0*230",  its  distance  will  be  89G800  semidiameters  of 
the  earth's  orbit.     We  shall  consequently  have,  for  Sinus, 

896800»  ..«.o* 

^  ^  ^ = 5;488;75o;ooo = ^^^-^^  * 

From  which  it  appears  that  Sirius  is  a  sun,  whose  lustre  is  such 
as,  if  placed  in  the  centre  of  the  solar  system,  would  diffuse  a  light 
to  the  surrounding  planets  140-53  times  more  intense  than  that 
afforded  by  the  actual  sun.  If,  therefore,  the  intensity  of  the  lustre 
of  the  surface  of  this  stupendous  sphere  be  equal  to  that  of  the  sun, 
it  must  have  a  diameter  12*11  times  greater  than  that  of  our  sun; 
and  since  the  diameter  of  the  latter  is  882,000  miles,  that  of 
Sirius  would  be. 

882000  X  1211  =  10,676,600  miles. 

3329.  AUrometric  table  of  190  principal  stars. — In  the  fol- 
lowing table  (see  pp.  682-3,)  are  collected  the  results  of  the  oh- 
aervations  of  Sir  J.  Herschel,  for  the  determination  of  the  relative 
lustre  of  190  principal  stars.  In  addition  to  their  astrometric  mag- 
*  nitndes,  as  determined  by  Sir  J.  Herschel^  we  have  computed  from 
the  data  supplied  by  him,  their  relative  brightness  compared  with 
that  of  the  star  a  Centauri  as  a  standard,  and  also  their  light  in  bil- 
lionths  of  the  light  of  the  sun. 

8330.  Use  of  the  telescope  in  stellar  observations,  —  Since  no 
telescope,  however  great  might  be  its  power,  has  ever  presented  a 
'  fixed  star  with  a  sensible  disk,  it  might  be  inferred  that,  for  the 
purposes  of  stellar  investigation,  the  importance  of  that  instrument 
must  be  inferior  to  that  which  it  may  claim  in  other  applications. 
Nevertheless  it  is  certain,  that  in  no  department  of  physical  science 
has  the  telescope  produced  such  wonderful  results  as  in  its  applica- 
tion to  the  analysis  of  the  starry  heavens. 

Two  of  the  chief  conditions  necessary  to  distinct  vision  are,  iSrst, 
tEat  the  image  on  the  retina  shall  have  sufficient  magnitude;  or, 
what  is  equivalent  to  this,  that  the  object  or  its  image  shall  subtend 
at  the  eye  a  visual  angle  of  suificient  magnitude  (1116) ;  and, 
aecondly,  it  must  be  sutliciently  iiluDiinatcd  (1100).  When,  by 
reason  of  their  distance  from  the  observer,  visible  objects  fail  to 

*8ir  J.  Herscbel  makes  tbe  proportion  6302  which  is  certainly  incorrect, 
that  being  the  ratio  of  the  intrinsic  brightocss  of  Sirius  to  that  of  a  Cen- 
tauri and  not  that  of  Sirius  to  the  sun.    See  Astronomy,  p.  553,  edit  1849 


ASTRONOMY. 
TABLE. 

-s,  from  Ibe  firsi  lo  the  third  tna^itaje  i 


Idmnl 

Aldcburu. 
OiDturi.... 


X  Soorpii-. 

■  Oypii;.. 


S3-2i 
22-!t 
B2-27 


II.  3  Mas. 

B  Orai.. 

J  s-giir.::;:: 

^  Anilroin  .. 

flC«ti 

*  Argm 

flAnrign... 

IlL  3  M«g.  ' 


/  y  Leoniii... 


0-134 
O-lflZ 
0-187 


0-1  as 
O'lSl 
O'Mfl 


O'las 

B-130 
0'131 


0  Omiii  mi 

•  Orloniii.. 
r  Uemin... 
i  Orioni!.. 

Algol  .... 
.P..sn.,i,., 
y  Drnconii 
^  LfodIi.,, 
a  0(,hiuchi 

r  Cypni'!!'. 

fl  PfK»ji .,' 

a  CoroniE .. 
,.  Brs*  uii. 
iScorpii  .. 

K' "»..'.'.! 
s  Pbo-Dicil 

1  Bootii .'!.'! 

*  Lupl  

1  CenUuri. 
•I  Cnnla  .... 

e  Aquaril  .... 
i  Soorpii  .... 

'CjRni 

„  Ophiu^hi... 

r"""' 

aCephoi 

xCrnlaiiri... 


1I-9S 

D 

SH,'. 

0 

?-qfi 

2-1111 

n 

B-(KI 

S'OO 

a-iii! 

0 

a-01 

3-oa 

n 

S-03 

a-nt 

n 

3-IU 

n 

S-(14 

0 

.-<■«« 

ij 

3-OB 

S-IO 
S-I3 

0 

.1-tS 

n 

a-lH 

0 

II 

M-ltl 

11- 

a-?s 

fi- 

.fits 

0- 

a-26 

0- 

S-?7 

n- 

:f-:Hi 

11- 

3-31 

0- 

UAONITUDE  AND  LUSIBE  OF  THE  STABS. 


683 


Atlro- 

metric 

tu«i«. 

aCeii< 

tauri 

a  1. 

3-33 

3-35 

335 

3-36 

3-37 

3-37 

3-38 

3-38 

»••••• 

3-39 

!••••• 

3-39 

3-40 

3-40 

3-41 

3-41 

3-42 

3-42 

3-43 

3-46 

3-47 

3-48 

3-49 

3-49 

•••••• 

3-50 

i • •••• 

3-52 

3-52 

3-63 

3-54 

3-55 

3-55 

»••••• 

3-56 

3-58 

3-59 

361 

3-61 

3-63 

nat. 

3-63 

3-64 

3-65 

••••• • 

3-67 

3-67 

>••  ••• 

3-67 

3-67 

3-68 

3-68 

3-69 

3-69 

•  ••••a 

3-70 

>••••• 

3-71 



3-72 

SUr'a  Light 


a  Can- 
Uari 
a  I. 


0-0902 
0-0891 
0-0891 
0-0886 
0-0881 
00881 
0-0875 
00875 
0-0870 
0-0870 
0-0865 
0-0865 
00860 
00860 
0-0855 
0-0855 
0-0850 
00835 
00830 
0-0826 
00821 
0-0821 
00816 
0-0807 
0-0807 
00803 
0-0798 
00793 
0-0793 
00789 
00780 
0-0776 
0-0767 
0-0769 
00759 
00759 
0-0755 
0-0751 
0-0742 
0-0742 
00742 
0-0742 
00738 
00738 
0-0734 
00734 
0-0730 
00726 
0-0723 


Bil. 
lioDth* 
of  SUr't 
Light. 


4 
4- 
4 
4 
4 
4 
3 
3 
3 
3' 
3 
3 
3 
3 
3' 
3- 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 


11 
06 
06 
03 
01 
01 
99 
99 
95 
95 
94 
94 
92 
92 
89 
89 
87 
80 
78 
76 
74 
74 
72 
68 
68 
65 
63 
61 
61 
59 
55 
53 
49 
49 
46 
46 
44 


3-42 


•38 
•38 
•38 
•38 
■36 
•36 
34 
34 
33 
31 
29 


Bun. 


III.  3  Mag. 

/3Ar» 

a  Touc&ni 

(3  Capric 

f>  Argus 

^AquilsB 

/3Cygni  

Y  Persei 

H  Ursadmaj.... 
/3  Triang.  bor. 

ir  Scorp 

P  Leporis 

y  Lupi 

i  Persei 

^  UrssB  maj. .. 

(  Aurig. 

0  Scorp 

t  Orion 

Y  Lyncis 

(Drao 

a  ArsB 

w  Sagitt 

w  Here 

/?  Can  min.  ? .. 

f  Tauri 

3Drac 

fi  Qemin 

Y  Boot. 

c  Gemin 

a  MuscaB 

aHydri? 

T  Scorp 

5  Here 

6  Gemin 

^  Orion 

0  Cephei 

0  Ursa) maj.... 

(^Ilydnfi 

y  Hydrad 

(i  Triang.  aus. 

1  UrsaB  maj.... 
ff  Aurig 

Y  Lyrae 

rj  Gemin 

Y  Ceph 

K  Ursao  maj. .. 

c  Cassiop 

S  Aquil 

9  Scorp 

r  Argus 


Aitro> 

metric 

Marni. 

tud«. 


aCen* 
tauri 
■>  1. 


3-72 
3-73 
3-73 
3-73 
3-73 
8-74 
3-75 
3-76 
3-76 
3-76 
3-76 
3-77 
8-77 
3-77 
V.  3-78 
3-78 
8-78 
8*80 
3-81 
8-81 
3-81 
382 
882 
8*83 
3-83 
3-83 
3-84 
3-84 
3-84 
3*85 
3-85 
3-85 
8-85 
8-86 
8-86 
8-86 
3-86 
3*87 
3-87 
8-87 
3-87 
8-88 
8-89 
8-89 
8-90 
8-90 
3-91 
8-91 
3*91 


ltar>li  Lif lit. 


aCen. 
tauri 
B  L. 


0-0723 
0-0719 
0-0719 
0-0719 
00719 
0-0715 
0-0711 
0-0707 
0-0707 
0-0707 
0-0707 
00704 
0-0704 
0-0704 
0-0700 
00700 
0-0700 
0-0693 
0*0689 
0-0689 
0-0689 
0-0685 
0-0685 
0-0682 
0-0682 
00682 
0-0678 
0-0678 
0-0678 
0-0675 
0-0675 
0-0676 
0-0675 
0-0671 
0-0671 
00671 
0-0671 
0-0668 
00668 
0-0668 
0-0668 
0-0664 
0-0661 
0-0661 
0-0657 
00657 
00654 
00654 
0-0654 


BU. 

liontha 

of  Sun's 

Light. 


8-29 
3-27 
3-27 
3-27 
3-27 
3-26 
3-24 
3-22 
8-22 
3-22 
3-22 
3-21 
3-21 
3-21 
3-19 
8-19 
8-19 
8-16 
3-14 
8-14 
3-U 
8-12 
8-12 
8-10 
8-10 
810 
8-09 
309 
309 
8-07 
3-07 
8-07 
3-07 
3-06 
3-06 
3-06 
306 
304 
3-04 
3-04 
304 
303 
301 
-01 
-99 
•99 
•98 
-98 


8- 
2- 
2- 
2- 
2- 
2-98 


ASTROSOSIT. 

r  or  both  of  llieee  conditionB,  the  telescope  is  capable  of 

uiDg  them.     It  augmebts  the  visual  angle  by  suWitDtliig 

Mv  distaaC  object,  which    the   obseryer   ouiDot   approach,  an 

.^til  image  of  it  close  to  his  ejc,  'which  he  can  approach ;  and  it 

nients  the  illnminBtioo  by  collecting,  on  each  point  of  such 

ge,  OS  many  raya  aa  c<id  enter  (he  aperture  of  the  object  gl>^ 

.■end  of  the  more  liioitcd  numbor  which  can  enter  the  pupil  ^  the 

ked  eye ;  allowance,  nevertheless,  being  made  for  the  light  lo»t  bj 

Hnr<tion  from  (he  surfaces  of  the  lenses,  and    by  the  imperfeci 

rency  of  their  material, 

increafe  of  the  visual  angle  ia  determined  by  the  ratio  of  the 
jngih  of  the  object  glass  to  that  of  the  eye  glass  (1212),  and 
sreose  of  illuiuiDatina  is  determined  by  the  ralio  of  the  aiei 
aperture  of  the  object  glass  to  that  of  the  pupil,  which  ireai 
.  ...  oporliooat  to  the  squares  of  the  diameters  of  the  object  glva 
the  pupil.     The  illumination  will,  therefore,  vary  in  the  ratio 
IB  Btjuarea  of  the  aperture  of  the  telescope. 
Lo  explain  the  effect  of  the  l«leecope  applied  to  stellar  obser?a- 
•D,  let  the  sun  or  any  similar  objeot  he  imagined  to  be  transferred 
a  gradually  increased  distance  from  the  observer.     The  eSect  will 
00  the  gradual  decrease  of  its  risual  diameter,  and  a  coirecpondiDg 
decrease  uf  the  linage  oii  the  rrtina.      The  brightness  or  intensity 
of  illumiotttioo  of  that  image  will  remain  always  the  same  (1133); 
and,  consequently,  the  total  quantity  of  light  which  falls  upon  it 
will  be  decreased  in  the  exact  ratio  of  its  superScial  magnitude, — 
that  is,  in    the   ratio  of  the  square  of  its  diameter.      But  tbit 
diameter  is  alwiiys  proportional  to  the  visual  angle  subtended  at  the 
eye   hy  the  object;    and    this  angle  decreases  as  the   distance  of 
the  ohjcft   increases.      It  follows,  therefore,  that  the  total  quantity 
of  light  incident  on  the  retina,  from  the  same  or  similar  objects 
at  difltretit  distances,  decreases  as  the  square  of  the  distance  in- 
creases. 

Now,  let  the  distance  of  the  sun  from  the  observer  be  imagined 
to  he  increased  until  the  visual  angle  hecomes  so  small  that  no  sen- 
sible  iuiprossion  of  the  form  or  magnitude  of  the  object  is  produced. 
Let  this  distance  be  expressed  by  d'.  The  appearance  of  the  sna 
would  then  be  that  of  a  mere  luminous  point,  without  apparent 
magnitude  or  form.  It  would  in  fact,  therefore,  have  the  same 
appearance  os  that  of  a  star  or  planet.  Vision  would  depend  on  the 
mere  eicitation  of  the  retina  hy  the  quantity  of  light  acting  upon  it, 
and  not  on  the  form  or  magnitude  of  the  picture  produced  upon  it 
The  first  of  the  above-mentioned  conditions  of  distinct  vi.sion  would 
foil  to  be  fulfilled,  but  the  second  would  be  still  fulfilled.  Light 
without  form  or  magnitude  would,  therefore,  be  the  sensible  impres- 
sion on  the  observer. 

If  we  now  ima^M  the  sun  to  continue  to  be  transferred  to 


MAGNITUDE  AND  LUSTRE  OF  THE  STARS.      .  685 

greater  and  greater  distances,  the  image  on  the  retina  will  be  pro- 
portionally diminished  in  magnitude;  but  as  its  magnitude  has 
already  ceased  to  be  sensible  because  of  its  minuteness^  this  decreaso 
of  magnitude  will  necessarily  also  be  insensible.  But  the  total 
quantity  of  light  falling  upon  the  retina  will  also  be  decreased, 
and  this  decrease  will  be  in  the  ratio  of  the  increase  of  the  square 
of  the  distance.  Now,  since  the  apparent  brightness  of  the  lumi- 
nous point  to  which  the  sun  would  be  in  this  case  reduced,  must 
depend  altogether  on  the  total  quantity  of  light  falling  on  the  retina 
this  brightness  will  be  in  the  inverse  ratio  of  the  square  of  the 
distance. 

Let  il  be  the  total  quantity  of  light  falling  on  the  retina,  or  the 
apparent  brightness  of  the  object  at  the  distance  d'  at  which  it 
oeases  to  have  a  sensible  disk,  and  let  L  be  its  apparent  brightness, 
at  any  greater  distance  D.  We  shall  then,  according  to  what  has 
just  been  explained^  have 

L  :  l'  : :  d'^  :  D*; 
and  consequently, 

L  =  L'x-„ 

from  which  it  appears  again  that  L  will  decrease  as  d'  increases. 

By  the  continual  increase  of  D,  therefore,  the  apparent  brightness 
of  the  luminous  point  to  which  the  object  has  been  reduced,  would 
be  continually  diminished,  and  it  would  successively  assume  the 
appearance  of  stars  of  less  and  less  magnitude,  until  at  length  the 
quantity  of  light  falling  on  the  retina  would  become  so  small  that 
it  would  be  insufficient  to  produce  a  sensible  impression  on  the 
organ,  and  the  object  would  cease  to  be  seen.  Let  the  dbtance  at 
which  this  would  take  place  be  d". 

It  appears,  then,  that  in  the  gradations  of  the  optical  impression 
produced  by  such  a  contiDually  receding  object,  there  are  two  limit- 
ing distances,  the  lesser  d'  at  which  it  ceases  to  have  sensible  mag- 
nitude but  continues  to  be  visible  as  a  lucid  point,  and  the  greater 
j/*  at  which  it  ceases  to  be  seen  altogether ;  and  that  at  intermediate 
distances  D  it  appears  as  a  lucid  point  of  all  degrees  of  brightness, 
less  than  that  which  it  has  at  the  distance  d'. 

If  this  reasoning  be  applied  to  different  objects,  it  is  evident  that 
ihe  distance  d'  will  vary  with  the  real  diameter  of  the  object,  and 
will  be  exactly  proportional  to  it.  The  distance  d"  for  objects  hav- 
ing the  same  real  diameter,  will  vary  with  their  intrinsic  lustre,  or 
the  relative  quantities  of  light  which  they  emit  from  their  visible 
hemispheres,  and  will  be  greater  in  the  ratio  of  the  square  root  of 
the  abiBolute  quantity  of  light  emitted. 

K  a  telescope  be  directed  to  a  star  at  any  distance  D  greater  than 
lf\  its  magnifying  power  will  be  incapable^  however  great  it  ma^ 

III.  58 


A&XllONOMT. 

lenting  the  visual  angle  to  auch  ao  exteot  u  to  render  tt 

1  it  KDuU  be,  if  the  star  ncrc  at  the  liiEtance  d',  &t  which 

>i  ungle  becomes  so  small  as  to  be  inopprecioble  bjllie  ey«. 

._   the  eamc  case,  the  power  of  the  telescope  to  iDcrcase  the 

;itj  of  light  which  enters  the  pupil,  will  produce  eflecta  which 

I-  only  very  sensible,  but  which  may  be   increased  nlmost 

ly,  by  augmentJDg  the  aperture  of  the  telescope.     In  thia 

ough  the  magnifyiiig  power  is  altogether  incSciicioQa  so 

9     iintcs  to  the  viiiual  angle  of  the  object,  ite  power,  m  fur  u 

B     I     he  incrcose  of  light  or  increase  of  apparent  bnjihtDFse  of 

objei      bccotnes  of  the  greatest  importance.     Thua  it  is  evident, 

!Ope  of  a  certain  aperture  directed  to  a  star  of  the  »sth 

the  light  of  which,  according  to  the  estimate  of  Sir  S. 

,  -)  about  the  100th  part  of  the  light  of  such  a  star  of  lb« 

.-^'nitude  as  a  Ceniauri,  would  render  it  equal  in  apparcDl 

ntncsB  to  the  lutter,  and  would,  therefore,  have  the  e^t  of 

-giug  it  so  much  Dcurcr  to  the  observer,  as  the  distance  of  to 

roge  star  of  the  first  aiaguitude  is  less  than  an  average  star  of 

'  sixth  magniiude.     But  since  the  apparent  brightness  decreuM 

the  square  of  the  distance  inereaees,  it  follows  that  n  star  of  tha 

jiith  magnitude,  being  100  times  leps  bright  than  a  star  of  the  first 

magnitude,  will   be  lU  times  more  dli-taiit.     The  ttloMope^  thert. 

fore,  in  this  case,  would  have  the  effect  of  bringing  the  star  10 

times  nearer  to  the  observer. 

By  knowing  the  relation  of  the  aperture  of  the  telescope,  whether 
it  be  B  refractor  or  reflector,  to  the  magnitude  of  the  pupil,  and  the 
proportion  of  light  lost  in  being  transmitted  to  the  eye  by  the  lenses 
or  specula  of  the  instrument,  it  b  easy  to  calculate  the  ratio  in  which 
it  will  increase  the  apparent  brightness  of  a  star,  and  this  ratio 
being  known,  it  will  be  easy  to  ascertain  bow  much  more  distant 
fiuch  a  star  is  than  one  which  to  the  naked  eye  would  have  the  soma 
apparent  brightness. 

Let  m  espresH  the  ratio  in  which  the  telescope  increases  the 
apparent  brightness  l  of  s  star,  and  let  l'  be  the  brightness  of  the 
same  star  seen  through  the  telescope.     We  should  then  have 


Now,  let  d  be  the  distance  of  the  star,  and  let  d"  be  the  distance 
,t  which,  seen  with  the  naked  eye,  it  would  have  the  brigbtaess  l'. 
Ve  shall  then  have 


MAaNITUDE  AND  LUSTRE  OF  THE  STARS.  687 

The  star  is,  therefore,  brought  nearer  to  the  observer  in  the  ratio 

of  %/m  to  1.  

3331.  Space-penetrating  power, — This  Dumber  y/m  which  ex- 
presses the.  power  of  the  telescope  to  bring  a  star  nearer  to  the 
obeeryer,  or  what  is  the  same,  to  enable  the  obserrer  to  see  distant 
stars  with  the  same  degree  of  distinctness  or  brightness  as  if  they 
were  at  less  distances,  is  called  the  bpace-penetratinq  power. 

Thus,  if  the  light  of  8  star  of  the  sixth  magnitude  be  100  times 
less  than  that  of  a  star  of  the  first  magnitude,  a  telescope  which 
woald  augment  the  light  100  times,  would  exhibit  it  with  the  same 
apparent  brightness  as  a  star  of  the  first  magnitude ;  and  for  such 

a  telescope  we  should  have  m  =  100,  and  therefore  >/ m  =  10,  so 
that  the  star  of  the  sixth  magnitude  would  be  ten  times  more  dis- 
tant than  the  stars  of  the  first  magnitude. 

Thus,  for  example,  the  reflecting  telescope  used  by  Sir  William 
Herschel,  in  some  of  his  principal  stellar  researches,  had  an  aper- 
ture of  eighteen  inches,  and  twenty  feet  focal  length  with  a  magni- 
fying power  of  180.  The  space-penetrating  power  of  this  instru- 
ment was  found  to  be  seventy-five,  the  meaning  of  which  is,  that 
when  directed  to  a  star  of  any  given  brightness,  it  would  augment 
its  brightness  so  as  to  make  it  appear  the  same  as  it  would  be  if  at 
seventy-five  times  less  distance,  or  what  is  the  same,  that  a  star 
which  to  the  naked  eye  would  appear  of  the  same  brightness  as  that 
star  does  when  seen  in  the  telescope  would  require  to  be  removed  to 
seventy-five  times  the  actual  distance,  so  that  when  seen  through 
the  telescope  it  would  have  the  brightness  it  has  when  seen  with 
the  naked  eye.  Thus  a  star  of  the  sixth  magnitude,  if  removed  to 
seventy-five  times  the  actual  distance,  would  appear  in  such  an  in- 
stroment  still  as  a  star  of  the  sixth  magnitude  would  to  the  naked 
eye,  and  if  we  assume  with  Sir  John  Herschel,  that  a  star  of  the 
sixth  magnitude  has  a  hundred  times  less  light  than  a  Centauri, 
and  18  therefore  at  ten  times  a  greater  distance,  it  will  follow  that  a 
Centauri  would  require  to  be  removed  to  seven  hundred  and  fifty 
times  its  actual  distance,  so  that  when  viewed  through  such  a  tele- 
scope it  would  be  seen  as  a  star  of  the  sixth  magnitude  is  to  the 
naked  eye. 

If,  then,  it  be  assumed,  as  it  may  fairly  be,  that  among  the  innu- 
merable stars  which  are  beyond  the  range  of  unaided  vision,  and 
brought  into  view  by  the  telescope,  a  large  proportion  must  have 
the  same  magnitude  and  intrinsic  brightDcss,  as  the  average  stars 
of  the  first  magnitude,  it  will  follow  that  these  must  be  at  distances 
750  tiroes  greater  than  the  distance  of  an  average  star  of  the  first 
magnitude,  such  as  a  Centauri.  But  it  has  been  already  shown 
(3308,)  that  the  distance  of  a  Centauri  is  such  that  light  would 
require  3-54325  years  to  come  from  it  to  the  earth.     It  would. 


ASTROK  OMT. 

llov  ikxl  tbf  distance  of  iho  teleaoopio  stua  joat  n 
)     ,.,  sooh  tLat  ligbt  trouid  tako  to  come  from  them  to  the 

8'5-1325  X  750  =  2G57-4375  yeare. 
If  it  be  desired  to  ascertain  ihe  distance  of  snoh  atare.  taking  the 
h's  distance  from  the  Gun  as  the  unit,  we  shall  have 
225916  X  750  =  169,437,000. 
appears,  therefore,  that  the  distance  of  such  a  star  wonid  b« 
t  one  hundred  and  seventy  inilHoa  tiaics  the  distanoe  of  the 
■"•a,  and  since  the  distance  of  the  snn  expressed  in  round  numhera 
one  hundred  millions  of  miles,  it  vill  follow  that  the  distance  of 
oh  a  Ebar  is  seventeen  thousand  billiona  of  miles. 
^e  arrive,  therefore,  at  the  some'nbat  astooishiog  conclusion  thai 
I  distance  of  these  objects,  the  existence  of  which  the  t«lescope 
ne  has  disclosed  to  us,  must  be   such  that  light,  moving  at  the 
of  192000  miles  per  second,  takes  upwards  of  2600  years  to 
c  from  them  to  us,  and  consequently  that  (he  objects  we  nnir 
are  not  those  which  now  exist,  but  those  which  did  exist  2600 
ira  ago ;  and  it  is  within  the  scope  of  physical  possibility  thai 
mej  roay  have  changed  tboir  conditions  of  existt'nce,  and  conse- 
quently of  appearance,  or  even  have  ceased  to  exist  altogether,  mora 
Uian  2000  years  ago,  although  we  actually  see  them  at  thia  moment. 
This  incidentally  shows  that  the  actual  perception  of  a  visibla 
object  is  no  conclusive  evidence  of  its  present  existence.    It  is  only 
a  proof  of  its  existence  at  some  anterior  period. 

3332.  Telescopic  stars.  —  It  appears,  therefore,  that  there  are 
numerous  orders  of  stars,  which  by  reason  of  their  rcmoteneaa  are 
invisible  to  the  naked  eye,  but  which  arc  rendered  visible  by  the 
telescope;  and  these  stars  arc,  like  those  visible  to  the  naked  eye, 
of  an  infiuite  variety  of  degrees  of  magnitude  and  brightness,  and 
have  accordingly  been  classed  by  aslronomers  according  to  an  order 
of  magnitudes  in  numerical  continuation  of  that  which  has  been 
Bomcwhat  iudchuitely  or  arbitrarily  adapted  fur  the  visible  stars. 
Thus,  supposing  that  the  last  order  of  stars  visible  without  telescopic 
aid  is  the  seventh,  the  Brat  order  disclosed  by  the  telescope  will  be 
the  eighth,  and  from  these  the  telescopic  stars,  decreasing  in  mag- 
nitude, have  been  denominated  the  ninth,  the  tenth,  eleventh,  ttc., 
U>  the  sixteenth  ur  seventeenth  magnitude,  tbe  last  being  the 
smallest  stars  which  are  capable  of  being  rendered  distinctly  visible 
by  the  most  powerful  telescope, 

S3'63.  Sl'tkir  nomencliilare.  —  Besides  the  clapsification  of  stars 
according  to  their  estimated  degrees  of  magnitude  or  br 
they  are  also  designated  according  to  their  distribution  i 
imaginary  surface  of  the  celestial  sphere.  Whether  the  apparent 
grouping  of  thcro  objects  depends  on  any  physical  relation  existing 


MAGNITUDE  AND  LUSTRE  OF  THE  STARS.  689 

I 

between  the  members  composing  each  group,  or  is  the  result  of  the 
fortuitous  relation  of  the  visual  lines  directed  to  them,  the  principal 
oollections  of  the  more  conspicuous  stars  thus  placed  in  near  appa- 
rent vicinity,  have  been  recognised  from  the  most  remote  antiquity, 
and  such  groups  have  been  commonly  denominated  constellations. 

Although  in  certain  cases,  it  is  probable  that  some  physical  rela- 
tion may  exist  between  the  more  close  neighbours  in  these  constel- 
lations, it  is  certain  that  the  apparent  juxta-position  and  relative 
arrangement  of  the  component  stars  generally  is  altogether  for- 
toitous.  Imagination  has,  however,  connected  them  together,  and 
invested  such  constellations  with  the  forms  of  mythological  figures, 
animals,  such  as  bears,  dogs,  lions,  goats,  serpents,  and  so  on,  from 
which  they  severally  take  their  names.  Unreasonable  as  such  a 
system  must  be  allowed  to  be,  it  is  not  without  its  use  as  a  means 
dT  reference  and  an  artificial  aid  to  the  memory.  That  a  better 
system  of  signs  and  symbols  might  have  been  devised  for  these 
parposes,  may  be  admitted;  but  when  it  is  considered  that  the 
names  and  forms  of  the  most  conspicuous  constellations  have  had 
their  origin  in  remote  antiquity — that  they  were  handed  down  from 
the  Chaldeans  to  the  Egyptians,  from  the  Egyptians  to  the  Greeks, 
and  from  these  to  the  modems  —  that  they  are  referred  to  in  the 
works  of  every  past  astronomer,  and  registered  in  the  memory  of 
every  living  observer — that  they  are  associated  with  the  productions 
of  art,  and  supply  illustrations  to  the  orator  and  the  poet  —  it  will 
be  readily  admitted  that,  even  though  a  general  change  of  the  stel- 
lar nomenclature  and  symbols  were  practicable,  it  would  neither  be 
advantageous  nor  advisable. 

As  an  example  of  a  constellation,  the  group  of  seven  conspicuous 
stars,  arranged  nearly  in  the  form  of  a  note  of  interrogation,  vbible 
in  the  northern  part  of  the  firmament,  and  in  these  latitudes  always 
above  the  horizon,  may  be  referred  to.  This  constellation  is  called 
Ursa  major  (the  great  bear).  The  seven  stars  are  only  the  more 
conspicuous  of  those  which  compose  the  constellation,  the  entire 
nomber  being  eighty-seven,  most  of  them,  however,  being  tele- 
scopic ;  of  the  seven  chief  stars  one  only  is  of  the  first  magnitude, 
three  of  the  second,  and  three  of  the  third. 

The  seven  principal  stars  of  this  constellation  being  all  less  than 
forty  degrees  from  the  north  pole,  will  be  always  above  the  horizon 
in  latitudes  greater  than  forty  degrees.  Hence  it  is  that  this  con- 
stellation is  so  familiarly  known.  They  may  serve  as  standards  or 
moduli  by  which  the  astronomical  amateur  may  estimate  the  orders 
of  magnitudes  of  the  stars  generally.  It  is  in  the  quarter  of  the 
heavens  opposite  to  that  in  which  the  sun  is  in  the  month  of  March, 
and  is  therefore  visible  at  midnight  near  the  meridian  above  the 
pole  at  that  season.  In  the  month  of  September  it  is  visible  at  mid- 
night below  the  pole. 

58* 


ASTROKOMT. 

t  vhich  compose  a  constell&tioD  are  denignated  nsuall; 

..jra  of  the  Greek  alphabet,  the  first  IpIIcts  being  gene- 

-.■,1^'Dcd  to  the  most  coni^picaous.     The  order  of  the  letters, 

er,  does  not  alwuja  foUuw  strictly  the  order  of  magniludcs. 

.11  the  Btars  are  not  designated  bj  letters,  thej  are  dUttagiiishcd 

numbers,  and  this  is  mostly  the  coee  witli  the  smaller  stars. 

[t  is  usual  to  exprosa  (be  constellationg  by  theii  Latin  DttoM, 

id  to  designate  the  individual  stars  by  ibe  letter  or  Diiinber  and 

-lo   constellation,  as  a  Lj/rm,  ^    Unse   major!*,   61    Ophiuchi,  24 

mm,  &a. 

[n  the  cases  of  some  of  tbc  more  conspieiious  stars,  snch  as  have 
en  objects  of  observation  in  remote  ages,  tbcy  are  also  frequ^tly 
ttinguished  by  proper  names.     Tbng,  a  VanU  major.\s  more  <»ii>. 
jnly  called  Siriue,  and  souietimos  the  Dog-star,  and  is  known  n 
e  moat  resplendent  of  the  fixed  stars.     In  like  manner  a  Pitcit  is 
Tttjs  called   Fomalhant,  a.  and  d  Geniini  are  called    Catlor  and 
/lux,  jl  Orionis  is  known  as  R^jrl,  a  Taitri  as  Aldebarao,  a  Fm<- 
»V  as  Spiat,  a  Bootit  as  Arctuni*,  and  so  ou. 
The  practical  nscfulness  of  the  imaginary  figures  which  gin 
»  to  the  oonetelktioDs,  will  tbos  be  understood.     If  we  deair« 
press  the  position  of  the  star  if  Urtte  fnnjarit,  for  example,  in 
Bay  that  it  is  at  the  tip  of  ihp  tiiii  of  the  Great  Hear.     We  indi- 
cate, in  like  manner,  the  place  of  three  remarkable  stars,  by  saying 
that  they  form  the  belt  of  Orion,  and  another  Rigel  by  saying  that 
it  is  on  his  foot.     The  star  Sirius  is  on  the  nose  of  Canis  major, 
and  the  bright  star  ^  on  his  right  thigh. 

31)34.  tse  of  poiiiicrs.  —  Those  who  desire  to  obtain  an  acquaint- 
ance with  the  stars,  will  find  much  advantage  in  practising  the 
method  of  pointers,  by  which  the  position  of  conspicuous  stars  with 
which  the  ob.'ierver  is  well  acquainted  is  used  to  ascertain  the  plaeos 
of  others  which  are  less  known  and  less  easily  identified.  This 
method  consists  in  assigning  two  conspituous  stars  so  placed,  that  a 
straight  line  imagined  to  be  drawn  between  them,  and  continued  if 
necessary  in  the  same  direction,  will  pass  through  or  near  the  Etar 
whose  position  it  is  desired  to  ascertain. 

The  most  useful  example  of  the  application  of  this  method,  is  the 
case  of  the  pole  star,  which  is  »  Ursa:  nimorii,  a  star  of  the  third 
magnitude.  Let  the  observer  direct  his  eye  lo  the  two  conspicuous 
stars,  o  and  J3  I'rfa:  nuijoris,  and  supposing  a  straight  line  drawn 
from  (3  to  a,  let  him  carry  his  eye  along  that  line  beyond  a  to  a 
distnuec  about  six  times  the  space  between  a  and  )3,  he  will  arrive 
at  the  Polo  Star. 

3335.  Uscof  Klar  maps.  —  To  comprehend  tlie  preceding  para- 
graphs, and  profit  by  the  instructions  given  in  them,  it  will  be 
necessary  for  the  student  to  have  in  his  hands  a  set  of  sIat  maps. 


MAGNITUDE  AND  LUSTRB  OF  THE  STARS.  691 

The  6un>R  to  the  Stars'^  will  be  found  to  be  one  of  the  most 
convenieDt  works  for  this  purpose.  In  the  maps  there  given,  will 
be  found  indications  of  the  most  useful  applications  of  this  method 
of  pointing. 

3836.  Use  of  the  celestial  globe.  —  A  celestial  globe  may  be 
defined  to  be  a  working  model  of  the  heavens.  It  is  mounted  like 
a  common  terrestrial  globe.  The  visible  hemisphere  is  bounded  by 
the  horizontal  circle  in  which  the  globe  rests.  The  brass  circle  at 
right  angles  to  this,  is  the  celestial  meridian.  The  constellations 
with  outlines  of  the  imaginary  figures  from  which  they  take  their 
names,  are  delineated  upon  it. 

The  globe  will  serve,  not  merely  as  an  instrument  of  instruction, 
but  will  prove  a  ready  and  convenient  aid  to  the  amateur  in  astro- 
nomy, superseding  the  necessity  of  many  calculations  which  are 
often  discouraging  and  repulsive,  however  simple  and  easy  they  may 
be  to  those  who  are  accustouied  to  such  ioquiries.  Most  of  the 
almanacs  contain  tublcs  of  the  principal  astronomical  phenomena,  of 
the  places  of  the  sun  and  moon,  and  of  the  principal  planets  as  well 
as  the  times  wheu  the  most  conspicuous  stars  are  on  the  meridian 
after  sunset.  These  data,  together  with  a  judicious  use  of  the  globe 
and  a  tolerable  telescope,  will  enable  any  person  to  extend  his 
acquaintance  with  astronomy,  and  even  to  become  a  useful  contri- 
butor to  the  common  stock  of  information  which  is  now  so  fast 
increasing  bv  the  zeal  and  ability  of  private  observers  in  so  many 
quarters  of  the  globe. 

To  prepare  the  globe  for  use,  let  small  marks  (bits  of  paper 
gummed  on  will  answer  the  purpose)  be  placed  upon  it,  to  indicate 
the  positions  of  the  sun,  moon,  and  planets,  at  the  time  of  observing 
the  heavens.  The  place  of  the  sun  on  the  ecliptic  is  usually  marked 
on  the  globe  itself.  If  not,  its  right  ascension  (that  is,  its  distance 
from  the  vernal  equinoctial  point,  measured  on  the  celestial  equator), 
and  its  declination,  (that  is,  its  distance  north  or  south  of  the 
equator),  are  given  in  the  almanac,  for  every  day.  The  moon's 
right  ascension  and  declination  are  likewise  given. 

3337.  To  find  the  j)Iace  of  an  object  on  the  globe  when  its  right 
(ucension  and  declination  are  known. — Find  the  point  on  the 
equator  where  the  given  right  ascension  is  marked.  Turn  the  globe 
on  its  axis  till  this  point  be  brought  under  the  meridian.  Then 
count  off  an  arc  of  the  meridian  (north  or  south  of  the  equator,  ac- 
cording as  the  declination  is  given)  of  a  length  equal  to  the  given 
declination,  and  the  point  of  the  globe  immediately  under  the  point 
of  the  meridian  thus  found,  will  be  the  place  of  the  object.  By 
this  rule,  the  position  on  the  globe  of  any  object  of  which  the  right 

*  Twelve  Planispheres,  forming  a  Guide  to  the  Stars  for  every  Night  in 
the  Year,  with  an  Introduction.  —  Taylor  and  Walton^  London. 


ASTROKOMT. 

declination  arc  koown,  mu;  be  imincdiatelj  fouDd, 

(poodiQg  mark  put  upon  it. 

iijust  the  globe  so  as  to  use  it  as  n  guide  to  the  pwi^on  of 

a  on  the  hcaTCQ»,  and  ii»  a  ineEiiia  nf  ideuiifjing  the  stars  aod 

iDg  their  names,  let  the  lower  claiaping-scrow  of  the  meridian 

,uosencd,  and   let   Ihc  north   pole  of  the  globe  be  elevated  bj 

,'irig  the  brass  meridian  uiilil  the  arc  of  this  mEridian  between 

pole  and  the  horizon  he  eqnal  to  Ihe  latitude  of  the  place  of 

rralion.     Let  the  ulamping-scrcv  be  then  tightened,  eo  is  to 

QttUQ  the  meridian  ia  this  pasition.     Let  the  globe  be  tben  h 

ed  that  the  bmfe  meridian  shall  be  directed  due  north  and  soolh, 

lole  being  turned  to  tbe  north.     Thia  being  done,  ibe  globe 

correEpond  nith  the  heavens  so  far  as  relates  to  the  poles,  the 

dian,  and  tbe  points  of  the  borixon. 

)  asecrtain  tbe  aspect  of  the  firmament  at  any  hour  of  the  night, 
1  now  only  nccegsary  tjj  turn  tbe  globe  upon  its  axis  until  the 
k  indicating  tbe  place  of  tbe  sun  shall  he  under  the  hoHion  in 
game  position  as  the  sun  itself  nctualljr  is  at  the  hour  in  qaes- 
.     To  effect  thig,  let  the  globe  be  turned  until  the  mark  indi- 
g  the  position  of   the  sun  is  brought  under  the   meridian, 
^rve  the  hour  marked  on  the  point  of  the  equator  which  is  tben 
uuucr  the  meridian.     Add  lo  this  hour  the  hour  ut  whieii  tbe  obser- 
Tatiou  is  about  to  be  taken,  and  turn  the  globe  until  the  point  of 
the  equator  on  which  is  marked  tbe  hour  resulting  from  this  addi- 
tion ia  brought  under  the  meridian.     The  position  of  the  globe  will 
tben  correspond  with  that  of  the  firmament.     Every  object  on  the 
one  will  correspond  in  its  position  with  its  representatire  mark  or 
ijmhol  on  the  other.     If  we  imagine  a  line  drawn  from  the  centre 
of  the  globe  through  the  mark  upon  its  surface  indicating  any  star, 
SQcb  a  line,  if  continued  outside  the  surface  toward  tbe    heavens, 
vould  be  directed  to  the  star  itself. 

For  example,  suppose  that  when  the  mark  of  the  sun  is  brought 
under  the  oieridian,  the  hour  5b.  40m.  la  found  to  be  on  the  equator 
at  the  meridian,  and  it  is  required  to  find  the  aspect  of  tbe  heavens 
at  half-past  ten  o'clock  in  the  evening. 

To     5     40 

Add 10     30 


Let  the  globe  be  turned  until  16h.  10m,  is  brought  under  the  n: 
ridiau,  and  the  aspect  given  by  it  will  be  that  of  the  heavens. 


PERIODIC  STARS.  698 


CHAP.  xxvn. 

PERIODIC^  TEMPORARY,  AND   MULTIPLE  STARS. — ^PROPER  MOTION 
OF  STARS. — ^MOTION  OF  THE  SOLAR  SYSTEM. 

3338.  Telescopic  observations  on  individual  stars.  —  Besides 
briDgiDg  within  the  range  of  obseryation  objects  placed  beyond  the 
Bpbere  which  limits  the  play  of  natural  vision,  the  telescope  has 
greatly  multiplied  the  number  of  objects  yisible  within  that  spherCi 
bj  enabling  us  to  see  many  rendered  invisible  by  their  minuteness, 
or  confounded  with  others  by  their  apparent  proximity.  Among 
the  stars  also  which  are  visible  to  the  naked  eye,  there  are  many, 
respecting  which  the  telescope  has  disclosed  circumstances  of  the 
hiffhest  physical  interest,  by  which  they  have  become  more  closely 
mlbed  to  our  system,  and  by  which  it  is  demonstrated  that  the  same 
material  laws  which  coerce  the  planets,  and  give  stability,  uni- 
formity, and  harmony  to  their  motions,  are  also  in  operation  in  the 
most  remote  regions  of  the  universe.  We  shall  first  notice  some  of 
the  most  remarkable  discoveries  respecting  individual  stars,  and 
•hall  afterwards  explain  those  which  indicate  the  arrangement, 
dimensions,  and  form  of  the  collective  mass  of  stars  which  compose 
the  visible  firmament,  and  the  results  of  those  researches  which  the 
telescope  has  enabled  astronomers  to  make  in  regions  of  space  still 
more  remote. 

I.   PERIODIC   STARS. 

8339.  Stars  of  variable  lustre,  —  The  stars  in  general,  as  they 
are  stationary  in  their  apparent  positions,  are  equally  invariable  in 
their  apparent  magnitudes  and  brightness.  To  this,  however,  there 
are  several  remarkable  exceptions.  Stars  have  been  observed, 
sufficiently  numerous  to  be  regarded  as  a  distinct  class,  which 
exhibit  periodical  changes  of  appearance.  Some  undergo  gradual 
and  alternate  increase  and  diminution  of  magnitude,  varying  between 
determinate  limits,  and  presenting  these  variations  in  equal  intervals 
of  time.  Some  are  observed  to  attain  a  certain  maximum  magni- 
tude, from  which  they  gradually  and  regularly  decline  until  they 
altogether  disappear.  After  remaining  for  a  certain  time  invisible, 
they  re-appear  and  gradually  increase  till  they  attain  their  maximum 
splendour,  and  this  succession  of  changes  is  regularly  and  periodi- 
cally repeated.  Such  objects  are  called  periodic  stars, 
'  3340.  Remarkable  stars  of  this  class  in  the  constellations  of 
Cetus  and  Ferseus.  —  The  most  remarkable  of  this  class  is  the  star 
called  Omlkron,  in  the  neck  of  the  Whale,  which  was  first  observed 
by  David  Fabricius,  on  the  13th  August,  1596.  This  star  retains 
its  greatest  brightness  for  about  fourteen  days,  being  then  equal  to 


ABTROSOMT. 

i  htge  star  of  the  second  magnitude.  It  tben  dccroases  oolttinaaUT 
rftw  tbrec  months  nnlil  it  becomta  tnyisible.  It  renjsins  ioviBiblo 
I 'for  five  niontlia,  iclien  it  re-appcan,  sod  increases  graJuilly  fur 
p'Aree  monlbfl  uoti]  it  rei^overs  ilB  maximum  eplcndonr.  Tliis  it 
Mhe  general  eUMCsfiion  of  its  pliasea.     Its  entire  period  is  khaot 

■  832  days.  This  period  is  not  alnaj's  the  same,  and  the  gradtiliooi 
of  brightness  tbrough  which  it  piLsaes  are  s^d  to  be  sabject  lo  nriv 
tion.  UevcliuB  states  that,  in  the  interval  between  1GT2  and  1676, 
it  did  not  appear  at  all. 

Snnio  recent  observations  and  researches  of  N.  Argelander, 
render  it  probablo  Ibat  tbo  period  of  this  star  is  subject  to  a  varii- 
tioD  which  is  itself  periodical,  the  period  being  allemately  ang- 
mented  and  diniinished  to  the  extent  of  25  days.  The  vsmlioos 
of  the  mssimum  lugtro  are  also  probably  periodical. 

The  star  called  Algol,  in  the  head  of  Metiiiia,  in  the  conatelUlim 
of  Pertevt,  aSbrds  a  slriliiDg  example  of  the  rapidity  widi  whicb 

'  tiicse  periodical  changes  sometimes  succeed  each  other.  Tbia  star 
generally  appears  as  one  of  tbe  second  magnitude;  bat  an  iateml 

'    rtf  seven  boure  occurs  at  the  expiration  of  every  Mxty-two,  dnrng 

■  11m  first  three  hours  and  a  half  of  which  it  gradoallj  dimi^shea  is 
'  Irrigbtness  till  it  is  reduced  to  a  star  of  tbe  fonrth  magnitude,  ud 

during  the  remainder  of  the  interval  it  again  gradually  iiicresses 
until  it  recovers  ila  original  mugnitude.  Tlius,  if  wo  sujipnst!  it  lo 
have  attained  its  maximum  splendour  at  midnight  on  the  first  dij 
of  the  month,  its  changes  would  be  as  follows ; — 

0  0  0  to  2  14  0  It  appears  of  second  magnitude. 
2  14  0  to  2  17  24  It  decreases  gradually  to  fourth  magnitude. 
2  17  24  to  2  20  48  It  increases  gradually  lo  second  magnitude. 
2  20  48  to  5  10  48  It  appears  of  second  magnitude. 
fi  10  48  to  5  14  12  It  decreases  to  fourlh  magnitude. 
6  14  12  to  5  17  3ti  It  increases  to  second  magnitude. 
^c.  &c.  &c. 

This  star  presents  an  interesting  example  of  its  class,  as  it  is  con- 
stantly visible,  and  its  period  is  EC  short  that  its  succession  of  phases 
may  be  frequently  and  conveniently  observed.  It  is  situate  near 
the  foot  of  the  constellation  Andromeda,  and  lies  a  few  degrees 
Dorth-east  of  three  stars  of  the  fourth  magnitude  which  form  a 
triangle. 

Goodrickc,  who  discovered  the  periodic  phenomena  of  Alffol  in 
1782,  explained  these  i<pj>carances  by  the  supposition  that  soma 
opaque  body  revolves  round  it,  being  thus  periodically  interposed 
bctWL'OQ  the  earth  and  tlie  star,  so  as  to  intCKept  a  large  portion  of 
Its  light. 

Tbe  more  recent  observations  on  this  star  indicate  a  decrease  of 


PBRIODIC  STARS. 


B95 


its  period,  which  proceeds  with  accelerated  rapidity.  Sir  J.  Her- 
Bchel  thinks  that  this  decrease  will  attain  a  limit,  and  will  he  fol- 
lowed by  an  increase,  so  that  the  Tariation  of  the  period  will  prove 
itself  to  be  periodic. 

The  stars  6  in  Cepheus  and  3  in  Lt/ra  are  remarkable  for  the 
regular  periodicity  of  their  lustre.  The  former  passes  from  its 
least  to  its  greatest  lustre  in  thirty-eight  hours,  and  from  its  greatest 
to  its  least  in  ninety-one  hours.  The  changes  of  lustre  of  the  latter, 
according  to  the  recent  observations  of  Argelander,  are  very  com- 
plicated and  curious.  Its  entire  period  is  12  days  21  hrs.  53  min. 
10  sec,  and  in  that  time  it  first  increases  in  lustre,  then  decreases, 
then  increases  again,  and  then  decreases,  so  that  it  has  two  maxima 
and  two  minima.  At  the  two  maxima  its  lustre  is  that  of  a  star 
of  the  3*4  magnitude,  and  at  one  of  the  minima  its  lustre  is  that  of  a 
star  of  the  4-3,  and  at  the  other  that  of  a  star  of  the  4*5  magnitude. 

In  thb  case  also  the  period  of  the  star  is  found  to  be  periodically 
Tariable. 

3341.  Table  of  the  periodic  stars,  —  In  the  following  Table  the 
stars  periodically  variable,  discovered  up  to  1848,  are  given,  with 
their  periods  and  extremes  of  lustre.  This  Table  has  been  collected 
from  various  astronomical  records  by  Sir  J.  Herschel. 


Ma. 


1 

2 
8 
4 
5 


6 
7 
8 
9 


10 
11 
12 


13 
14 
15 
IS 
17 
18 
19 
20 


/?  Persei  (Algol) 

X   Tauri 

Gepbei 

n   AquilsB 

•  CanoriR.  A.(1S00)) 

«  8*  S2-5-  N.  P.  \ 
D.  70<»  ly J 

^   Geniinoram 

p  LyrsB 

«  Hereulis 

59B.ScttUR.A.(1801)) 
«  18*  37-  N.  P.  \ 
D.  =  »5«67' J 

c   AarigSB  

•  Ceti  (Mira) 

•  8erpenti8R.A^I828) ) 

«=  15*  46"  45-  P.  \ 
D.  74°  20' 30". ..J 

X  Cygni 

•  HyUnB(B.A.C.450I) 

•  Cephei(B.A.C.7582) 
34  Cyni  (B.  A.  C.  6990) 

•  Leonis  (B.  A.  G.  3345) 

c   Bagifctaru 

^  Leonu 

t   Cygni 


Period. 

Chanftof 
Mac. 

d.d*e. 

from 

to 

2-8673 

2 

4 

4dr 

4 

5-4 

5-3664 

3-4 

5 

7-1763 

3-4 

4-5 

9-015 

7-8 

10 

10-2 

4-3 

4-5 

12-9119 

3-4 

4-5 

63  it 

3 

4 

71-200 

5 

0 

250  zh 

3 

4 

331-63 

2 

0 

335  ± 

7? 

0 

396-875 

6 

11 

494  d= 

4 

10 

5  or  6  years 
18  years  db 
Many  years 
Ditto 

3 
6 
6 
3 

6 
0 
0 
6 

Ditto 

6 

0 

Ditto 

4-5 

5-6 

DiteoYend  bj 


Goodricke,  1782. 
Bazendelly  1848. 
Goodrioke,  1784. 
Pigott^  1784. 

Hind,  1848. 

Schmidt,  1847. 
Goodricke,  1784. 
Herschel,  1796. 

Pigott>  1795. 

Heis,  1846. 
Fabricios,  1596. 

Harding,  1826. 

Kirch,  1687. 
Maraldi,  1704. 
Herschel,  1782. 
Janson,  1600. 
Koch,  1782. 
Halley,  1676. 
MoDtaoari,  1667. 
Her8chel,Jnn.,1842? 


ASTROHOMT. 


1 

„.. 

r.<i^ 

"■*  " 

•  vitgioi.R.A.(igion 

l)«B' 1 

lis  d>;( 

IflJ  mont!.. 

!/""' 

I>..B 

8<>SMy«n 
DillA 

SorSjmnT 
»Sdnr>r 
2ilorS0d.y.? 

DnkiiowD 

Ditto 

Ditto 

IliHo 

Ditto 
Many  7™" 

8  D 

a      s 

1  I'S 
1-3      > 

S         J-3 

2  SI 
!S       S 

er     D 
s      0 

9  0 

7'S       0 

8         0-lfl 
2?       2-3 

Hvdinc  1814. 

Plpitt,  1T94. 
Pi«ii.  ITllS. 
BBr(h.n,  ISIT. 
Renel»l,JiuL,IStS. 
Ditto.  18W. 

SUM.  ista. 

Blni«,  1888. 
DiM»,  18S7. 
Uind.  IMS. 

DUlo,  1MB. 

IKtte,lHB. 

Rilmkw. 

Prbunueher. 
MoH«  of  etoenJ 

•  Osnw  Bur.  (B.  4. 1 
CSMfl) ) 

T  Ari.Il.(B.  A.  C.  SSI 

,    U»>IU}Mi<._ 

!5 
3« 

nrdnT.":;:::::::::; 

■  K.A.(lS«|  =  2a' 
M"ST>K.P.D. 
-BBOIJ-M"... 

•  B.  A.  (lS46)-7' 

SaoM-Z-N.P.It. 
■~M'\Vbf'.... 

•  B.  A,  llfl«t)  —  T' 

«-103-N,P.D. 
^  flS"  S3'  39" 

iM-'i'isisTN.r. 

•  B.   A.  tmif)   u^' 

«-illl*«'K.P.D. 
ICH'W'Si" 

Iril  1< 


r.  Hid 


Tkte  tha  eatiJaRUB  of  tb< 

1  before  Uia  D«me  t(  tlii 

.     6in«  IhU  Tabic  nl 

rom  (be  8th  or  Vth  maKnilndt  la  Hi 


e  pUc 


I  fotlOK 


I'e'  38"  (1846);  ().| 
8'43-8',8li'>  li' (18U0);  (4.)  S2' 12- »-,  82°  SB'24"(1800).  Ur.  Iliad  nniufci 
that  about  e»v«rHl  Tirinhle  iiars  tome  degttt  of  huineu  ia  perceptible  at  Ibtir 
Binimum.  llnve  Iho?  clouds  rfvolving  round  Ihem  u  plsnetsi?  or  eotatUiJ 
Bttcnd»nt«f  He  aiso  dmw!  aMenlion  lo  the  fact  th»t  tbe  red  colour  ptedoni- 
Mtei  among  Tariablii  XiirB  Bcnfrallj.  Tbe  double  Jtar,  No,  2718  of  SiruTt'i 
CaUiloKuc,  lu  *.  20'  :I4'°  P.  K.  17°  ^4',  <i  lUli^d  by  Sir  John  Hcrecbel  (0  U 
Tirinble.  Cuplain  fwyt]!  (Cclettbl  Cyelo,  i.  274)  luenlu.tiB  aleo  3  Leonii  >Bd 
IS  LeoDla  as  varinbic,  the  former  (torn  B"  to  «,  p  ^  78  dsm  ;  tbe  latler  tram 
6-  lolO".  r^SII'l:!",  bill  Biihout  citing  anj  auihoritj.  Piaiii  eeia  down  (1 
■Dd  U7  A'irgiiiia  aud  38  ILrtulii*  a>  variable  stars. 

Ia  the  case  of  many  of  ibc  stars  in  tbe  preceding  Table,  tbe  T*m- 
tions  of  luslre  are  subject  to  considerable  itregularilies.  Tbua  No. 
13  was  Bcarcoly  visible  fnirn  1C98,  for  the  interval  of  three  jews, 
even  at  ibe  epochs  nbcn  it  ought  to  have  bad  its  greatest  lustn. 
The  extremes  of  luslre  of  No.  9  are  also  very  variable  and  irregular. 
In  general  tbe  v&ria.tionB  of  No.  22  are  so  JDConaide table  ss  to  b« 


PEBIODIC  STARS.  697 

Bcarcelj  perceivable,  but  they  become  suddcDlj  so  great  that  the 
star  wholly  disappears.  The  variatioDs  of  No.  25  were  very  con- 
spicuous from  1836  to  1840^  and  again  in  1849^  being  much  less 
so  in  the  intermediate  time. 

3342.  Ifypotheses  proposed  to  eaplatn  the  phenomena, — Several 
explanations  have  been  proposed  for  these  appearances. 

1.  Sir  W.  Herschcl  considered  that  the  supposition  of  the 
existence  of  spots  on  the  stars  similar  to  the  spots  on  the  sun,  com- 
bined with  the  rotation  of  the  stars  upon  axes,  similar  to  the  rota- 
tion of  the  sun  and  planets,  afforded  so  obvious  and  satisfactory  an 
explanation  of  the  phenomena,  that  no  other  need  be  sought. 

2.  Newton  conjectured  that  the  variation  of  brightness  might  be 
produced  by  comets  falling  into  distant  suns  and  causing  temporary 
conflagrations.  Waiving  any  other  objection  to  this  conjecture,  it 
is  put  aside  by  its  insufficiency  to  explain  the  periodicity  of  the 
phenomena. 

3.  Maupcrtuis  has  suggested  that  some  stars  may  have  the  form 
of  thin  flat  disks,  acquired  either  by  extremely  rapid  rotation  on  an 
axis,  or  other  physical  cause.  The  ring  of  Saturn  affords  an 
example  of  this,  within  the  limits  of  our  own  system,  and  the 
modern  discoveries  in  nebular  astronomy  offer  other  examples  of  a 
like  form.  The  axis  of  rotation  of  such  a  body  might  be  subject  to 
periodical  change  like  the  nutation  of  the  earth's  axis,  so  that  the 
flat  side  of  the  luminous  disk  might  be  present  more  or  less  towards 
the  earth  at  different  times,  and  when  the  edge  is  so  presented,  it 
might  be  too  thin  to  be  visible.  Such  a  succession  of  phenomena 
are  actually  exhibited  in  the  case  of  the  rings  of  Saturn^  though 
proceeding  from  different  causes. 

4.  Mr.  Dunn'*'  has  conjectured  that  a  dense  atmosphere  surround- 
ing the  stars,  in  different  parts  more  or  less  pervious  to  light,  may 
explain  the  phenomena.  This  conjecture,  otherwise  vague,  inde- 
finite, and  improbable,  totally  fiEuls  to  explain  the  periodicity  of  the 
phenomena. 

0.  It  has  been  suggested  that  the  periodical  obscuration  or  total 
disappearance  of  the  star,  may  arise  from  transits  of  the  star  by  its 
attendant  planets.  The  transits  of  Venus  and  Mercury  are  the 
basis  of  this  conjecture. 

The  transits  of  none  of  the  planets  of  the  solar  system,  seen  from 
the  stars,  could  render  the  sun  a  periodic  star.  The  magnitudes, 
even  of  the  largest  of  them,  are  altogether  insufficient  for  such  an 
effect.  To  this  objection  it  has  been  answered  that  planets  of  vastly 
greater  comparative  magnitude  may  revolve  round  other  suns.  But 
if  the  magnitude  of  a  planet  were  sufficient  to  produce  oy  its  transit 
these  considerable  obscurations,  it  must  be  very  little  inferior  to  the 

•  Phil.  Trans.  Vol.  Lll. 
ni.  59 


if  tlio  sun  itself,  or  at  nil  evenlA,  it  n 

auie  proportion  to  the  magnitude  of  the  sun  ;  in  which  csue 

ay  be  objected  tUsit  the  prcdominaacc  of  attraction  neeessarj-  to 

jtaia  the  sun  in  the  centre  of  ita  sfstem  could  Dot  be  secured. 

this  objection  it  ia  ansnered,  that  although  the  planet  may  ba^e 

(jTcat  comparatiTo  magnitude,  it  may  have  a  very  small  compank- 

ve  density,  and  the  gravitating  attraation  depending  on  the  actual 

>s  of  matter,  the  predominance  of  the  solar  mass  maj  be  rendered 

i"'eot  with  the  great  relative  iu.-j,-itude  of  the  planet  by  eu[K 

^•=  ■'ensity  of  the  one  vastly  greater  than  that  of  the  other. 

of  tho  sun  is  much  greater  than  the  density  of  Saturn. 

1  been  suggeBted  that  there  may  be  eystems  in  nhicb  tii« 

jody  U  a  planet  attended  by  a  lesser  sun  revolving  round  It 
joon  revolves  round  the  earth,  and  in  that  ease  the  periodical 
.ui»tion  of  the  sun  may  be  produced  by  its  passage  once  in  oach 
ilution  behind  the  central  planet. 

inch  arc  the  various  conjecturea  which  have  been  proposed  to 
lain  the  periodic  slaxa ;  and  as  they  are  merely  conjcctans, 
jcely  deser\iag  tho  name  of  hypotheses  or  theories,  we  rfall 
ive  them  to  be  taken  for  what  they  are  worth.  ,^^^^| 

IT.   T£MPORABY   STARS. 

Phenomena  in  most  rcspecta  similar  to  those  just  described,  but 
exhibiting  no  recurrence,  repetition,  or  periodicity,  have  been 
observed  in  many  stars.  Thus,  Stars  have  front  time  to  time 
appeared  in  various  parts  of  the  firmament,  have  shone  with  extra- 
ordinary Rplendour  for  a  limited  time,  and  have  then  disappeared 
and  have  never  again  been  observed. 

3343.  Temporary  stars  seen  in  oTicient  timet. — The  first  star  of 
thip  class  which  has  been  recorded,  is  one  observed  by  Hipparchiu, 
123  B.  c,  the  disappearance  of  which  is  said  to  have  led  that  astm- 
DOmer  ta  make  his  celebrated  catjilogue  of  the  fixed  stars ;  a  work 
which  has  proved  in  modern  times  of  great  value  and  interest  Id 
the  S89th  year  of  our  cia,  a  star  blazed  forth  near  a  Aqtiilte,  which 
shone  for  three  weeiiB,  appearing  as  splendid  as  tbe  planet  VeoDS, 
after  which  it  disappeared  and  baa  never  siuce  been  seen.  In  tbe 
years  945,  1264,  and  1572,  brilliant  stars  appeared  between  the 
cooElellatioDS  of  Ceplieut  aod  Cassiopeia.  Ttie  accounts  of  tbe 
posiiions  of  these  objccla  are  obscure  and  uncertain,  but  the  inter- 
vals between  the  epochs  of  Iheir  appearances  being  nearly  equal,  it 
has  been  cotijectured  that  they  were  successive  returns  of  the  same 

Eriodic  star,  the  period  of  which  is  about  300  years,  or  possibly 
If  that  interval. 

The  appearance  of  tbe  star  of  1572  was  very  remarkable,  and 
having  b«en  witneased  by  the  most  eminent  astronomers  of  that  day, 


TEMPORARY  STARS.  099 

the  acconnt  of  it  may  be  considered  to  be  well  entitled  to  oonfideooe. 
TjfcJu)  Brake,  happening  to  be  on  his  return  on  the  evening  of  the 
1 1th  November  from  his  laboratory  to  his  dwelling-house,  found  a 
crowd  of  peasants  gazing  at  a  star  which  he  was  sure  did  not  exist 
half  an  hour  before.  This  was  the  temporary  star  of  1572,  which 
was  then  as  bright  as  the  Dog-star,  and  continued  to  increase  in 
splendour  until  it  surpassed  Jupiter  when  that  planet  is  most  bril- 
liant, and  finally  it  attained  such  a  lustre,  that  it  was  visible  at  mid- 
day. It  began  to  diminish  in  December^  and  altogether  disappeared 
in  March,  1574. 

On  the  10th  October,  1604,  a  splendid  star  suddenly  burst  out 
in  the  constellation  of  SerpentariuSy  which  was  as  bright  as  that  of 
1572.     It  continued  visible  till  October,  1605,  when  it  vanished. 

3344.  Temporary  star  observed  by  Mr.  Mind.  —  A  star  of  the 
fifth  magnitude,  easily  visible  to  the  naked  eye,  was  seen  by  Mr. 
Hind  in  the  constellation  of  Ophiuchus,  on  the  night  of  the  28th 
April,  1848.  From  the  perfect  acquaintance  of  that  observer  with 
the  region  of  the  firmament  in  which  he  saw  it,  he  was  quite  certain 
that,  previous  to  the  5th  April,  no  star  brighter  than  those  of  the 
ninth  magnitude  had  been  there,  nor  is  there  any  star  in  the  cata- 
logues at  all  corresponding  to  that  which  he  saw  there  on  the  28th. 
This  star  continued  to  be  seen  until  the  advance  of  the  season  and 
its  low  altitude  rendered  it  impossible  to  be  observed.  It,  however, 
constantly  diminished  in  lustre  until  it  disappeared^  and  has  not 
Binoe  been  seen. 

8345.  Missing  stars. — To  the  class  of  temporary  stars  may  be 
referred  the  cases  of  numerous  stars  which  have  disappeared  from 
the  firmament.  On  a  careful  examination  of  the  heavens,  and  a 
oomparison  of  the  objects  observed  with  former  catalognes,  and  of 
catalogues  ancient  and  modem  with  each  other,  many  stars  formerly 
known  are  now  ascertained  to  be  missing;  and  although,  as  Sir 
John  Hersehel  observes,  there  is  no  doubt  that  in  many  instances 
these  apparent  losses  have  proceeded  from  mistaken  entries,  yet  it  is 
equally  certain  that  in  numerous  cases  there  can  have  been  no  mis- 
take in  the  observation  or  the  entry,  and  that  the  star  has  really 
existed  at  a  former  epoch,  and  as  certainly  has  since  disappeared. 

When  we  consider  the  vast  length  of  many  of  the  periods  of  as- 
tronomical phenomena,  it  is  far  from  being  improbable  that  these 
phenomena  which  seem  to  be  occasional,  accidental,  and  springhig 
from  the  operation  of  no  regular  physical  causes,  such  as  those  indi- 
cated by  the  class  of  variable  stars  first  considered,  may  after  all  be 
periodic  stars  of  the  same  kind,  whose  appearances  and  disappear- 
ances are  brought  about  by  similar  causes.  All  that  can  be  certainly 
known  respecting  them  is,  that  they  have  appeared  or  disappeared 
once  in  that  brief  period  of  time  within  which  astronomical  obser* 
fmdons  have  been  made  and  recorded.     If  they  be  periodic  atarii 


'  7W  ABTEONOMr. 

tbe  longtli  of  whose  period  exceeds  tli&t  iDterTal,  Uicir  <3aapt 
vaM  only  have  beun  once  exhibited  to  us,  and  after  agee  bftve  ra£l. 
BWaj,  nud  tiiuB  ha*  couvorLed  Uic  future  into  tiie  ph^t,  aMtooaoMt 
may  witness  the  next  occurreuce  <>{  their  phsaee,  aod  discovei  tbil 
to  be  regular,  hAmiouious,  aod  periodte,  which  appears  to  lu  «a- 
dental,  oceasional,  aad  Bnomulous. 

UI.   DOUBLE  BTAItS. 

Whan  tho  stara  are  examined  individually  by  telescopes  of  j 
certain  power,  it  is  fouud  that  many  which  to  the  naked  eye  appMt 
to  be  single  slurs  are  in  reality  two  stars  placed  so  close  KgeAe 
that  thoy  appear  as  one.     Tbe»e  are  called  JouUt  tiart. 

3346.  Rm-nrvhe^  of  Sir  W.  a>ul  Sir  J.  ifevJW.  — A  vaj 
limited  number  of  these  objects  hod  been  disooTered  befon  Ibl 
lelesoope  had  received  the  vast  occeseinn  of  power  which  wu  ptm 
to  il  by  the  labour  and  genius  of  Sir  William  Hcrachel.  That  i^ 
tronomer  observed  and  catalogued  600  double  stars  ;  and  Bali»qwnl ' 
ohaervers,  among  whom  bis  son,  Sir  John  ITcrsehel,  holds  the  fure- 
most  place,  have  augmented  the  number  to  tiOOO. 

3347.  Stars  aptkally  douUe. — The  close  apparent  justa-posi^ 
of  two  Btars  on  the  firmament  is  a  phenomenon  which  might  be 
easily  eiplaincd,  and  which  could  create  no  surprise.  Snch  ta 
occurreuea  would  be  produced  by  the  accidental  circumstances  of 
the  lines  of  direction  of  the  two  atar^  as  seen  from  the  earth,  fann- 
ing a  very  small  angle,  in  which  case,  akhougb  the  two  stars  might 
in  reality  be  as  far  removed  from  each  other  as  any  stars  in  llu 
heavens,  thoy  would  neverthelcsa  appear  close  together.  ITiO  fg. 
874,  will  render  this  easily  understood.     Let  a  and  b  be  the  t*D 


Fig.  8TJ. 

Btars  Bocn  from  c.  The  star  a  will  be  seen  relatively  to  b,  is  if  it 
were  at  rt,  and  the  two  objects  vrill  seem  to  be  in  close  juilaposi- 
tion;  and  if  tho  angle  under  the  lines  ca  and  c(i  be  less  than  tho 
sum  of  the  apparent  scmi-diaraeters  of  (he  stars,  they  would  actuaHj 
appear  to  touch. 

S34S.    TJii't   siijijiosllion  tuit  genf rally  oiWisiiUe.  —  If  such  ob- 
jects were  few  inBaia\jci,\\ia^iio4aol  ^li'^imsL^'ios.'isi.Tiiv^'Owt, 


DOUBLE  STABS.  701 

admitted ;  and  sach  may,  in  fact,  be  the  cause  of  the  phenomenon 
in  Bome  instances.  The  chances  against  such  proximity  of  the  lines 
of  direction  are  howcTer  so  great  as  to  be  utterly  incompatible  with 
the  vast  number  of  double  stars  that  have  been  discovered,  even 
were  there  not,  as  there  is,  other  conclusive  proof  that  this  proz- 
imi^  and  companionship  is  neither  accidental  nor  merely  apparent, 
but  that  the  connection  is  real,  and  that  the  objects  are  united  by  a 
physical  bond  analogous  to  that  which  attaches  the  planets  to  the 
san. 

But  apart  from  the  proo&  of  real  proximity  which  exist  respect- 
ing many  of  the  double  stars,  and  which  will  presently  be  explained, 
it  has  l>een  shown  that  the  probability  against  mere  optical  juxta- 
position, such  as  that  described  above,  is  almost  infinite.  Professor 
Stmve  has  shown  that,  taking  the  number  of  stars  whose  existence 
has  been  ascertained  by  observation  down  to  the  7th  magnitude 
inclusive,  and  supposing  them  to  be  scattered  fortuitously  over  the 
entire  firmament,  the  chances  against  any  two  of  them  having  a 
position  so  close  to  each  other  as  4"  would  be  9570  to  1.  But 
when  this  calculation  was  made,  considerably  more  than  100  cases 
of  such  duple  juxtaposition  were  ascertained  to  exist.  The 
■ame  astronomer  also  calculated  that  the  chances  affaiust  a  third 
star  &lling  within  32"  of  the  first  two  would  be  173524  to  one ; 
yet  the  firmament  presents  at  least  four  such  triple  combina- 
tions. 

Among  the  most  striking  examples  of  double  stars  may  be  men- 
tioned the  bright  star  Castor^  which,  when  sufficiently  magnified, 
IB  proved  to  consist  of  two  stars  between  the  third  and  fourth  mag- 
niUides,  within  five  seconds  of  each  other.  There  are  many,  how- 
ever, which  are  separated  by  intervals  less  than  one  second ;  such 
ms  f  Arietu^  AUas  Fleiadum,  y  Q>r(mas,  fj  and  {*  JSkradis,  and  t  and 
^  Ophitichi, 

3349.  Argument  against  mere  optical  double  itars  derived  from 
their  proper  motion. — Another  argument  against  the  supposition  of 
mere  fortuitous  optical  juxtaposition,  unattended  by  any  physical 
connection,  is  derived  from  a  circumstance  which  will  be  fully  ex- 
plained hereafter.  Certain  stars  have  been  ascertained  to  have  a 
proper  motion^  that  is,  a  motion  exclusively  belonging  to  each  indi- 
vidual star,  in  which  the  stars  around  it  do  not  participate.  Now, 
aome  of  the  double  stars  have  such  a  motion.  If  one  individual  of 
the  pair  were  afiected  by  a  proper  motion,  in  which  the  other  does 
not  participate,  their  separation  at  some  subsequent  epoch  would 
become  inevitable,  since  one  would  necessarily  move  away  from  the 
other.  Now,  do  such  separation  has  in  any  instance  been  witocsscd. 
It  follows,  therefore,  that  the  proper  motion  of  one  equally  affects 
the  other,  and,  consequently,  that  their  juxtaposition  is  real  and  not 
merely  optical. 

59* 


ASTROHOMT, 

Struve'i  classification  a/ douhle  gtart.  —  The  a3rEtemalio 
1  of  double  Btara,  and  their  reduation  lo  s  catnli^ae  with 
luiu  deECriptioDS,  omiiicnceil  by  Sir  W.  Hersuhr],  baa  ht-aa 
lUed  with  great  activity  and  iaccesa  by  Sir  J.  Har^chel,  Sir 
>uth,  and  I^fessor  Strave,  so  that  the  number  of  these  objects 
r  known,  na  to  cbaraolcr  sad  posidoo,  amounts  to  acToral  than- 
i,  the  indiTidua.la  of  each  pair  being  lesd  than  32"  unndcr. 
ij  have  been  claased  by  Professor  Struvo  according  to  their  dis- 
hes aannder,  tbo  firat  class  being  separated  by  a  distance  not 
ine  1",  tbo  aecond  between  1    and  2",  the  third  between  2" 
,  ike  fourth  between  4"  and  S",  the  Gfih  between  S"  and  1^°, 
.u^th  betweoa  12"  aod  IG",  the  eeventb  between  16"  and  24", 
J  ligUlh  between  24"  and  32". 

1.  Stleciion  u/ double  tiart. — The  double  stars  in  the  follow- 

<Bulo  have  been  selected  by  Sir  J.  Hcrschel  from  Strnve's 
logue,  as  Tcuiarlcablo  exainplea  of  each  class  well  ndapted  for 
rvations  by  amatearB,  who  may  be  disposed  to  try  by  them  the 
may  of  telescopes.      (iSte  nextpar/e.') 

52.  Coloured  dotihU  elan.  —  One  of  the  characters  obserred 
•ug  the  doable  Btsrs  \a  the  frequent  ooonrrence  of  stan  of  diff«- 
colours  found  together.  Sometimes  these  colours  are  Maple- 
meolary  (1059) ;  andwiieu  tiiia  occura,  it  la  passible  that  the  faiuter 
of  the  two  may  bo  a  white  star,  whicb  appears  to  have  the  Ofilour 
coin  pic  mentary  to  tliat  of  tbe  more  LrJllJant,  in  coQeequcDce  cf  a 
well- understood  law  of  vision,  by  which  the  retina  being  bighly 
excited  by  light  of  a  particular  colour  is  rendered  inseoaibte  U 
le&a  intense  light  of  tbe  same  coloar,  so  that  tbe  complement  of  tbe 
whole  light  of  the  fainter  star  finds  the  retina  more  sensible  Ihsa 
that  part  which  is  identical  in  colour  with  the  brighter  star,  and 
the  impression  of  tie  complemcDtary  colour  acoordingly  prevails. 
In  many  cases,  however,  the  difference  of  colour  of  the  two  atara 
is  real. 

When  the  colours  are  coin  piemen  lary,  tbe  moro  brilliant  alar  ij 
generally  of  a  bright  red  or  orange  colour,  the  amaller  appearing 
blueish  or  greenish.  The  double  stars  i  Caucri  and  y  Andrumachx 
are  examples  of  this.  According  t«  Sir  J.  Hci^chol,  insulated  stan 
of  a  red  colour,  some  almost  blood-red,  occur  in  many  parta  of  the 
henvenij ;  but  no  example  has  been  met  with  of  a  decidedly  green  or 
blue  star  unassucialed  with  a  much  brighter  conipauioa. 

3il5.5.  TripU  and  other  multiple  stars. — When  telescopes  of  the 
icreatest  efficiency  arc  directed  upon  some  stars,  which  to  more  ordi- 
nary instruments  appear  only  double,  they  prove  to  consi.=t  of  three 
or  more  stars.  In  some  cases  one  of  tbe  two  companions  only  is 
double,  so  that  the  entire  combination  is  triple.  In  others,  both 
are  double,  the  whole  being,  therefore,  a  quadruple  star.  An  ej- 
am|il(,  of  thia  latter  class  is  presented  by  the  star  i  hyrto.     Some- 


DOUBLE  STABa 


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A8TE0N0MT. 


times  the  third  slar  is  much  gmaller  than  tbe  principal  ones,  for 
esamplc,  in  the  cases  of  C  Cancri,  i  Scorpii,  11  Monocesos,  and  12 
Ljnois.  In  others,  m  in  e  Orioais,  tUe  four  component  stare  Me 
all  eoni:picuous. 

(3354.  AltcmpU  to  discover  the  ttcllar  parallax  bj/  double  tiart. 
— -^  When  the  attention  of  astrononiera  waa  first  attnctsd  to  double 
■tars,  it  was  thought  they  would  afford  a  most  proim»ng  means  of 
^^^^^^^^  determining  the  annual  paraUai,  and  thereby  dis- 
^^^^^^^^  covering  the  distance  of  the  stars.  If  we  euppof« 
^H^^H^I  the  two  iodiTiduals  composing  a  double  star,  being 
^^^^^^H  situate  very  neariy  iu  the  same  direction  as  seen 
^^^^^^^H  from  tbe  earth,  to  be  at  very  different  dist3Dce«, 
^^^^^^^H  it  might  be  expected  that  their  apparent  rclativs 
^^^^^^^H  position  would  vary  at  different  seasons  of  the 
^^^^^^^^  year,  by  reasoa  of  the  chaoge  of  positioD  of  tbe 
^^^^^^1    earth. 

^^^^^^^H        Let  A  and  B,  fi'j.  875,  represent  the  two  in- 

^^^I^^^H    dividuala  composing  a  double  star.     Let  c  and  o 

^^^^^^^H    represent  two  positiona  of  the  earth  iu  i\n  annoal 

^^^^^^^^^^1    orbit,  separated  by  an  interval  of  balf  a  year,  aud 

^B^^^^^^^^l    placed  ^erefore  on  opposite  sides  of  the  sun  it. 

^^^^^^^H     When  viewed   from  c,  the  star  B  will   be   to  the 

^^^^^^^^H     left  of  the  star  a  ;  and  wheu   viewed   from   d,  it 

^^^^^^^H    will  be  to  tbe  right  of  it.     During  the  iotenae- 

^^^^^^^H     diatc  six  monlha  the  relative  change  of  position 

^^^^^^^H    would  gradually   be  effected,  and  tho    one  star 

^^^^^^^^"     would    thus   appwu   oilher    to   revolra    aoDuatty 

Fig.  S7S.        round  the  other,  or  would  oscillate  semi-annually 

from  side  to  side  of  the  other.     Tbe  extent  of  its 

play  compared  with  tbe  diameter  c  D  of  the  earth's  orbit,  would 

mpply  the  data  necessary  to  determine  the  proportion  which  the 

distance  of  the  stars  would  bear  to  that  diameter. 

The  great  problem  of  the  stellar  parallas  seemed  thus  to  be  re- 
duced to  the  measurement  of  the  small  iuterval  between  the  indi- 
viduals of  double  stars;  and  it  Lappcocd  fortunately,  that  tbe 
micrometers  used  in  astronomical  iastruments  were  capable  of 
measuring  these  minute  angles  with  much  greater  relative  accuracy 
than  could  be  attained  in  the  observations  on  greater  angular  dis- 
tances. To  iheso  advantages  were  added  the  absence  of  all  pos- 
sible errors  arising  from  refraction,  errors  iocidenlal  to  tho  gradua- 
tion of  instruments,  from  uucertainty  of  levels  and  plumb-]iDe!>, 
from  al!  estimations  of  aberration  and  precession ;  in  a  word,  from 
all  effects  which,  equally  affecting  both  the  individual  stars  observed, 
could  not  interfere  with  the  results  of  the  observations  whatever 
they  might  be. 

8355.  Observations  of  Sir  W.  Serschel.  —  These  considerations 
raised  groat  liopcs  &'moTi^aa\,t<iTLtna«M,  that  tbe  means  were  in  tbcir 


DOUBLE  STARS.  705 

hands  to  resolve  finally  the  great  problem  of  the  stellar  parallaz, 
and  Sir  William  Herschcl  accordingly  engaged,  witb  all  his  charac- 
teristic ardour  and  sagacity,  in  an  extensive  series  of  observations 
on  the  numerous  double  stars,  for  the  original  discovery  of  which 
science  was  already  so  deeply  indebted  to  his  labours.  He  had 
not,  however,  proceeded  far  in  his  researches,  when  phenomena  un- 
folded themselves  before  him,  indicating  a  discovery  of  a  much 
higher  order  and  interest  than  that  of  the  parallax  which  he  sought. 
He  found  that  the  relative  position  of  the  individuals  of  many  of 
the  double  stars  which  ho  examined  were  subject  to  a  change,  but 
that  the  period  of  this  change  had  no  relation  to  the  pefiod  of  the 
earth's  motion.  It  is  evident  that  whatever  appearances  can  pro- 
ceed from  the  earth's  annual  motion,  must  be  not  only  periodic  and 
regular,  but  must  pass  annually  through  the  same  series  of  phases, 
always  showing  the  same  phase  on  each  return  of  the  same  epoch 
of  the  sidereal  year.  In  the  changes  of  position  which  Sir  William 
Herschel  observed  in  the  double  stars,  no  such  series  of  phases  pre- 
sented themselves.  Periods,  it  is  true,  were  soon  developed;  but 
these  periods  were  regulated  by  intervals  which  neither  agreed  ?rith 
each  other  nor  with  the  earth's  annual  motion. 

3356.  HU  discovery  of  binary  stars.  —  Some  other  explanation 
of  the  phenomena  must,  therefore,  be  sought  for;  and  the  illus- 
trious observer  soon  arrived  at  the  conclusion,  that  these  apparent 
changes  of  position  were  due  to  real  motions  in  the  stars  themselves ; 
that  these  stars,  in  fact,  moved  in  proper  orbits  in  the  same  manner 
as  the  planets  moved  around  the  sun.  The  slowness  of  the  suo- 
eession  of  changes  which  were  observed,  rendered  it  necessary  to 
watch  their  progress  for  a  long  period  of  time  before  their  motions 
could  be  certainly  or  accurately  known ;  and  accordingly,  although 
these  researches  were  commenced  in  1778,  it  was  not  until  the  year 
1803  that  the  observer  had  collected  data  sufficient  to  justify  any 
positive  conclusion  respecting  their  orbital  motions.  In  that  and 
the  following  year.  Sir  William  Herschel  announced  to  the  Koyal 
Society,  in  two  memorable  papers  read  before  that  body,  that  there 
exist  sidereal  systems  consisting  of  two  stars  revolving  about  each 
other  in  regular  orbits,  and  constituting  what  he  called  binary  stars, 
to  distinguish  them  from  double  stars,  generally  so  called,  in  which 
no  such  periodic  change  of  position  is  discoverable.  Both  the  indi- 
viduals of  a  binary  star  are  at  the  same  distance  from  the  eye  in  the 
same  sense  in  which  the  planet  Uranus  and  its  attendant  satellites 
are  said  to  be  at  the  same  distance. 

More  recent  observation  has  fully  confirmed  these  remarkable 
discoveries.  In  1841,  Madler  published  a  catalogue  of  upwards 
of  100  stars  of  this  class,  and  every  year  augments  their  number. 
These  stars  require  the  best  telescopes  for  their  observation,  being 
generally  so  close  as  to  render  the  use  of  very  high  magnifying 
powers  indispensable. 


I 


7W  ASTROSOMT. 

3SST.  -Extension  of  lfi«  ?«»  of  gritmtatxim  to  the  ^art,  —  TIis 
noin^Dt  the  revolution  of  one  star  round  another  was  aaoertniopd, 
Ibc  idnu  of  the  poaelblc  exIensioD  of  the  groat  principle  of  grariU- 
tion  to  lliese  remote  regions  of  the  univeree  natnrally  Bi]^gest«J 
itself.  NewtoD  has  proved  io  his  Princlpia,  Ibat  if  a  bodj'  reTolve 
ID  HD  ellipee  bj  an  attractive  force  directed  to  the  focus,  tLat  fotce 
will  vary  according  to  the  law  which  charact«riseB  gravitatioo. 
Thus  an  elliptical  orbit  becnme  a.  leal  of  the  presence  and  sway  of 
the  law  of  gravitation.  If,  then,  it  coulil  bo  ascertained  that  ibe 
orbits  of  the  double  stars  were  ellipee!),  wc  should  at  once  airiTe  it 
the  (act  that  the  law  of  which  thediscovery  conferred  such  celebritj 
on  the  name  of  Newton,  is  not  confined  to  the  solar  system,  bal 
prevails  throughout  the  unirersc- 

3S58.  Orbit  of  aar  arnvnil  Har  etHpli'-. —  The  first  distisrt 
BjBtem  of  calculation  by  which  the  true  elliptic  element*  of  tte 
orbit  of  a.  binary  star  were  ascertained,  woa  supplied  ia  1$30,  bj  M. 
Savcry,  wbo  showed  that  the  motion  of  one  of  the  most  remarkable 
rf  these  stars  (i  C'rMtc  majonV),  indicated  an  elliptio  Otbit  described 
in  581  jean.  Professor  Enck^,  by  another  process,  arrived  at  the 
&6t  that  the  star  CO  Ophmchi  moved  in  an  ellipse  villi  s  period  of 
74  yeara.  Several  oiher  orbits  were  aseerbined  and  compnled  bj 
Sir  John  Horschel,  MM.  Madler,  Hind,  Smjlh.  and  others. 

The  following  Table  is  given  by  Sir  J.  Uerschel,  as  containing  tin 
principal  results  of  obeervalion  in  this  part  of  stellar  ostroaoniTin 
to  1850. 


. 

1. 

\ 

» 

3 

i 

■| 

■'TSESf*'' 

1 

4> 

1.          HrraL 

»=^ 

'^ 

WM 

MS 

S29-M 

Kadte     * 

^ 

S       C         ^ 

■O 

t       i     r™     n, 

t  -ifla 

K      2G 

^^^^B 

Stffl 

W*(»l 

I     rsoas                  1  WW        a 

Ji  j- 

B       f  BwCb            WHO  \iy     17     869  69 

00  SB 

d  JSIL 

s.     !cr«»                         -w     a 

0      y     nbit       i-srn  1                  u 

^jon. 

B-  »0 

H-»- 

sse  ~i            2- 

»i 

SIM    J8SS   fil 

WUim. 

£9         11  W     S^SW 

HM4S 

Oil           sa     B(9   W 

Ubv 

u    Sc 

■1    33   1     H         -OOO 

»*) 

DO0BLK  STARS.  707 

Tha  Blemeota  Nos.  I.  2,  S,  4,  o,  G,  S,  a,  7,  11  b,  12,  s,  are  eilracted  from 
M.  tISdIer's  Bjnoptio  riew  of  tbe  hiBtoiy  of  double  sbirs,  in  toI.  ii.  of  the 
Vorpat  ObMrrstions :  4  b,  from  tha  Connoiis.  des  Temps,  1830 ;  4  b,  6  b, 
aod  11  a,  from  vol.  t.  Trans.  Aetroa.  Soc.  Loud, :  6  a,  from  Berlin  Epbe- 
neru,  18»2;  >'o.  8,  from  Trans.  Aatron.  Sac.  tol.  vi. :  Ko.  0,  II  a,  12  b, 
sod  13  from  Kolicue  of  llio  Aatronomical  Socielj,  vol.  vii.  p.  22,  and  riii. 
p.  I5i<.  nnd  No.  10  fron  Sir  Jobn  Herechei's  "  Kesulta  of  Astrononiical  Ob- 
MTTstiont,  &c.,  Ht  tbe  Cupe  of  Qood  Hope."  p.  297.  The  £  prefixed  to  No. 
7  dcDotea  the  niTmber  of  the  star  in  M.  Slrure'e  Dorpat  Catalogue  (Cuta- 
\og\i*  Novus  lilellurum  Uuplicium,  &o.,  Dorpat,  1827),  irhich  contaiiis  (he 
places  for  l>:l:>r.  otltllLl  of  these  objects. 

The  "  position  of  the  Dode  "  in  col.  4  eipresses  tbe  angle  of  pasition  of 
the  line  (if  inlersectiun  of  the  plane  of  the  orbit,  vith  the  plane  of  the 
beuvcnH  on  nliich  il  is  Been  projected.  The  "  inclinatioD  "  in  col.  C  is  the 
incliniitiuH  of  these  two  planes  to  one  another.  Col.  5  shows  the  angle 
actually  included  in  Ihr  plane  of  the  orbil,  hvtimnn  the  line  of  nodes  Idcfincd 
as  aboTcJ  anil  the  line  of  apsides.  Tbe  cletoents  assigned  in  this  table  to 
•  Lcoois.  {  Bootis,  and  Castor  must  bo  considered  as  very  doubtftil,  and  the 
aame  may  perhaps  be  said  of  thoee  ascribed  to  )i  2  Bootis,  which  rest  on  bo 
mall  an  arc  of  the  orbit,  and  that  too  imperfectly  obserred,  to  afford  a 
•eeore  basia  of  caloulatioo. 

3359.  Remarkable  eaie  off 
Tirginii, — The  moat  remark- 
ablo  of  these,  according  to  Sir 
John  Herschel,  is  y  Virffinii; 
not  otilj  on  BccouDt  of  tfae 
length  of  its  period,  bnt  by 
reason  alao  of  the  great  dimi- 
nntjon  of  apparent  distance  sod 
rapid  increase  of  aogular  motioa 
about  each  other,  of  the  iodi- 
Tiduals  composing  it.  It  ia  & 
bright  star  of  the  fourth  mag- 
nitude, and  its  component  Blara 
are  almost  exactly  eqtial.  It 
has  been  known  to  consist  of 
two  Btais  since  the  begianing 
of  the  eighteenth  century,  their 
distance  being  then  between 
six  and  seven  seconds;  so  that 
any  tolerably  good  telescope 
would  resolve  it.  Since  that 
time  they  have  been  constantly 
approaching,  and  are  at  present 
hardly  more  than  a  single  second 
asunder;  bo  that  no  telescope 
that  is  not  of  very  superior 
quality,  ia  competent  to  shew 
them  otherwise  than  as  a  single 


ASTEOSOMT. 

iBt  lengtbcned  io  one  iJircction,     It  fordmatcljr  Lnppena 

..ey,  in   1718,  notJced  and  recofded,  in  tUe  margin  of  one 

ii  obiuirvatioD-bookG,  the  apparent  direction  of  tbeir  line  of 
ioD  as  being  parallel  to  tbot  of  two  remarkable  stars  a  and  t  of 
tme  eoDstclktiou,  as  eeea  hj  the  nalied  eye.  The;  are  entered 
IS  distinct  aims  id  Majer's  cataloguo ;  and  tliis  affords  bIm 
.nx  muaes  of  recovering  tbeir  relative  silualiun  at  tbe  date  of  bit 
nlioDB,  wbicb  were  made  about  the  year  17S6.  Without  p»r- 
ilariaing  individual  measurements,  nbicli  will  be  found  in  ibfir 
icr  repositoricB,  it  will  sufBce  to  reniurk,  that  tbeir  whole  eetivt 
.prescD'ed  bj  an  ellipse. 

3^C0.    Singular  phruomeHa  proiJiicai  irff  one  lol'tr  tjfulrm  Ona 
vinnff  round  anothrr.  — To  understand  the  curions  efFcels  wbKh 
it  attend  the  eape  of  a  It^sser  snn  with  its  uttcndant   planeli 
jlvioff  round  »  greater,  let  the  larger  snn,  Ji;/.   876,   with  ill 
nets  DC  represented  at  s,  in  the  foeits  of  an  ellipse,  in  whieb  the 
<«r  sun   accompanied  by  !(g  plauets  moveii.     At  A  ibis  laller  ran 
in  its  peribeliiin,  and  nearest  to  the  (rreatcr  sun  s.     Moving  in  iu 
imlical  course  to  B,  it  is  at  its  mea:     istanoe  from  the  emt  a.    Al 
t  is  at  aphelion,  or  its  most  distant  pc     i,  and  finally  returns  through 
O  10  ila  perihelion  A.     The  sun  B,  beeaiiso  of  it'  vast  disfanpe  from 
the  system  a  would  appear  to  tbe  inhabitants  of  the  planets  of  the 
system  a  much  smaller  than  tlieir  proper  sun ;  but,  on  the  other 
hand.  Ibis  effect  of  distance  would  be  to  a  certain   eitent  compen- 
sated by  its  greatly  superior  magnitude;  for  analogy  justifies  tbe 
inference  tlmt  the  sun  s  is  greater  than  tbe  sun  a  in  a  proportion 
equal  to  that  of  tbe  magnitude  of  our  sun  to  one  of  the  planets. 
Tbe  inhabitants  of  the  planets  of  the  system  A  will  then  behold  tbe 
ppeclaclc  nf  lico  suns  in  their  firmament.      The  annual  motion  rf 
one  of  these  suns  will  be  determined  by  the  motion  of  the  planet 
itself  in  its  orbit,  but  that  of  tbe  other  and  more  distant  sun  will  be 
determined  by  the  period  of  the  lesser  sun  around  the  greater  in  the 
orbit  A  B  D  c.     The  rotation  of  the  planets  on  their  axes  will  prodnoe 
two  days  of  eigual  length,  but  not  commencing  nor  ending  simulta- 
neously.    There  will  bo  in  general  tico  tunn'sfs  and  lino  tumtttl 
When  a  planet  is  situate  in  the  part  of  its  orbit  between  the  two 
Buns,  there  will  be  do  night.     The  two  buds  will  then  be  placed 
exactly  as  our  sun  and  moon  are  placed  when  the  moon  is  full. 
When  the  one  sun  sets,  the  other  will  rise;  and  when  the  one  rises, 
the  other  will  set.     There  will  bo,  therefore,  continual  day.     On  the 
other  hand,  when  a  planet  is  at  such  a  part  of  its  orbit  Chat  both 
suns  lie  iu  nearly  the  same  direction  as  seen  from  it,  both  suns  will 
rise  and  both  will  set  together.     There  will  then  be  the  ordinary 
alternation  of  day  and  night  as  on  the  earth,  but  the  day  will  have 
more  than  the  usuol  splendour,  being  enlightened  by  two  suoa. 
Ic  all  intermediate  scusons  (be  two  suns  will  rise  and  set  at  dif- 


DOUBLE  STARS.  700 

ferent  times.  DariDg  a  part  of  the  day  both  will  be  seen  at  once  in 
the  heaTens,  occupjing  different  places,  and  reaching  the  meridian 
at  different  times.  There  will  be  two  noons.  In  the  morning  for 
some  time,  more  or  less,  according  to  the  season  of  the  year,  one 
sun  only  will  be  apparent,  and  in  like  manner,  in  the  evening,  the 
mm  which  first  rose  will  be  the  first  to  set,  leaving  the  dominion  of 
the  heavens  to  its  splendid  companion. 

The  diurnal  and  annual  phenomena  incidental  to  the  planets 
attendinff  the  central  sun  s  will  not  be  materially  different,  except 
that  to  them  the  two  suns  will  have  extremely  different  magnitudes, 
and  will  afford  proportionally  different  degrees  of  light.  The  lesser 
sun  will  appear  much  smaller,  both  on  account  of  its  really  inferior 
magnitude  and  its  vastly  greater  distance.  The  two  days,  therefore, 
when  they  occur,  will  be  of  very  different  splendour,  one  being  pro- 
bably as  much  brighter  than  the  other  as  the  light  of  noonday  is  to 
that  of  full  moonlight,  or  to  that  of  the  momins  or  evening  twilight. 

But  these  singular  vicissitudes  of  light  will  become  still  more 
flrtriking,  when  the  two  suns  diffuse  light  of  different  colours.  Let 
118  examine  the  very  common  case  of  the  combination  of  a  cnmsan 
with  a  blue  sun.  In  general,  they  will  rise  at  different  times. 
When  the  blue  sun  rises,  it  will  for  a  time  preside  alone  in  the 
heavens,  diffusing  a  blue  morning.  Its  crimson  companion,  how- 
ever, soon  appearing,  the  lights  of  both  being  blended,  a  white  day 
will  follow.  As  evening  approaches,  and  the  two  orbs  descend 
toward  the  western  horizon,  the  blue  sun  will  first  set,  leaving  the 
orimaon  one  alone  in  the  heavens.  Thus  a  ruddy  evening  closes 
this  curious  succession  of  varying  lights.  As  the  year  rolls  on, 
these  changes  will  be  varied  in  every  conceivable  manner.  At  those 
seasons  when  the  suns  are  on  opposite  sides  of  the  planet,  crimson 
and  blue  days  will  alternate,  without  any  intervening  night;  and  at 
the  intermediate  epfx^hs  all  the  various  intervals  of  rising  and  setting 
of  the  two  suns  will  be  exhibited. 

8361.  Magnitudes  of  the  stellar  orbits. — It  is  evident  that  in  any 
case  in  which  the  parallax  of  a  binary  star,  and  conscqucutly  its 
distance  from  eur  system,  has  been  or  may  be  discovered,  the  mag- 
nitude of  the  orbit  of  one  described  round  the  other  can  be  deter- 
mined with  a  precision  and  certainty  proportional  to  those  with 
which  the  parallax  is  known.  For,  in  that  case,  the  linear  value 
of  I"  at  the  star  will  be  found  by  dividing  the  earth's  distance  from 
the  sun  by  the  parallax  expressed  in  seconds. 

The  binary  stars  61  C^f/ni  and  a  Centauri  supply  examples 
of  the  application  of  this  principle.  The  parallax  of  these  stars 
baa  been  ascertained  (2605).  That  of  61  Cygni  is  0348,  and  the 
semi-axis  of  the  elliptic  orbit  of  one  star  round  the  other  is  15*5''. 
The  semi-diameter  of  the  earth's  orbit  being  d,  therefore,  the  linear 
ui.  60 


A5TR0S0MT. 


therefore,  tbat  the  Bcmi-axia  of  tbe  Dibit  ie  gnnlcr  ihia 

tune's  orbit  id  tbe  intia  of  3  to  2. 

Kobteniled  by  t1  mi-dxis  of  tbe  eltiptie  orbtt  ef 

s  not  so  cprtain]  q,  bat  is  taken  to  be  thnt 

purallax  of  tbia  t  ing  0-913",  we  Aaali  tbta 


=  13  14  D. 


12 
"  =  ''^0:913 
of  the  stellar  orbit  would,  tbercfore,  be  about  oa»hlf 
_-_  .je  orbit  of  Saturn. 

Jtauei  of  binary  itan  determined  by  (hmr  parallax  W 
jnrrtoa. — Since  by  (2624J  the  relation  of  the  semi-ajds  of  the  orbiO 
aad  the  periodic  litnea  determines  the  relative  masses  of  the  centnl 
bo-Jios,  wo  arc  cnabliyl  to  compare  tbe  mass  of  (he  ceoln!  Etar  of  a 
binary  system  with  that  of  the  sun,  in  all  cases  in  which  the  real 
Bcui-azis  of  the  orbit  and  the  periodic  time  are  known.  Thus,  let 
U'  be  the  mass  of  the  central  etar,  a'  tbe  scmi-azis  of  the  orbit,  and 
p"  the  periodic  time,  and  let  H  be  tbe  mass  of  the  son,  a  the  teai- 
axis  of  the  earth's  orbit,  and  P  tbe  earth's  period,  and  we  shill 

m'  :  M  r :  -=  :  -;. 
p™    P* 

The  periods  of  the  binary  stars  of  known  parallax  have  not  been 
certainly  determined ;  bjt  if  it  be  assumed,  aa  It  may  probably  br, 
that  the  period  of  (il  Cygni  is  about  500  times  that  of  ibe  earth,  ve 
eh  all  have 

44-54»    , 

and,  therefore, 

m'  =  0  3533  m; 
eo  that  the  mass  of  the  central  star  would  be  a  Uttle  inor«  thin 
one-third  of  that  of  the  aun. 


IV.   PBOrER  MOTION  OF  THE  STAR,"!, 

3363.  In  common  parlance  the  stars  are  said  to  be_^t«?.     Tbey 
ha^o  receWed  l^iia  efi\v\\ev  \!s  S\suii^\^  ^.W^sl.  ^i-wo.  the  planeli 

the   SUD,   and  ftlC   mwni,  iA\  ol  ■wV«;V  tuo^auS^^  tvxifbiGt^  <iaa>!^ 


PROPER  MOTION  OF  THE  STARS.  711 

of  apparent  position  on  the  surface  of  the  heavens.  The  stars,  on 
the  contrary,  so  far  as  the  powers  of  the  eye  unaided  hy  art  can 
discover,  never  change  their  relative  position  in  the  firmament,  which 
seems  to  be  carried  round  us  by  the  diurnal  motion  of  the  sphere, 
just  as  if  the  stars  were  attached  to  it^  and  merely  shared  in  its 
apparent  motion. 

But  the  stars,  though  subject  to  no  motion  perceptible  to  the 
naked  eye,  are  not  absolutely  fixed.  When  the  place  of  a  star  on 
the  heavens  is  exactly  observed  by  means  of  good  astronomical  in- 
struments, it  is  found  to  be  subject  to  a  change  from  month  to 
month  and  from  year  to  year,  small  indeed,  but  still  easily  observed 
and  certainly  ascertained. 

3364.  The  sun  not  a  fixed  centre,  —  It  has  been  demonstrated 
by  Laplace,  that  a  system  of  bodies,  such  as  the  solar  system,  placed 
in  space  and  submitted  to  no  other  continued  force  except  the  recip- 
rocal attractions  of  the  bodies  which  compose  it,  must  either  have 
its  common  centre  of  gravity  stationary  or  in  a  state  of  uniform 
rectilinear  motion. 

3365.  Effect  of  the  nurHs  sitpposed  motion  on  the  apparent  places 
of  the  stars. — The  chances  against  the  conditions  which  would  render 
the  sun  stationary,  compared  with  those  which  would  give  it  a  mo- 
tion in  some  direction  with  some  velocity,  are  so  numerous  that  we 
may  pronounce  it  to  be  morally  certain  that  our  system  is  in  motion 
in  some  determinate  direction  through  the  universe.  Now,  if  we 
suppose  the  sun  attended  by  the  planets  to  be  thus  moved  through 
space  in  any  direction,  an  observer  placed  on  the  earth  would  see  the 
effects  of  such  a  motion,  as  a  spectator  in  a  steamboat  moving  on  a 
river  would  perceive  his  progressive  motion  on  the  stream  oy  an 
apparent  motion  of  the  banks  in  a  contrary  direction.  The  observer 
on  the  earth  would,  therefore,  detect  such  a  motion  of  the  solar 
svstem  through  space  by  the  apparent  motion  in  the  contrary  direc- 
tion with  which  the  stars  would  be  affected. 

Such  a  motion  of  the  solar  system  would  affect  different  stars  dif- 
ferently. All  would,  it  is  true,  appear  to  be  affected  by  a  contrary 
motion,  but  all  would  not  be  equally  affected.  The  nearest  would 
appear  to  have  the  most  perceptible  motion,  the  more  remote  would 
be  affected  in  a  less  degree,  and  some  mi^ht,  from  their  extreme 
distance,  be  so  slightly  affected  as  not  to  exhibit  any  apparent  change 
of  place,  even  when  examined  with  the  most  delicate  instruments. 
To  whatever  degree  each  star  might  be  affected,  all  the  changes  of 
position  would,  however,  apparently  take  place  in  the  same  direction. 

The  apparent  effects  would  also  be  exhibited  in  another  manner. 
The  stars  in  that  region  of  the  universe  toward  which  the  motion 
of  the  system  is  directed,  would  appear  to  recede  from  each  other. 
The  spaces  which  separate  them  would  seem  to  be  gradually  aug- 
mented, while,  on  the  contrary,  the  stars  in  the  opposite  quartet 


TJff  ASTRONOMY. 

wnnid  socm  bi  be  croirdcd  more  cloeel^  together,  Oit  distaOMI  be- 
tween star  and  star  being  gradually  diuinUbLil.  This  will  be  ir — 
clearly  comprehended  ^y  Ji-j-  877. 


Fig.  8TT, 

Let  the  line  S  b'  rcprceent  the  direction  of  the  motioD  of  the 

li  tfBteni,  and  let  s  and  s'  rrpresctit  its  pofitions  at  any  two  epochs. 

l-j[t  B,  the  stars  ABO  would  be  separated  by  inteirals  measunid  by 

k'fte  angles  ASn,  and  BSC,  while  sX  s'  they  would  appear  aepanled 

I  tj  the  lesser  angles  A  6*  n,  and  B  s*  c.     Seen  from  &',  the  stars  ABO 

1  would  eeem  to  be  closer  together  than  they  were  when  seen  fron  t. 

r^DT  like  reason  the  stars  ahc,  towards  which  the  system  is  hen 

Apposed  to  move,  wnuld  seem  to  be  closer  together  when  seen  from 

B,  than  ivhen  seen  frum  s'.      Thus,  iu  llie  (juarlcr  of  (ho   heavMS 

towards  which  the  system  is  moving,  the  stars  might  be  expected  to 

separate  gradually,  while  in  the  oppof ilo  quarter  they  would  become 

more  condcntied.      In  all  the  intermediate  paria  of  the  heareos  they 

would  be  afteclcd  hj  a  motion  contrary  to  tliat  of  the  solar  system. 

Such  in  general  would  be  the  effects  of  a  prog'essive  motion  of  our 

8366.  Motion  of  the  mn  inferred  from  the  proper  muHon  of  the 
Uars. — Although  no  general  effect  of  this  kind  has  been  manifested 
in  any  conspicuous  manner  among  tbe  fixed  stars,  many  of  these 
objects  have  been  found,  in  long  periods  of  time,  to  hare  shifted 
their  position  in  a  very  sensible  degree.  Thus,  for  example,  the 
Uirco  stars,  S^irius,  Areturus,  and  Aldcbarnn,  have  undergone,  since 
the  time  of  Ilipparelius  (130  n.  c),  a  change  of  position  southwards, 
amounting  to  cousiderubly  more  than  half  a  degree.  The  doable 
Star  61  Cygiii  bai*,  in  half  a  century,  moved  through  nearly  4'5', 
the  two  stars  composing  it  being  carried  along  in  parallel  lines  with 
a  common  velocity.  Tbe  stars  t  Indi  and  />  Cassiopeia)  move  at  the 
rate  of  7-74"  and  3  74"  annually. 

Various  attempts  have  been  made  to  render  these  and  other  like 
changes  of  apparent  position  of  the  fixed  stars  compatible  with  some 
assumed  motion  of  the  sun.  Sir  W.  Ilerschel,  in  I7S3,  reasoning 
Upon  the  proper  motions  which  had  then  been  observed,  arrived  at 
the  conclusion,  tliat  sueh  appearances  migbt  be  explained  by-  sup- 
posing that  the  sun  has  a  motion  directed  to  a  point  near  the  star  x 


PROPER  MOTION  OF  THE  STARS.  718 

Hercalis.  About  tbe  same  time,  Prevost  came  to  a  like  conclasion, 
assigning,  however,  the  direction  of  the  supposed  motion  to  a  point 
differing  by  27°  from  that  indicated  by  Sir  W.  Ilerschel. 

Since  that  epoch,  the  proper  motions  of  the  stars  have  been  more 
extensively  and  accurately  observed,  and  calculations  of  the  motion 
of  the  sun  which  they  indicate,  have  been  made  by  several  astrono- 
mers. The  following  points  have  been  assigned  as  the  direction  of 
the  Bolar  motion  in  1790 : — 


R.  A. 

N.  P.  D. 

260°  34 

63°  43' 

Sir  W.  Herschel. 

256°  25' 

51°  23' 

Argelander. 

255°  10' 

51°  26' 

Ditto. 

261°  11' 

59°    2' 

Ditto. 

252°  53' 

75°  34' 

Luhndahl. 

261°  22' 

62°  24' 

Otto  Strove. 

The  first  estimate  of  Argelander  was  made  from  the  proper  motions 
of  21  stars,  each  of  which  has  an  annual  motion  greater  than  1"; 
the  second  from  50  stars  having  annual  proper  motions  between  1'' 
and  0*5",  and  the  third  from  those  of  319  stars  having  motions 
between  0*5"  and  0-1".  The  estimate  of  M.  Luhndahl  is  based  on 
the  motions  of  147  stars,  and  that  of  M.  Strove  on  392  stars. 

The  mean  of  all  these  estimates  is  a  point  whose  right  ascension 
18  259°  9',  and  north  polar  distance  5°  23',  which  it  will  be  seen 
differs  very  little  from  the  point  originally  assigned  by  Sir  W. 
Herschel. 

All  the  preceding  calculations  being  based  on  observations  made 
on  stars  in  the  northern  hemisphere,  it  was  obviously  desirable  that 
similar  estimates  should  be  made  from  the  observed  proper  motions 
of  southern  stars.  Mr.  Galloway  undertook  and  executed  those 
calculations ;  and  found  that  the  southern  stars  gave  the  direction 
of  the  solar  motion  for  1790,  to  be  towards  a  point  whose  right 
ascension  is  260°  1',  and  north  polar  distance  55°  37'. 

No  doubt  therefore^  can  remain  that  the  proper  motion  of  the 
stars  is  produced  by  a  real  motion  of  the  solar  system,  and  that  the 
direction  of  this  motion  in  1790  was  towards  a  point  of  space  which 
seen  from  the  then  position  of  the  system  had  the  right  ascension 
of  about  260°,  and  the  north  polar  distance  of  about  55°. 

3367.  Velocity  of  the  solar  motion. — It  follows  from  these  calcu- 
lations, that  the  average  displacement  of  the  stars  requires  that  the 
motion  of  the  sun  should  be  such  as  that  if  its  direction  were  at 
right  angles  to  a  visual  ray,  drawn  from  a  star  of  the  first  magnitude 
of  average  distance,  its  apparent  annual  motion  would  be  03392"; 
and  taking  the  average  parallax  of  such  a  star  at  0*209"^  if  D 
express  the  semi-axis  of  the  earth's  orbit,  the  annual  motion  of  the 
son  would  be 

60* 


ASTROSOMT. 


=  1023  D 


=  422,000  mOes; 


lI     b,  fore,  that  the  annual  niutioa  of  iho  atin  woalil  be 

3  X  95,000,000  =  154,200,000  mJleg; 
<  thi  otion 

154,200,000 
3651        '' 
In.  ID  the  faurtli  of  thfl  euth'i 

t  ^Tobahle  raitre  of  soiar  motion. — The  motion  of  lh« 

WDiQu  uAA  been  computed  in  what  precedes,  ia  that  which  h 

at  a  psrCioulir  epoch.     No  account  ia  t^eii  of  the  posMble  m 

able  changes  of  tUrection  of  eueh  motion.     To  suppose  that  ihe 

f  eyatem  sbmild  move  contiDoously  in  one  and  the  saine  diree- 

irc         «  e<]uival«Dt  to  the  euppositioa  that  oo  body  or  collec- 

*" '         I  in  the  univeree  would  exercise  nay  attractioD  upon  iL 

_ly  more  coosinlent  with  probability  and  analogy,  that 

of  the  eysum  is  orbital,  tiiat  is  to  Bay,  that  it  revolres 

u  sume  remote  centre  of  attraction,  and  that  (be  dirretion  "fits 

motion  must  continually  change,  although  such  change,  owing  to 
the  great  magnitude  of  its  orbit,  aud  the  relative  slowneas  of  its 
motion,  be  so  very  slow  as  to  be  quit«  imperceptible  within  even 
the  longest  interval  over  which  a^tionomioul  records  extend. 

Attempts  have,  ncvertbcicss,  been  made  to  determine  the  centra 
of  the  solar  motion ;  and  Dr.  Madlcr  has  thrown  out  a  surmise  that 
it  lies  at  a  point  in  or  near  the  small  coustcUation  of  tbe  Pleiades. 
This  and  like  specuLitions  muttt,  however,  be  regarded  as  con- 
jectural for  the  present. 


CHAP.  XXVIII. 


3369,  Distribvlion  of  ttars  on  OiP,  firmamml.  —  The  aspect  of 
the  firmament  might,  at  first,  impress  the  mind  of  an  observer  with 
the  idea  that  the  numerous  stars  scailcred  over  it  ore  destitute  of 
any  law  or  regularity  of  arrangement,  and  that  their  distribution  is 
like  the  fortuitous  position  which  objects  flung  upon  such  a  surface 
might  be  imagined  to  assume.  If,  however,  the  different  regions  of 
the  heavens  be  moic  can^fully  examined  and  compared,  this  first  im- 


FORM  OF  STARS  IN  THE  FIRMAMENT.  716 

presaoD  will  be  corrected,  and  it  will,  on  tbe  contrary,  be  found 
that  tbe  distribution  of  the  stars  over  the  surface  of  the  celestial 
sphere  follows  a  distinct  and  well-defined  law;  that  their  density, 
or  the  number  of  them  which  is  found  in  a  given  space  of  the 
heavens,  varies  regularly,  increasing  continually  in  certain  directions 
and  decreasing  in  others. 

Sir  W.  Herschel  submitted  the  heavens,  or  at  least  that  part  of 
them  which  is  observable  in  these  latitudes,  to  a  rigorous  telescopic 
survey,  counting  the  number  of  individual  stars  visible  in  the  field 
of  view  of  a  telescope  of  certain  aperture,  focal  length,  and  magni- 
fying power,  when  directed  to  different  parts  of  the  firmament.  The 
result  of  this  survey  proved  that,  around  two  points  of  the  celestial 
sphere  diametrically  opposed  to  each  other,  the  stars  are  more  thinly 
scattered  than  elsewhere;  that  departing  from  these  points  in  any 
direction,  the  number  of  stars  included  in  the  field  of  view  of  the 
same  telescope  increases  first  slowly,  but  at  a  greater  distance  more 
rapidly ;  that  this  increase  continues  until  the  telescope  receives  a 
direction  at  right  angles  to  the  diameter  which  joins  the  two  opposite 
points  where  tbe  distribution  is  most  sparse ;  and  that  in  this  direc- 
tion the  stars  are  so  closely  crowded  together  that  it  becomes,  in 
some  cases,  impracticable  to  count  them. 

3370.  Galactic  circle  and  poles.  —  The  two  opposite  points  of 
the  celestial  sphere,  around  which  the  stars  are  observed  to  be  most 
sparse,  have  been  called  the  galagtio  poles  ;  and  the  great  circle 
at  right  angles  to  the  diameter  joining  these  points,  has  been  deno- 
minated the  QALACTIO  CIRCLE. 

This  circle  intersects  the  celestial  equator  at  two  points,  situate 
10°  east  of  the  equinoctial  points,  and  is  inclined  to  Uio  equator  at 
an  angle  of  63°,  and,  therefore,  to  the  ecliptic  at  an  ande  of  40°. 

In  referring  to  and  explaining  tbe  distribution  of  the  stars  over 
the  celestial  sphere,  it  will  be  convenient  to  refer  them  to  this  circle 
and  its  poles,  as,  for  other  purposes,  they  have  been  referred  to  the 
equator  and  its  poles.  We  shall,  therefore,  express  the  distance  of 
different  points  of  the  firmament  from  tbe  galactic  circle,  in  either 
hemisphere,  by  the  terms  north  and  south  oalactio  latitude. 

3371.  Variation  of  the  stellar  density  in  relation  to  this  circle, 
—  The  elaborate  series  of  stellar  observations  in  the  northern  hemi- 
sphere made  during  a  great  part  of  his  life,  by  Sir  W.  Herschel, 
and  subsequently  extended  and  continued  in  the  southern  hemi- 
sphere by  Sir  J.  Herschel,  has  supplied  data  by  which  tbe  law  of 
the  distribution  of  the  stars,  according  to  their  galactic  latitude,  has 
been  ascertained  at  least  with  a  near  approximation. 

The  great  celestial  survey  executed  by  these  eminent  observers, 
was  conducted  upon  the  principle  explained  above.  The  telescope 
used  for  the  purpose  had  18  inches  aperture,  20  feet  focal  length, 
and  a  magnifying  power  of  180.     It  was  directed  indiscrimioatelj 


ASTROHOSIY. 

he  cclestia]  sphere  vitiible  ia  the  latitude  of  tiw 

oy  means  or  a  Tist  Dumber  of  ili^tinct  obserTnliona  that 
.udt  the  posilicin  of  the  galactic  polea  wsa  ascertained.  The  . 
of  the  sUr^,  measured  by  ibe  number  ioeluded  in  eaeli  j 
i"  (as  the  field  of  view  wus  called),  wits  acarly  the  same  fot 
le  galactic  latilndc,  nnd  increased  id  proceeding  from  the  g>- 
M\e,  very  bIowI;  at  first,  but  with  great  rapidily  when  3ie 
1  tit. tide  was  much  diminisbed. 

vvf't  anal^iU  ly  vner*  ob>ercation>,  —  An  analysis 

;atJ0D3  of  Sir  W.  tici-sehel,  in  the  northern  hemisphere, 

jado  by  Professor  Strnve,  with  the  view  of  dotermiaiiig  the 

Lty  of  the  stare  in  successive  zones  of  galactic   latitude ; 

B  analysis  has  been  made  of  the  observations  of  Sir  J. 

.,  in  the  southern  hemisphere. 

so  imagine  the  celestial  sphere  resolved  into  a  succcwion  of 
each  tDCOsuring  15°  ia  breadth,  and  bounded  by  parallels  to 
actic  circle,  the  average  number  of  stars  included  within  a 
those  diameter  is  15',  and  whoee  magnitude,  therefore,  would 
,,ut  the  fourth  part  of  that  of  the  disk  of  ^e  sun  or  moon, 
)e  that  which  ia  given  in  the  second  column  of  the  following 

Average  Dumber 
Galactic  Latitude.  of  Stars  in  a  circle  15' 

diameter. 

N  00"  — 75°  4-32 

"   75°  — 60°  5-42 

u  60°  — 45°  8-21 

"  45°  — 30°  13-61 

"  30°— 15°  24  09 

«   i5o_    0=.  53.43 

S     0°  — 15"  5906 

"  15°  — 30°  2629 

"  30°  — 45°  1349 


"  75°— 90°  6-05 

'  It  appears,  therefore,  that  the  variation  of  the  density  of  the 
visible  stars  in  proceeding  from  the  galactic  plane,  cither  north  or 
south,  is  subject  almost  exactly  to  the  same  law  of  decrease,  the 
density,  however,  at  eaeh  latitude  being  somewhat  greater  in  the 
Boulhcrn  than  in  the  northern  hemisphere. 

3373.  T/ie  mMy  ,r-'>,  —The  regions  of  the  hcaTens,  which  ex- 
tend  to  a  certain  distance  on  one  side  and  the  other  of  the  galactic 
plane,  are  generally  so  densely  covered  with  aujall  stars,  as  lo  present 
to  the  naked  eye  the  ap^onuicc,  not  of  stars  crowded  together,  but 


rcRM  OF  .-TARS  IX  THE  FITLMAMENT.  717 

of  trhitish  nebulous  light.  This  appearance  extends  over  a  vast 
extent  of  the  celestial  sphere^  deviating  in  some  places  firom  the 
exact  direction  of  the  galactic  circle,  bifurcating  and  diverging  into 
two  branches  at  a  certain  point  which  afterwards  reunite,  and  at 
other  places  throwing  out  off-shots.  This  appearance  was  denomi- 
nated the  Via  Lacteal  or  the  galaxy,*  by  the  ancients,  and  it  has  re- 
tained that  name. 

The  course  of  the  milky  way  may  be  so  much  more  easily  and 
clearly  followed  by  means  of  a  map  of  the  stars,  or  a  celestial  globe, 
upon  which  it  is  delineated,  that  it  will  be  needless  here  to  describe  it. 

3374.  It  consists  of  innumerable  stars  crowded-  together, — When 
this  nebulous  whiteness  is  submitted  to  telescopic  examination  with 
instruments  of  adequate  power,  it  proves  to  be  a  mass  of  countless 
numbers  of  stars,  so  small  as  to  be  individually  undistinguishable, 
and  so  crowded  together  as  to  give  to  the  place  they  occupy,  the 
whitish  appearance  from  which  the  milky  way  takes  its  name. 

Some  idea  may  be  formed  of  the  enormous  number  of  stars  which 
are  crowded  together  in  those  parts  of  the  heavens,  by  the  actual 
number  so  distinctly  visible  as  to  admit  of  being  counted  or  esti- 
mated, which  are  stated  by  Sir  W.  Herschel  to  have  been  seen  in 
spaces  of  given  extent.  He  states,  for  example,  that  in  those  parts 
of  the  milky  way  in  which  the  stars  were  most  thinly  scattered,  he 
sometimes  saw  eighty  stars  in  each  field.  In  an  hour,  fifteen  de- 
grees of  the  firmament  were  carried  before  his  telescope,  showins 
successively  sixty  distinct  fields.  Allowing  eighty  stars  for  each  of 
these  fields,  there  were  thus  exhibited,  in  a  single  hour,  without 
moving  the  telescope,  four  thousand  eight  hundred  distinct  stars  1 
But  by  moving  the  instrument  at  the  same  time  in  the  vertical  di- 
rection, he  found  that  in  a  space  of  the  firmament,  not  more  than 
fifteen  degrees  long,  by  four  broad,  he  saw  fifty  thousand  stars,  large 
enough  to  be  individually  visible  and  distinctly  counted !  The  sur- 
prising character  of  this  result  will  be  more  adequately  appreciated, 
if  it  is  remembered  that  this  number  of  stars  thus  seen  in  the 
space  of  the  heavens,  not  more  than  thirty  diameters  of  the  moon's 
disk  in  length  and  eight  in  breadth,  is  fifty  times  greater  than  all 
the  stars  taken  together,  which  the  naked  eye  can  perceive  at  any 
one  time  in  t^:  heavens,  on  the  most  serene  and  unclouded  night! 

On  presenting  the  telescope  to  the  richer  portion  of  the  via  lactea^ 
Herschel  found,  as  might  be  expected,  much  greater  numbers  of 
stars.  In  a  single  field  he  was  able  to  count  588  stars;  and  for 
fifteen  minutes,  the  firmament  being  moved  before  his  telescope  by 
the  diurnal  motion,  no  diminution  of  number  was  apparent,  so  that 
he  estimated  that  in  that  space  of  time,  116,000  stars  must  have 
passed  in  review  before  him;  the  number  seen  at  any  one  time 

*  From  the  Greek  irord  ydXa  ydXaxTos,  milk. 


1  onn  be  Keen  by  the  nalced  eye,  on  tlie  entin 

on  the  clearest  nights. 
.  II  ne  proliahle  form  of  tiie  itralum  of  sfart  in   Khi^Jt  Af 
«~^. — It  may  be  coDsiJered  aa  establbhcd  by  a  body  of 
Jence,  having  all  the  force  of  denjonatratioQ,  llmt  the 
e  self-lumiDoas  bodies,  Eimilar  to  our  eun ;  and  ibit 
-nnv  niay  differ  moro  or  leaa  from  our  eun  and  from  eaek 
ude  and  intrinsic  luatre,  they  have  a  certain  avei9t>e 
'  th.      ''re'       '     "ha  main,  the  grent  differenees 
it  iu  Lueir  t  ,  are  to  bo  ascribed  to  difference 

auming,  theu,  they  arc  separated  trvm  each 

ices  analogous  to  dietaDccs  from  the  bug,  itjelf 

^nera!  phenomena  wnicn  have  been  described  aboTB, 
"c  rapid  ioereaso  of  stellar  density  in  approaching  the 
),  eoinbiaed  with  the  observed  form  of  the  milky  iray, 
ring  the  galactic  plane  in  its  general  coarse  departt 
■IBM  from  it  at  some  points,  bifurcates,  resolving  itself  inU 
ig  branches  at  others,  and  at  others  throtrs  out  irregular 
onduetcd  Sir  W.  Uerschel  to  the  conclusion,  that  the 
.  our  firmament,  including  those  which  the  telescope  renders 
lOie,  aa  well  as  those  visible  to  the   naked  eye,  inMcrtd  of  being 
Boattered  indiSerently  in   all  directions   around    the  solar  system 
through  the  depths  of  the  universe,  form  a  stratum  of  definite  form 
and  dimensions,  of  which  the  thickness  bears  a  very  small  proportion 
to  the  length  and  breadth,  and  that  the  sun  and  solar  system  ia 
placed  within  this  stratum,  very  near  its  point  of  bifurcation,  rela- 
tively to  its  breadth  near  its    middle  point,  and  relatively  to  its 
thickness  (as  would  appear    from    the   more    recent   observations) 
nearer  to  its  northern  than  to  its  southern  surface. 

Let  A  c  II D,  fff.  8T8,  represeot  a  rough  outline  of  a  section  of 
BQch  a  stratum,  made  by  a  plane  passing  through  or  near  its  centre. 
Let  AB  represent  the  intersection  of  this  with  the  plane  of  the 
galactic  circle,  so  that,  z  being  the  place  of  the  solar  system,  z  o 


FDIIM  OF  STARS  IN  THE  FIRMAMENT.  719 

will  be  the  direction  of  the  north,  and  z  D  that  of  the  soath  galactic 
pole.  Let  z  H  represent  the  two  branches  which  bifurcate  from  the 
chief  stratum  at  B.  Now,  if  we  imagine  visual  lines  to  be  drawn 
from  z  in  all  directions,  it  will  be  apparent  that  those  %  o  and  z  D, 
which  are  directed  to  the  galactic  poles,  pass  through  a  thinner  bed 
of  stars  than  any  of  the  others )  and  since  z  is  supposed  to  be  nearer 
to  the  northern  than  to  the  southern  side  of  the  stratum,  20  will 
pass  through  a  less  thickness  of  stars  than  z  D.  As  the  visual  lines 
are  inclined  at  greater  and  greater  angles  to  2;  A,  their  length  rapidly 
decreases,  as  is  evident  by  comparing  2  A,  2;  E,  and  z  F,  which 
explains  the  fact  that  while  the  stars  are  as  thick  as  powder  in  the 
direction  z  A,  they  become  less  so  in  the  direction  z  E,  and  still  less 
in  the  direction  z  F,  until  at  the  poles  in  the  directions  z  0  and  z  D^ 
they  become  least  dense. 

On  the  other  side,  z  b  being  less  than  2;  A,  a  part  of  the  galactic 
circle  is  found  at  which  the  stars  are  more  thinly  scattered;  but  in 
two  directions,  z  h  intermediate  between  z  B  and  the  galactic  poles, 
they  again  become  nearly  as  dense  as  in  the  direction  zA. 

This  illustration  must,  however,  be  taken  in  a  very  general  sense. 
No  attempt  is  made  to  represent  Uie  various  off-shoots  and  variations 
of  length,  breadth,  and  depth  of  the  stratum  measured  from  the 
position  of  the  solar  system  within  it,  which  have  been  indicated 
bj  the  telescopic  soundings  of  Sir  W.  Herschel  and  his  iUustrious 
Bon,  whose  wondrous  labours  have  effected  what  promises  in  time, 
by  the  persevering  researches  of  their  successors,  to  become  a  com- 
plete analysis  of  this  most  marvellous  mass  of  systems.  Meanwhile 
It  may  be  considered  as  demonstrated  that  it  consists  of  myriads  of 
stars  clustered  together : 

**  A  broad  and  ample  road,  whose  dust  is  gold, 
And  payement  stars,  as  stars  to  ub  appear ; 
Seen  in  the  galaxy,  that  Milky  Way, 
Like  to  a  oiroling  zone  powder'd  with  stars.** — Milton. 

The  appearance  which  this  mass  of  stars  would  present  if  viewed 
from  a  position  directly  above  its  general  plane,  and  at  a  sufficient 
distance  to  allow  its  entire  outline  to  be  discerned,  was  represented 
by  Sir  Wm.  Herschel  as  resembling  the  starry  stratum  sketched 
in  Plate  XXVI. 

He  considered  that  it  was  probable  that  the  thickness  of  this  bed 
0/ stars  was  equal  to  about  eighty  times  the  distance  of  the  nearest 
of  the  fixed  stars  from  our  system ;  and  supposing  our  sun  to  be 
near  the  middle  of  this  thickness,  it  would  follow  that  the  stars  on 
its  surface  in  a  direction  perpendicular  to  its  general  plane  would 
be  at  the  fortieth  order  of  distance  from  us.  The  stars  placed  in 
the  more  remote  edges  of  its  length  and  breadth  he  estimated  to  be 
in  some  places  at  the  nine-hundredth  order  of  distance  from  us^  so 


I  ASTRONOMY. 

mm  length  mnj'  be  said  to  be  ia  roand  namben  kbottt 

..d  the  distance  of  tbe  nearest  fiiud  sUra  from  onr  ^ytiem. 

1  i-ijatG  ligUt  would  take  20,000  years  to  move  over,  moving 

■■■at  time  at  the  rate  of  neurlj  200,000  miles  between  eveiy 

licks  of  a  comiDoa  clock  ! 


76.    T}ie  tlari  wln'rh  fimii  ih«  Jlrmftmtml  a  iltUar  dutUr. — 

'  l^HO'iff  the  pnifiahle  erUUnce  ofolhen. — It  appeon,  then, 
'  eun  is  an  iudividuil  star,  forming  ddI^  a  single  anit  ia  a 
T  or  tnasa  of  maay  milliona  of  other  similur  stars;   that  this 
)t  boa  liiuited  dimecsioDs,  Las  nscertainablc  Icogth,  breadth,     i 
tbicVness,  kiid  in  abort,  forms  what  maj  be  expressed  by  \ 
■rte  of  tolar  tfftfemf.     The  miod,  still  nasatiBfied,  is  as  nrpat     i 
Fore  in  its  queetionH  regarding  the  remain^fr  of  vaimatni^l 
uwpvcr  vast  the  dimensiona  of  this  mass  of  sons  bo,  tbej  are 
nevenliclL'ps  finite.     However  sfupemious  be  fbe  ^pife  inclniled 
within  thent,  it  is  still  notkinff  compared  to  the  inmensit;  which 
lies  outside  I     Is  that  immensity  a  vast  solitnde  ?     Are  ite  unex- 
plored realms  dark  and  silent  ?     Baa  Omoipoteoco  circumscribed 
Its  agency,  and    has   Infinite  Beneficence  left  those   nnfathomed 
regions  destitute  of  evidence  of  His  power? 

That  the  infinitude  of  space  should  exist  without  a  purpose,  un- 
occupied bjr  any  works  of  creation,  is  plainly  iocompatiblc  with  all 
,  our  notions  of  the  character  and  attributes  of  the  Author  of  the 
universe,  whether  derived  from  the  voice  of  revelation  or  from  the 
light  of  nature.  AVe  should  therefore  infer,  even  in  the  absence  of 
direct  evidence,  tbtit  sonic  works  of  creation  are  dispersed  through 
those  spaces  which  lie  beyond  the  limits  of  that  vast  stellar  cluster 
in  which  our  system  is  placed.  Nay,  we  should  be  led  by  the  most 
obvious  analogies  to  conjeclure  that  other  aldlar  cluidcri  like  oar 
own,  are  dispersed  through  immensity,  separated  probably  by  dis- 
tances as  much  greater  thau  those  which  intervene  between  star  and 
star,  as  the  latter  arc  greater  than  those  which  separate  the  bodies 
of  the  solar  system.  Uut  if  such  distant  clusters  existed,  it  may  be 
objected,  that  they  must  be  visible  to  us;  that  although  diminished, 
perbap.s,  to  mere  spots  on  the  firmament,  they  would  still  be  ren- 
dered apparent,  were  it  only  as  confused  whitish  patches,  by  the 
telescope ;  tWt,  as  iW  aVa-t^  o^  \,Vie  wilky  way  assume  to  the  naked 
eye  the  appeutancc  ot  vftcte '«\i\\\^  \iOuN^>s*\Vi,  «a  ■iJiti  t«  more 
distant  BtuTs  of  otVcr  t\\jsVpv»i'w\;\'ii«:s>'u,ii<iX"VK-S«'ieYst^-(^  ^^V-^ 


STELLAR  CLUSTERS  AND  KEBULiB.  T21 

the  naked  eye,  woald,  to  telescopes  of  adeqaate  power,  present  the 
same  whitbh  nebulous  appearance ;  and  that  we  might  look  forward 
without  despair  to  such  augmentation  of  the  powers  of  the  telescope 
as  may  even  enable  us  to  perceive  them  to  be  actual  dusters  of  stars. 

3377.  Such  clusters  of  stars  innumerable, —  Such  anticipations 
have  accordingly  been  realised.  In  various  parts  of  the  firmament 
objects  are  seen  which,  to  the  naked  eye,  appear  like  stars  seen 
through  a  mist,  and  sometimes  as  nebulous  specks,  which  might  be, 
and  not  unfrequcntly  are  mistaken  for  comets.  With  ordinary  tele- 
scopes these  objects  are  visible  in  very  considerable  numbers,  and 
were  observed  nearly  a  century  ago.  In  the  Connoissance  des 
Temps,  for  1784,  Messier,  then  so  celebrated  for  his  observations  on 
comets,  published  a  catalogue  of  103  objects  of  this  class,  of  many 
of  which  be  gave  drawings,  Tvith  which  all  observers  who  search  for 
comets  ought  to  be  familiar,  to  avoid  being  misled  by  their  resem- 
blance to  them.  The  improved  powers  of  the  telescope  speedily  dis- 
closed to  astronomers  the  nature  of  these  objects,  which,  when  ex- 
amined by  sufficient  magnifying  powers,  prove  to  be  masses  of  stars 
clustered  together  in  a  manner  identical  with  that  cluster  in  which 
our  sun  is  placed.  They  appear  as  they  do,  mere  specks  of  whitish 
light,  because  of  their  enormous  distance. 

3378.  Distribution  of  clusters  and  nebtdee  on  the  firmament.  ^- 
Tbese  objects  are  not  distributed  fortuitously  and  indifferently  on 
all  parts  of  the  heavens.  They  are  wholly  absent  from  some  regions, 
in  some  rarely  found,  and  crowded  in  amazing  profusion  in  others. 
This  disposition,  however,  is  not  like  that  of  the  stars  in  general, 
determined  by  a  great  circle  of  the  sphere  and  its  poles.  It  was 
supposed  that  they  showed  a  tendency  to  crowd  towards  a  zone  at 
right  angles  to  the  galactic  circle,  but  a  careful  comparison  of  their 
position  does  not  confirm  this.  According  to  Sirs  W.  and  J.  Her- 
schel,  the  nebulao  prevail  most  around  the  following  parts  of  the 
celestial  sphere : — 

1  The  North  Galactic  Pole.  6  Canes  Venatici. 

2  Leo  mag  or.  6  Coma  Berenici. 

8  Leo  minor.  7  Bootes  rprecedingly). 

4  Ursa  major.  8  Virago  (head,  wings  and  shoulder;. 

The  parts  of  the  heavens,  on  the  other  hand,  where  they  are  found 
in  the  smallest  numbers,  are : — 

1  Aries.  7  Draco. 

2  Tatiras  8  Hercules. 

8  Orion  (head  and  shoulders).  9  Serpentarins  (northern  part). 

4  Anriga.  10  Serpens  (tail). 

5  Perseus.  11  Aquila  (tail). 

6  Camelopardos.  12  Lytv 

In  the  southern  hemisphere  their  diair\\>xi.\vya  S&  m^t^  '^QSfi&ssrc&.. 
HI.  61 


ASTROHOMT. 

Cmttilution  of  the  clutter*  and  ntbuJm.  —  WliM  A« 

■re,  and  of  what  they  severaUy  consist^  admita  of  uo  rcasoD- 

-uubt.     So  fnr  as  relates  to  the  stellar  clu&tere,  their  conalitueot 

tre  viuble.     They  are,  aa  their  Damn  imports,  mases  of  fan 

ited  together  at  certaia  poiubi  in  the  regions  of  spaoe  which 

lb  beygod  the  limits  of  our  ow^  cluBter,  and  are  by  distance  w 

»°4  in  the  visual  magnitude  ibat  sd  entire  rinster  will  appeir 

naked  eye,  if  it  be  visible  &t  all,  as  a  sioglc  etar,  and  when 

itb  the  teleseope  will  bo  included  viihiu  the  limit  of  a  unglc 

— "ew. 

r'  'blusters  exhibit  their  component  etare  seen  with  the 

ying  power  more  or  less  daslinctly.     This  may  be  ex- 

^d  :r  by  difference  of  dislancc,  or  by  ihe  supposition  ihrt 

I  uuusiet  of  stars  of  different  real  magaitudcs,  aod  crowdeil 

less  c1o8cly  together.     The  former  supposiiion  is,  however^ 

■  the  more  oaturai  and  probable. 

ne  appcaraoce  of  the  stars  conpouog  BOtne  of  the  clasten  ii 

I  gorgeous.     Sir  J.  Eerscbel  says,  that  the  cluster  which  ntr- 

ds  ■  Cracis  in  the  southern  hemisphere,  occupies  the  4Stb  part 

.  square  degree,  or  about  the  tenth  part  of  the  superficial  ma^ 

miude  of  the  moon's  (ilsl;,  and  coii?ista  of  about  110  slurs  from  Ifae 

7th  magnitude  downwards,  eight  of  tbe  more  conspicuous  stars  being 

ootoured  with  various  liuts  of  red,  green,  and  blue,  so  as  to  gi<re  to 

the  whole  the  appearance  of  a  ricb  piece  of  jewellery. 

Cluster  compared  with  cluster  show  all  gradations  of  smallness 
ud  closeness  of  the  compoaent  stars,  until  they  assume  the  ap- 
pearance of  patches  of  starry  powder.  These  varieties  are  meet 
obviously  ascribable  to  varying  distances. 

Then  follow  those  patches  of  starry  light  which  are  seen  in  so 
many  regions  of  tbe  heavens,  and  which  have  been  denominated 
nebulo!.  That  these  are  still  clusters,  of  which  tbe  component  stars 
are  indistinguishable  by  reason  of  tbeir  remoteness,  there  are  tbe 
strongest  evidence  and  moat  striking  analogies  to  prove.  Every 
augmentation  of  power  and  improvement  of  efficiency  the  telescope 
receives,  augments  tbe  number  of  ncbultc  which  are  converted  by 
that  instrument  into  clusters.  Nebuloe  which  were  irresolvable 
before  tbe  time  of  Sir  W.  Ilerscbel,  yielded  ia  large  numbers  to  the 
powers  of  the  instruments  which  that  observer  brought  to  bear  upon 
them.  The  labours  of  Sir  J.  Ilerscbel,  tbe  colos^  telescope  con- 
etrucied  by  Lord  Ropse,  and  tbe  erection  of  observatories  in  multi- 
plied numbers  in  elimalea  and  under  skies  more  favourable  to 
observation,  have  all  tended  to  augment  tbe  number  of  nebul» 
wbich  have  been  resolved,  and  it  may  be  expected  that  this  progress 
will  continue,  the  resolution  of  these  objcota  into  stellar  clusters 
beiug  co-extensive  with  the  improved  powers  of  the  telescope  and 
the  incrcaeed  ntimW  B,ad  teal  of  observers. 


.STKl.LAK   >  l.rSTi:HS  AND   XKIlTL.!:.  T2P> 

S380.  Nebular  hypothesis. — A  theory  was  put  forward  to  explain 
these  objects,  based  upon  views  not  in  aocoi^ance  with  what  has 
just  been  related.  It  was  assumed  hypothetioallj  that  the  nebulous 
matter  was  a  sort  of  lumioous  fluid  diffused  through  difierent  parts 
of  the  universe  ;  that  by  its  aggregation  on  certain  laws  of  attraction 
nolid  luminous  masses  in  process  of  time  were  produced^  and  that 
these  nebulae  grew  into  clusters. 

It  would  not  be  compatible  with  the  limits  of  this  work,  and  the 
objects  to  which  it  is  directed,  to  pursue  this  speculation  through 
its  consequences,  to  state  the  arguments  by  which  it  is  supported 
and  opposed ;  and  it  is  the  less  necessary  to  do  so,  seeing  that  such 
an  hypothesis  is  not  needed  to  explain  appearances  which  are  so 
much  more  obviously  and  simply  explicable  by  the  admission  of  a 
gradation  of  distances. 

3381.  Forms  apparent  and  real  of  the  clusters. — ^The  apparent 
forms  of  these  objects  are  extremely  various,  and  subject  to  most 
extraordinary  and  unexpected  changes,  according  to  the  magnifying 
power  under  which  they  are  viewed.  This  ought,  however,  to 
excite  no  surprise.  The  telescope  is  an  expedient  by  which  a  well- 
defined  and  strongly  illuminated  optical  image  of  a  distant  object  is 
formed  so  close  to  the  observer,  that  he  is  enabled  to  view  it  with 
microscopes  of  greater  or  less  power,  according  to  the  perfection  of 
its  definition,  and  the  intensity  of  its  illumination.  Now,  it  is 
known  to  all  who  are  familiar  with  the  use  of  the  microscope,  that 
the  apparent  form  and  structure  of  an  object  change  in  the  most 
remarkable  and  unexpected  way  when  viewed  with  different  micros- 
copic powers.  The  blood,  for  example,  which  viewed  with  the 
naked  eye,  or  with  low  powers,  is  a  uniformly  red  fluid,  appears  as 
a  pellucid  liquid,  having  small  red  disks  floating  in  it,  when  seen 
with  higher  powers  (46).  Like  effects  are  manifested  in  the  cases 
of  the  nebulse,  when  submitted  to  examination  with  different  and 
increasing  magnifying  powers,  of  which  we  shall  presently  show 
many  striking  examples. 

The  apparent  forms  of  the  stellar  clusters  are  generally  roundish 
or  irregular  patches.  The  stars  which  compose  them  are  always 
much  more  densely  crowded  together,  in  going  from  the  edges  of  the 
cluster  towards  the  centre,  so  that  at  the  centre  they  exhibit  a  per- 
fect blaze  of  light. 

The  apparent  form  is  that  of  a  section  of  the  real  form,  made  by 
a  plane  at  right  angles  to  the  visual  ray.  If  the  mass  had  a  motion 
of  rotation,  or  any  other  motion  by  which  it  would  change  this  plane, 
so  as  to  exhibit  to  the  eye  successively  different  sections  of  it,  its 
real  form  could  be  inferred  as  those  of  the  planets  have  been.  But 
there  are  no  discoverable  indications  of  any  such  motion  in  these 
objects.  Their  real  forms,  therefore,  can  only  be  conjectured  from 
comparing  their  apparent  forms  with  their  structural  appearance. 


ASTRONOMY. 

.laBters  hdvicg   rouod  apptireDl  tonna,  and  of  wbich  the 

I  nptdly  more  dense  tow&rds  tbe  centres,  are  inferred  to  b« 

globular  or  spheroidul  masses  of  stars,  the  greater  apparent 

..y  in  passing  fruiu  the  edges  to  the  centre  being  eiplaiiied  hy 

;reat«r  thickness  of  the  mass,  ia  thedirootionofcbe  Tisoal  liac-. 

iters  of  irrcgukr  on  til  oe  which  show  also  a  density  incrcatiog 

drds,  are  also  inferred,  for  like  reBsona,  to  bo  masses  of  stare, 

xe  dimensions  in  the  direction  of  the  visual  rays  correspond  with 

ir  diineDsiona  iu  the  direction  at  right  angles  to  ihose  rajs. 

t382.   Fbrms  apparent  and  reai  of  Ihe  nehiilx. — These  objects 

hibit  forms  mnch  more  Tarioos  than  those  presented  by  the  clut- 

j.     Some  are  circular,  with  more  or  teas  preciaioo  of  outline. 

nc  are  elliptical,  the  oval  ontlioe  having  degrees  of  ec«entricitj 

nitcly  various,  from  one  which  scarcely  differs  from  a  circle,  to 

I  which  is  compressed  into  a  form  not  sensibly  different  from  a 

light  lino.     In  short,  the  minor  aiia  of  the  ellipses  bears  all 

[wrtions  to  the  major  axis,  until  it  becomes  a  very  small  bactioD 

ho  latter. 

aO  infer  tho  real  from  the  apparent  forms  of  these  objects  with 
f  certainty,  there  are  no  sufficient  data.  But  in  tbe  cases  in 
n^ich  the  brightoesB  increases  rapidly  towards  the  centre,  which  it 
very  generally  does,  it  may  be  prohiilily  coiijeclureil  that  iheir  forma 
are  globular  or  spheroidal,  for  the  reasons  already  explained  ia 
retatioD  to  the  clusters,  and  this  becomes  the  more  probable  when 
it  is  considered,  that  these  ncbulse  are  in  fact  clusters,  the  stars  of 
which  are  reduced  to  a  nebulous  patch  by  distance. 

Nevertheless,  these  nehulaj  may  he  strata  of  stars,  of  wbicfa  the 
thickness  is  small  compared  with  their  other  dimensions;  and  sup- 
posing their  real  outline  to  he  circular,  they  will  appear  elliptical  if 
the  plane  of  the  stratum  be  inclined  to  the  visnal  line,  and  more  or 
less  eccentrically  elliptical,  according  ss  the  angle  of  iuclination  is 
more  or  less  acute.  In  cases  iu  which  the  brightness  does  not 
increase  in  a  striking  degree  fnun  tbe  edges  inwards,  this  form  is 
more  probable  than  the  globular  or  the  spheroidal. 

Nebulae  may  be  couvmiently  classed  according  to  their  apparent 
form  and  structure;  but  whatever  arrasgemcot  ma;  be  adopted, 
these  objects  exhibit  such  varieties,  assume  such  capricious  and 
irregular  form?,  and  undergo  such  strange  and  unexpected  changes 
of  appearance  according  to  the  increasing  power  of  the  telescope 
with  which  they  are  viewed,  that  it  will  always  be  found  that  great 
numbers  of  them  will  remain  unavoidably  unclassified. 

3383.  DoMc  nehulie.  —  Like  individual  stars,  nebula)  are  found 
to  he  combined  in  pairs  too  frequently  to  be  compatible  with  ibe 
supposition  that  such  comhinatioos  arise  from  tbe  fortuitous  results 
of  the  small  obhquity  of  the  visual  rays,  which  causes  mere  optini 
juxtaposition, 


STELLAR  CLUSTERS  AND  NEBULJI.  729 

These  doable  nebulae  are  generally  circnlar  in  their  apparenty  and 
therefore  probably  globular  in  their  real  form.  In  some  cases  they 
are  resolyable  clusters. 

That  such  pairs  of  clusters  are  physically  connected  does  not 
admit  of  a  reasonable  doubt,  and  it  is  highly  probable  that,  like  the 
binary  stars,  they  move  round  each  other,  or  round  a  common  centre 
of  attraction,  although  the  apparent  motion  attending  such  revo- 
lution is  rendered  so  slow  by  their  immense  distance  that  it  can  only 
be  ascertained  after  the  lapse  of  ases. 

3384.  Planetary  nehulm,  —  Tnis  class  of  objects  derive  their 
name  from  their  close  resemblance  to  planetary  disks.  They  are  in 
general  either  circular  or  very  slightly  oval.  In  some  cases  the  disk 
is  sharply  defined,  in  others  it  is  hazy  and  nebulous  at  the  edges. 
In  some  the  disk  shows  a  uniform  surface,  and  in  some  it  has  an 
appearance  which  Sir  J.  Herschel  describes  by  the  term  curdled. 

There  is  no  reason  to  doubt  that  the  constitution  of  these  objects 
is  the  same  as  that  of  other  nebulas,  and  that  they  are  in  fact  dusters 
of  stars  which,  by  mutual  proximity  and  vast  distance,  are  reduced 
to  the  form  of  planetary  disks. 

These  objects,  which  are  not  numerous,  present  some  remarkable 
peculiarities  of  appearance  and  colour.  It  has  been  already  observed 
that,  although  the  companion  of  a  red  individual  of  a  double  star 
appears  blue  or  green,  it  is  not  certain  that  this  is  its  real  colour, 
the  optical  effect  of  the  strong  red  of  its  near  neighbour  being  such 
as  would  render  a  white  star  apparently  blue  or  green,  and  no  ex- 
ample of  any  single  blue  or  green  star  has  ever  been  witnessed. 
The  planetary  nebulae,  however,  present  some  very  remarkable 
examples  of  these  colours.  Sir  J.  Herschel  indicates  a  beautiful 
instance  of  this,  in  a  planetary  nebula  situate  in  the  southern  con- 
stellation of  the  Cross.  The  apparent  diameter  is  12'^,  and  the  disk 
IS  nearly  circular,  with  a  well-defined  outline,  and  a  ''  fine  and  ftiU 
blue  colour  verging  somewhat  upon  green."  Several  other  plane- 
tary nebulae  are  of  a  like  colour,  but  more  faint. 

The  magnitudes  of  these  stupendous  masses  of  stars  may  be  con- 
jectured from  their  probable  distances.  One  of  the  largest,  and 
therefore  probably  the  nearest  of  them,  is  situate  near  the  star  3 
Ursae  majoris  (one  of  the  pointers).  Its  apparent  diameter  is  2'  40". 
Now,  if  this  were  only  at  the  distance  of  61  Cygni,  whose  parallax 
is  known  (2603),  it  would  have  a  diameter  equal  to  seven  times  that 
of  the  extreme  limit  of  the  solar  system  ;  but  as  it  is  certain  that  its 
distance  must  be  many  times  greater,  it  may  be  conceived  its  di- 
mensions must  be  enormous. 

3385.  Annular  nebulse,  —  A  very  few  of  the  nebulae  have  been 
observed  to  be  annular.  Until  lately  there  were  only  four.  The 
telescopes  of  Lord  Rosse  have,  however,  added  five  to  the  number, 
by  showing  that  certain  nebulae  formerly  supposed  to  be  small  round 

61* 


ASTBONOMT. 

really  aiiDDlar.     It  is  extremely  probable,  tbat  mnj 
.  uic  smaner  class  of  round  nebuloj  irilt  prove  to  be  asDalar, 
^abmitted  to  further  eiomtuatioa  with  teleecopes  of  adeqiule 
.  snd  efGoiency. 

86.  Spiral  nebulae.  —  The  discovery  of  this  class  of  objects, 
most  extraordimiry  and  uueipecteil  which  tnodero  researcfa  bas 
disclosed  in  8l«l!ar  aBtroDomy,  is  due  to  Ix)rd  Rosse.     Tbeir 
leral  form  and  character  may  be  conceived  by  refcTTing  to  lho?e 
■escnted  in  Plate  XXU.ffft.  1  and  3,  and  Plate  XXin./y.  1. 
ae  extraordinary  forma  are  60  entirely  removed  from  all  analogy 
'O  any  of  the  phenomena  presented  either  in  the  motions  of  tBe 
tr  Bystcm,  or  the  comets,  or  those  of  any  other  objects  to  which 
ervalioD  hns  been  directed,  that  all  conjecture  as  to  the  physical 
idiUon  of  the  massea  of  stars  which  could  asHome  such  forms 
lid  be  vain.     The  number  of  instances  bb  yet  detected,  in  which 
I  form  prevails,  is  not  great;  but  it  is  mfficient  to  prove  that  ibe 
nomcnon,  whatever  he  its  cause,  is  the  result  of  tbo  operation  of 
le  general  law.     it  is  pretty  certain,  that  when  the  same  powerful 
ailments  which  have  rendered  these  forma  visible  in  objeota  which 
i  already  been  so  long  under  tbe  scrutiny  of  the  most  emmeni 
•servers  of  the  last  hundred  years,  including  Sir  W.  and  Sir  J. 
derschel,  aided  by  the  vast  telescopic  powers  at  their  di.'pneition, 
irithout  raising  even  a  pucpieiim  of  their  rc;il  fibrin   and  strui'lurc, 
bave  been  applied  to  other  nebulae,  other  cases  of  the  same  pheno- 
menon will  be  brought  to  light.    In  this  point  of  view  it  is  much  to 
be  regretted,  that  the  telescopes  of  Lord  Rosse  cannot  have  the  great 
advantage  of  being  used  under  skies  more- favourable  to  stellar  re- 
■earches,  since  tbe  discovery  of  such  forms  as  these  not  only  requires 
instruments  of  such  power  as  Lord  llosse  alone  possesses  at  present, 
but  also  the  most  favourable  atmospheric  conditions. 

8387.  Kii7n/>fr  o/ n^iii/ffi.— The  number  of  these  objeels  is 
ooutttless.  The  catalogues  of  Sir  J.  Hcrschel  contain  above  4000, 
of  which  tbe  places  arc  assigned,  and  the  magnitudes,  forms,  and 
apparent  characters  described.  As  observers  are  multiplied,  and  the 
telescope  improved,  and  especially  when  the  means  of  observation 
have  been  extended  to  places  tbat  sre  more  favourable  for  such 
observations,  it  may  be  expected  that  the  Dumber  observed  will  be 
indefinitely  augmented. 

3388.  Rt-mtirknlle  n^-fcute.  —  Having  noticed  thus  briefly  the 
characters  and  appearances  of  the  principal  elapses  of  (hese  object.a, 
it  will  be  useful  to  illustrate  these  general  observations  by  reference 
to  examples  of  nebula!  and  tluslcrs  of  each  class,  assigning  the 
position  of  each  by  its  right  ascension  and  north  polar  distance,  and 
■Upplying,  wherever  it  can  be  done  on  satisfactory  sutborily,  a 
telescopic  view  of  such  object.  In  the  selection  of  these  examples, 
It  will  be  ODc  of  our  chief  purposes  to  show  the  eztraordinary  differ- 


ASTRONOMY. 

•fcM  an  realTy  aanukr.     It  is  eitremel;  probable,  thsl  manj 
n  of  the  BnuUor  class  of  round  nebulie  itill  prove  to  be  SDOalar, 

■dII  Bubmitted  to  further  cxamiualioa  with  tcleecopea  of  ade<jaate 
ver  nid  effidenoy. 

1386,  ^/iral  nebula:.  —  The  discovery  of  this  class  of  objects, 
:  most  QxttaordioHry  and  uneipectcd  nhkh  modem  research  baa 

»  diadooed  in  stellar  aBtrooomj,  is  duo  to  Lord  Rosse.  Their 
flBiiBnl  fimn  mti  character  may  be  conceived  bj  referring  to  ihopo 

.pMBcnted  in  PUfe  XXII,  fgt.  1  and  3,  and  Plate  XXIII.  /y.  1. 

hose  extnordinary  furnis  arc  so  entirely  removed  from  all  analogy 
nth  any  of  the  pheoomcna  prcBtnted  either  in  the  motions  of  tho 
ud«r  ^tem,  or  the  oomets,  or  tbow  of  any  other  objecta  to  wbieh 
obsemtioii  baa  been  directed,  that  all  ooDJeotore  aa  to  the  sbjiMal 
flondition  of  the  masaes  cpf  Btara  wbicb  ooold  anmtne  mcb  foroiH 
would  be  vain.     The  number  of  inatanoes  aa  yet  detected,  in  which 

lia  form  prevaila,  is  not  great ;  bnt  it  is  sufficient  to  prove  that  the 

benomenon,  whateyer  be  ila  cause,  is  the  result  of  the  operation  of 
bJbm  geneikl  law.  It  is  pretty  oertain,  that  when  the  nme  powerfnl 
iiurtrQmeDts  which  have  rendered  these  forms  visible  in  objeota  which 
kad  already  been  ao  long  under  the  scmtiny  <^  the  most  eninent 
obserrers  of  the  last  hundred  years,  including  Sir  W.  and  Sir  J. 
Herschel,  aided  by  the  vast  tcleseopio  powers  at  their  disposition, 
without  raising  even  a  suspicion  of  their  real  form  and  strncinre, 
have  been  applied  to  other  nebulse,  other  casoi  of  tbe  $ame  pheno- 
menon will  be  brought  to  light.  Id  this  point  of  view  it  is  much  to 
be  regretted,  that  Ihe  telescopes  of  Lord  Rotwe  cannot  have  the  great 
advantage  of  being  used  under  skies  more- favourable  to  stellar  re- 
searches, since  the  discovery  of  euch  forms  as  these  not  only  requires 
instraments  of  such  power  as  Lord  Itosse  alone  possesses  at  present, 
but  also  the  most  favourable  atmospheric  conditions. 

6387.  Ki'jnher  of  n^iute.  —  The  numl«r  of  these  objects  is 
countless.  The  catalogues  of  Sir  J.  Hcrschel  contain  above  4000, 
of  which  the  places  are  assigned,  and  the  magnitudes,  forms,  and 
apparent  characters  described.  As  observers  are  multiplied,  and  the 
telescope  improved,  and  especially  when  tbe  means  of  observation 
have  Men  eitended  to  places  that  are  more  favourable  for  such 
observations,  it  may  be  expected  that  the  number  observed  will  be 
indefinitely  augmented. 

3388.  liemorkulk  nihvla.  —  Having  noticed  thus  briefly  the 
characters  and  appearances  of  the  principal  classes  of  these  object.', 
it  will  be  useful  to  illustiate  these  general  observations  by  referent 
to  eiamptca  of  nebula!  and  clusters  of  each  class,  assigning  the 
position  of  each  by  its  right  ascension  and  north  polar  distance,  and 
supplying,  wherever  it  can  be  done  on  satisfactory  authority,  a 
telescopic  view  of  such  object.  In  the  selection  of  these  example, 
it  will  be  one  of  our  chief  purposes  to  show  the  extraordinary  differ- 


f. 


^uLlir  I 


A  A. 


Tit  r 


XF.IU'I.J    AM-  (  !  ^^"TrJ1S 


D 

m 

H 

^^^M 

NEBUl^F.  ANI>  Cl.rsTKKS 


ASTRosoar. 

H,  llwt  villi  Huh  increue  of  opdrsl  powrr,  Ilic  ftrnctnre  of  tbii  objoet 

■•  iDOrc  conpliFklcd  and  more  unlike  anything  which  eoald  ba  miipoitd 

mnlt  of  liny  fnrni  of  dynnnicm!  lav  of  vhich  ve  End  ■  foooterpart  in 

re  b  not  (be  liut  donbl,  uid  which  a  repretenUd  in  the  aketch,  adJi, 

lord  GoHc'*  opinion,  if  pasEihle,  to  the  diffiioltj  of  rorming  an;  eoneeiTmbl* 
.Dtheiis.  That  inch  a  aytlem  ahoold  txiii  vitfaoDt  inlemal  moTemcnt,  he 
eidere  In  the  left  degree  imnrobsble.  Oat  eoDKplioii  ma;  ba  aided  bj 
.ling  *ilb  the  id«a  of  motion  tho  etfecti  of  a  refilling  loediiiin ;  but  it  ii  im- 
iHlbla  to  imagine  sneh  a  eystem,  in  anj  point  of  tiev,  ai  a  ate  of  m*re  alatinl 
inilibrium.  MeoanieiDeDta  he  IherefDre  conaiden  of  the  bigbeit  intcreet,  but 
.'  Kreat  diOlmlty. 
Plalo  XXITI.  fy.  I.— Thta  object  Ii  [ho  <19th  in  Mcirier'a  fatalDgne.  Tbe 
ral  form  of  the  nebula,  repreiented  in  Plata  XXTI.  /g.  1,  vat  disearered  by 


vala,  il  ie  not  mrprining  that  it  did  not  diaclafte  the  spir^  form  preanmad  to 
'ong  to  the  othen,  and  it  i>  cot,  therefore,  unreaaocabla  to  hope,  aocordiDg  la 
Lordiblp,  that  vhanevar  tba  tontbem  hamijphare  iball  ba  ro^iamlned  with 
tramenta  of  greater  mver,  Iheie  two  remarkable  nebulai  vill  jield  aoma  iaU- 
,„tiBK  reaulta. 
Lora  Koiaa  ha>  diaeoterad  other  ipiral  ntbnln,  but  Uttij  an  oompaiBtirel; 


iOKoatthod 

Plate  XXII. 

,&1; 

9' 

'  12-  .■!2'. 

■D   BT 

■■45' 

'.    Length, 

3'.— Tbi.  il 

lUr 

.ch. 

■ryb 

right  ■ 

ided  nebula. 

,  vitb  aa  ap- 

ond  nuc 

km. 

wli 

licb,  howi 

if  ver' 

F  f,iii 

'  Plate  XXII. 

^9.3.- 

-Th. 

line  ohjo, 

a  by 

Lord  Ron^i 

Thisul.jrttwiB"a"r>t  oi 

ed 

with  the  , 

great 

■ope, 

24ih  Mareb 

',  iS46.  «t*B 

■lar  . 

'pir«l  for 

ed.     On  the 

Bth  Sl.rvh, 

1818,  in  more  !< 

ivourabl 

^r,  tbe  cpi 

ral  f< 

^di8 

tinctlv  seen 

<oanoMi,|J 

1  nebula 

11  [iicolved,  pa 

rlicala 

rljl 

ovvd<  lb.  , 

>eQ(re,  wb.'re 

it  vas  very  hri 

gbt. 

Plato  XXII. 

V  *■ 

22' 

'  58"  28'. 

D  rs" 

36'. 

Length  r. 

breadth  :.»■: 

— Deembed  bj 

■SirJol 

inH< 

srfc 

■bel  aj  pr. 

pttyl 

■right 

and 

resnlvablo,  i 

ind  eiieadrJ 

ful  whether  the  form  waa  strietlj  spiral,  or  whether  it  were  not  more  propirrlj 

Plale'xXIIL /s-  2.  RA  1' 2J'"  ]5',  NPD  00°  31'.  Dimensions  uncertain, 
but  tbe  diffused  nehulio  estimated  aa  extending  through  15'.  — Tbia  object  hai 
been  tbe  subjert  of  obBcrTotJon  by  all  the  eminent  obacrvera.  Sir  John  Uer- 
aehel  doacribea  it  as  cnorniouBly  large,  groning  tery  gmdually  brighter  luwanla 
the  middle,  and  baving  a  star  of  the  12th  magnitude,  north,  rL.ilowing  the  nuelcus. 
and  being  charnelerised  by  irregularitiea  of  light,  und  even  by  feeble  suburdin.iii; 
nuclei  and  many  amall  starK.  Tbe  drawing  repreaenta  it  aa  aeon  with  tbe  in^r.' 
powerful  telcjcopo  of  Lord  Hojce.  A  tendency  to  a  apiral  form  waa  di-tinvilv 
leen  on  tbe  Bth,  [Dth,  and  16th  Septemlier,  UK.  The  brighieai  of  the  /\.m.i 
arms  vaa  that  marked  a,  that  marked  I  waa  pretty  bright,  but  short ;  0  was  .11'. 
tinet,  and  •,  only  euaperted ;  the  branch  y  waa  fhinl.  Tho  whole  object  was  in. 
TOlved  in  a  faint  nebulositv,  which  probably  eitenda  paat  several  knots  whi-li 
lie  about  it  in  different  direeliona. 

PlateXXIL/jr.  8,  Rir'U-SO'.  n  r  n  HO"  II'.— This  is  described  by  Sir 
John  Ilerai'hel  as  a  curiniis  bright  drmble  or  an  elongated  bieerlral  iietiuU. 

Plata  XXIL  M  T.-The  same  ohjeel         

SSd  Deceoiber,  liH.     K  brisbli  star  wai 


■■,IUI..K    .\.\l)   ri.rsTlJ 


'^^ 

0 

« 

B 

D 

^ 

• 

• 

«» 

>> 

uW 

STELLAR  CLUSTERS  AND  NEBULiB.  729 

taOa  and  cnrred  filaments  iBsned.    The  ezutenee  of  an  annolus  sarronndlng  the 
two  ncba1«  wu  suspected. 

Plate  XXIII.  Jig.  U.  R  A  11^  lO"  2-.  k  p  d  75°  59'.  Length  4'.— Described 
by  c^ir  Juhu  Ueracbel,  us  large,  elliptical  in  furin,  with  a  round  nucleus,  and 
growing  pra^Iuallj  brighter  towards  the  middle. 

Plai«  XXIII.  fiij.  3.  —  The  same  object  as  shown  by  Lord  Ro8so*s  telescope, 
ZliX.  March,  LSJS.  Described  as  a  curious  nebula,  nucleus  resolvable,  having  a 
r|>iral  or  annular  arrangement  about  it.  It  was  also  observed  with  the  same 
results  on  the  l:«t  and  .3d  April. 

Plate  XXIII.  Jig.  5.  K  A  IS"  1«  i1\  N  p  d  33°  35'.  Length  50",  breadth  . 
20".  —  This  nebula  was  not  figured  by  Sir  John  ilersohel,  but  is  described  by 
bim  as  an  object  very  bright,  and  growing  much  brighter  towards  the  middle. 
The  drawing  Jig.  b,  represents  the  object  as  seen  in  Lord  Rosse's  telescope,  in 
April.  1848.  It  is  described  by  Lord  Rosse  as  a  very  bright  resolvable  nebula, 
but  that  none  of  the  component  stars  could  be  distinctly  seen  even  with  a  mag- 
nifying power  of  1000.  A  perfectly  straight  longitudinal  division  appeu's  in  the 
direction  of  the  major  axis  of  the  ellipse.  Resolvability  was  strongly  indicated 
towards  the  nucleus.  According  to  Lord  Rosso,  the  proportion  of  the  mfgor 
axis  to  the  minor  axis  was  8  to  1 ;  much  greater  than  the  estimate  of  Sir  John 
Herschel. 

PUteXXIIL^?^.  10.  R  A  12"  3.3- 54*.  h  p  d  50°  30'.— Described  by  Sir  John 
Herschel  as  a  nebula  of  enormous  length,  extending  across  an  entire  field  of  15', 
the  nucleus  not  being  well  defined.  It  was  preceded  by  a  star  of  the  tenth  mag- 
nitude, and  that  again  by  a  small  faint  round  nebula,  the  whole  forming  a  fine 
and  very  curious  combination. 

Plato  \X\\l.Jig.  4. — The  same  object  as  shown  by  Lord  Rosse's  telescope  on 
19th  April,  1849.  The  drawing  is  stated  to  be  executed  with  great  care,  and  to 
b«  Tory  accurate.  A  most  extraordinary  object,  masses  of  light  appearing 
through  it  in  knots. 

PUte  XXIL  Jig.  10.  r  a  C*"  29-  53*.  H  p  D  81®  7'.  —  Described  by  Sir  John 
Herschel  as  a  star  of  the  12th  magnitude,  with  a  bright  cometio  branch  issuing 
from  it,  fiO"  in  length,  forming  an  angle  of  60°  with  the  meridian,  passing  through 
it.  The  star  is  described  as  ill  defined,  the  apex  of  the  nebula  coming  exacUy 
np  to  it,  but  not  passing  it. 

Plate  XXIL  Jig.  9.  —  The  same  object  as  seen  with  Lord  Rosse's  telescope  on 
16th  January,  1850.  Lord  Rosse  observed  that  the  two  comparatively  dark 
spaces,  one  near  the  apex  and  the  other  near  the  base  of  the  cone,  are  very 
remarkable. 

Plate  XXIL  Jig.  12.  r  a  ll"  4-  49*.  k  p  d  34°  3'.  Diameter  19"  time.  —  De- 
■eribed  by  Sir  John  Herschel  as  a  large  uniform  nebulous  disk,  very  bright  and 
perfectly  round,  but  shar]ily  defined,  and  yet  very  suddenly  fading  away  into 
darkness.     A  most  extruordiuMry  object. 

Plate  XXII.y?(jr.  11.  —  The  same  object  as  shown  by  Lord  Rosse's  telescope. 
Two  stars  coni<iderably  apart,  seen  in  the  central  part  of  the  nebula.  A  dark 
penombra  around  each  spiral  arrangement  with  stars  as  apparent  centres  of  at> 
traction.  Stars  sparkling  iu  it  and  in  the  nebula  resolvable.  Lord  Rosse  saw 
two  large  and  very  dark  spots  in  the  middle,  and  remarked  that  all  around  its 
tdge  the  sky  appeared  darker  than  usual. 

Plate  XXIILyi^.  11.  r  a  7"  34-  2-.  n  p  d  101°  20'  25".  Diameter  3*75"  time. 
—  Described  by  Sir  John  Herschel  as  a  planetary  nebula,  of  a  faint  equal  light, 
and  exactly  round,  having  a  very  minute  star  a  little  north  of  the  centre.  Very 
Telrety  at  the  edges.  In  the  telescope  of  Lord  Rosse,  however,  it  appears  as  an 
annular  nebula  as  represented  in  the  figure,  with  two  stars  within  it. 

PlatoXXIIL^*/.  7.  RA23M7-42-.  npd48°  24' 24".  Diameter  12".— Fig- 
ure*! by  Sir  John  Herschel.  who  describes  it  as  a  fine  planetary  nebula.  With  a 
power  of  240  it  was  beautifully  defined,  light,  rather  mottled,  and  the  edges  the 
least  in  the  world  unshaped.  It  is  not  nebulous,  but  looks  as  if  it  had  a  double 
outline,  or  like  a  star  a  little  out  of  focus.     It  is  perfectly  circular. 

Plate  XXIII. /y.  6.  —  The  same  object  as  shown  in  Lord  Rosse's  telescope, 
16tb-19th  Deeember,  1843.    A  central  dark  spot  surrounded  by  a  bright  anuulus. 

Plate  XXIII.  jfiij,  9.    It  A  20''  54-''  b\    m  p  d  102"  2'  46".    Diameter  10"  to  12" 


ASTROS  OMT. 

■Slo  Hrndiil,  but  ii"  hj  V 
m.  —  Tbb  tgare  ii  tbat  gWr 

laneiary  oebaln  wiih  equable  lEj^bt  *D<]  blufish  irbiM  poIod 
^XXUL^S- 8.  — The  iBioeoI'  '  ■      •      ■- 

■  ilobo  turroundod  bj  a  ring  ii 
—  pUii*  of  the  riag. 

oXSIU./^.  13.    n»r«10-8*.    it»n  eS-'W. - 
lel  u  a  (iw  eiuU;  in  Ibi:  centre  of  ■  bright  ci  , 

.ler,  tba  tuu  bcbg  qaiUi  stellar,  anil  not  a  mete  ducIciu,  and  i«  a  moti 
-'■'"  object. 

iXllLfig.  12.  — The  tome  nljcct  a*  Bhotrn  bj  Lord  Rojte'i  tdorwpa 

»  •  rebruatj,  18*9  ;  de.cribed  by  btm  ai  a  moel  ailoniibiDg  gbJecL    It  iru 

■I  la  JsDUirjr,  IBSO,  with  power*  of  700  aoil  900,  wbso  both  Ibe  duk 

ht  ringa  «e«Tn«l  Dnnual  la  brosiltli. 

-  XXIlI  yly.  IS.    Ria'2T-T'.    BPn9fl''!'lB".  — The  (tari  OrioBifin- 

1  a  feeble  oebula  3'  In  diameter.    (Sir  J.  HencheL)    Xbe  dtaoing  abowi 

MD  with  Lord  RoisD'a  telcicope. 

MXXfig.3.    ail9'52-13-.    Bpn  67"  «'— Drawn  by  Sir  John  Hemhrt, 

deicrihea  it  aa  a  nebula  thaped  tike  k  dumb-bell,  double-headed  ihol,  or 

^-glaaa,  the  elliptia  outline  being  Dompleted  by  a  more  feeble  nebuloai  Itflii. 

Blii  of  ajmmelry  tfarangh  Ibo  cenlroa  of  the  two  cblef  malxea  iacliDHl  It 

»  the  meridian.     Diameter  ot  elliptie  light  bom  V  to  $'.     Not  teeuliaUf, 

four  atua  aie  riaible  on  it  of  the  13th,  lllb,  Aid  Utb  magDitnde.    Tba 

thero  bead  la  denaer  than  the  northern.     Tbii  extnotdlnat;  abject  wa*  alu 

nrad  by  6ir  W.  Benehel,  who  reoognlied  the  auna  penuliar  form.    Gii  J. 

lobel  eonaidara  that  tba  moat  remarkable  dronmHanoea  atUmdiDg  it  ia  Iba 

veru  Ibcm  into  protubcrnnccs,  bo  hs  Iu  renJer  llieKtoIeooliine  a  regular  ellipjt, 
having  for  ita  ahurter  axia  the  enmrnoo  aiia  ot  Iho  two  bright  mnstea.     If  it  be 

that  eaie,  be  con-'idera  thol  ila'reni  form  must  be  Ibet  of  an  oblate  rphereid;  and 

tbia  auppoeilion  n-ouUI  not  be  inrompalible  Kilh  ilTnamieal  Uwa,  at  leait  sup. 
poiing  its  parte  to  bo  eapsble  of  eierling  preasure  on  eaeh  other.  But  if  it  rod- 
aiit  of  diaiinct  ttaa  this  cnnnut  be  admilKil.  ami  nc  murt  Ihen  bsve  reeourje  la 
other  euppositiena  lo  neeouni  for  the  mainteuanro  of  iu  furm.  Sir  John  Jler- 
■ehel,  It  will  be  observed,-  failed  to  resalre  this  nrbnla. 

Plate  XXIV.  yV-  1.— The  nme  object  na  Ehnirn  by  the  telescope  of  Lord 
BoHe,  three  feet  aperture,  tweuty-seven  feet  focsl  lensib. 

Plate  XX.fy.  1.— The  Jnme  objoet  us  shown  with  (he  great  Iclescope  of  Lord 
BoBse,  six  feet  aperture.  Gfly-lbree  feet  focnl  length. 

The  diHerenee  hetiaecn  lhc«e  tno  repreaentmions  end  that  given  by  Sir  Jehu 
Herachel  of  the  snme  object,  »ill  illuslrnle  in  a  Tcry  slriking  manner  the  ob»r- 
TOtioni  already  made  on  the  eflecia  uf  different  mn^nifying  and  defining  powen 
upon  the  appearance  of  the  object  under  eiaminaliun.  The^e  Ihreo  figures  coold 
■eareety  be  conceived  to  be  reprcsentaliODS  of  the  rsnie  object. 

To  explain  the  difference  obser>'iible  between  the  draning,  PUte  XXIT.7!^.  1., 
made  with  the  smaller  leleseope,  and  tbe  drnwinp,  Plate  XX.  Jig.  I.,  made  with 
the  larger  instrument,  Lord  Rosse  obeerrea.  that  while  the  application  of  a  high 

pteiely  eilingiiiabea  nehuloiily  which  the  loner  power*  render  viaible.  The 
optical  rro^nn  for  this  wilt  b«  eacily  perceived ;  the  eircumalance  was  neverthe- 
leaa  nverlonkcd  when  the  obsorvatiana  were  made  from  wbieh  the  drawing,  PUI* 
XXIV.  yfy.  1.  Km  Uiken.  Only  on.-  mngnlMng  |...iver,  and  that  a  wry  hifih  one, 
waa  used  on  that  ocenslon,  the  ron~e(|Ui'nce  of  vbirh  «a=  Iliet,  although  Ihe  two 
huoba  of  the  dumb-brll  were  more  full)-  rcxokei).  iho  nebulous  manor  filling  the 
InierincdiHte  »[.Hce,  which  Hcrirhel  considered  tu  be  the  moel  remarliable  feature 
of  this  nebula,  was  entirely  eillnguiehed  in  the  opiical  image.  If  on  that  occa- 
■ioD  a  second  eye-]i<ece  had  been  ueed  of  lower  power,  the  inlermediata  nebnloai 
UtUet  VODld  h&ve  beeik  teen,  aa  repreaanted  in  Ihe  drawiug,  and  the  drawing 


STELLAR  CLUSTERS  AND  NEBULfi.  781 

Vkonld  b«  u  perfect  as,  aod  nearly  idenUcal  with,  that  obtained  with  the  greater 
telescope,  Plate  XX.  fig,  1.,  a  lower  power  being  tired. 

It  will  be  observed  that  the  genend  outline  of  this  remarkaMe  object  which  is 
BO  geometrically  exact  as  seen  with  the  inferior  power  uiied  by  Sir  John  Hervchcl, 
is  totally  effaced  by  the  applicaUon  of  the  higher  powers  uned  by  Lord  Roesc, 
and  consequently  Sir  John  Herschel's  theoreUeal  speculations  based  upon  this 
pMticuiar  form,  must  be  regarded  as  losing  much  of  their  force,  if  nut  wholly 
iuadmiii«ible ;  and  this  is  an  example  proving  how  unsafe  it  is  to  draw  any  the- 
oretical inferences  from  apparent  peculiarities  of  form  or  structure  in  the.«e 
objects,  which  may  be  only  the  effect  of  the  imperfect  impressions  we  receive  of 
tbcm,  and  which,  consequently,  disappear  when  higher  telescopic  powers  are 
applied.  The  cai>e  of  the  nebula  represented  in  Plato  XXII. y?^«.  1.  and  2.  prc- 
senLii  nnolhor  striking  example  of  the  force  of  these  observations. 

PI«teXX.y»^.4.  R A  8* 47- 13-.  HPD57*>ir.  — This  object,  drawn  by  Sir  J. 
llenrchel,  \a  the  annular  nebula  between  0  and  /  Lyrae.  Ho  estimates  its  diam- 
eter at  tt-5"  B  A.  The  annulus  is  oval,  its  longer  axis  being  inclined  at  67°  to  the 
meridian.  The  central  vacuity  is  not  btackf  but  filled  wilh  a  nebulous  light. 
The  edges  are  not  sharply  cut  off,  but  ill  defined;  they  exhibit  a  curdled  and 
confused  appearance,  like  that  of  stars  out  of  focus.  Ue  considers  it  not  well 
represented  in  the  drawing. 

Plate  XX.fijf.  2.  —  The  same  object  as  shown  in  tho  telescope  of  Lord  Rossc. 
This  drawing  was  made  with  the  smaller  telescope,  three  feet  aperture,  before  the 
great  telescope  had  been  erected.  The  nebula  was  observed  seven  times  in  1848, 
and  once  in  1849.  With  the  large  telescope,  the  central  opening  showed  con- 
siderably more  nebulosity  than  it  appeared  to  have  with  the  smaller  instrument. 
It  was  also  noticed,  that  several  small  stars  wero  seen  around  it  with  the  large 
instrument,  which  did  not  appear  with  the  smaller  one,  from  which  it  was  inferred 
that  the  stars  seen  in  the  dork  opening  of  the  ring  may  possibly  be  merely  acci- 
dental, and  have  no  physical  relation  to  the  nebula.  In  the  annulus  near  the 
eztremity  of  the  minor  axir.  several  minute  stars  were  visible. 

Plate  XX.  fig.  5.  r  A  13^  28-  63-.  k  p  d  107°  0'  50".  Diameter  of  faint  nebula, 
T.  Diameter  of  bright  part,  lU"  or  15".  —  Described  as  a  faint  large  nebula 
losing  itself  quite  imperceptibly;  a  good  type  of  its  class.     (Uerschel.) 

Plate  XX.  fig.  7.  r  a  1 7"  44-  42-.  k  p  d  66°  52'  41".  Perceptible  disk  1",  or 
l*y  diameter.  Surrounded  by  a  very  fuint  nebula. — A  curious  object.  (Iler- 
scbel.) 

Plate  XX.  fig.  8.  r  a  19"  40m  19-.  ^  p  ]>  390  54'._-A  most  curious  object  A 
star  of  the  11th  magnitude,  curroundcd  by  a  very  bri;;ht  and  perfectly  round 
planetary  nebula  of  uniform  light  Diameter  in  R  A  3*5",  perhaps  a  very  little 
nasy  at  the  edges.     (Ilerschcl.) 

Plate  XX.  fig.  9.  r  a  10"  28"  7'.  n  p  d  35°  36'  32".— A  bright  round  nebula, 
forming  almost  a  disk  15"  diameter,  surrounded  by  a  very  feeble  atmosphere. 
(HeraebeL) 

8889.  Larffi"  and  irrfgular  nebulas.  —  All  the  nebulae  described 
above,  are  objects  generally  of  regular  form  and  subtending  small 
▼isoal  angles.  There  are  others,  however,  of  a  very  different  cha- 
racter, which  cannot  bo  passed  without  some  notice.  These  objects 
cover  spaces  on  the  firmament,  many  nearly  as  extensive  as,  and 
Bome  mnch  more  extensive  than,  the  moon's  disk.  Some  of  them 
have  been  resolved.  Of  those  which  are  larger  and  more  diffused, 
Bome  exhibit  irregularly  shaped  patches  of  nebulous  light,  affecting 
forms  resembling  those  of  clouds,  in  which  tracts  arc  seen  in  every 
stage  of  resolution,  from  nebulosity  irresolvable  by  the  largest  and 
most  powerful  telescopes,  to  stars  perfectly  separated  like  parts  of 
the  milky  way,  and  "clustering  groups  suflBciently  insulated  and 
coDdensed  to  come  under  the  designation  of  irregular  and,  in  some 


ASTROKOMT. 

iTi        II     clusters,    But,  besidce  these,  tlicic  arc  also  deIioIs 

mliiice,  ™>th  regnlar  acd  irregular;  globular  clostere  in  eTery 

uf  CI  sstioD,  and  objects  af  a  nebnlons  cliaracter  qaite 

lare  do  analogy  in  auj  other  psrt  of  the  heavens. "* 

.  ..'uiMr  in  fhe  Centaur. — Tlic  staruCentauri  presents 

ui   voe  moat  striking  examples  of  the  claes  of  large  diffused 

a.      It  U  oearlj  round,  and  bas  an  apparent  diameter  e()a»I 

-thirds  of  that  of  the  moon.     This  remarkable  object  was 

irfd  in  Mr.  Dunlop's  catalogue  fPbil.  Trans.  182!*) ;  but  it  is 

erfatidDS  of  Sir  John  Ilerscbel,  at  the  Cape,  that  the 

».  its  splendid  character  is  deriTiHl.     That  aatronnmrr 

—  it,  beyond  all  comparison,  the  richest  and  largest  object 

'  in  the  heavens.     The  stars  eotopri^iag  it  are  litcrall; 

;    and  as  their  collective  light  affects  the  eye  haidlj 

-<a  iiiiiii  ihat  of  a  star  of  the  fifth  mngriitude,  the  niiouteneu  of 

of  ibcm  may  he  imagined.     The  apparent  magoitude  of  llib 

t  is  eucb  that,  when  it  was  com-cntric  with  the  field  of  Sir  J. 

^hel's  '20  ft.  telescope,  the  straggling  stars  at  the  edges  wen 

od  the  limit  of  the  field.     In  stating  that  the  diameter  is  two- 

Is  of  the  moon's  disk,  it  must  be  Qnderstood  to  apply  to  ibe 

oiaioc^l*T  of  the  conJeneed  clusler,  ntnJ  nut  to  iocludc  the  straggling 

atars  at  the  edges.     When  the  centre  of  the  cluster  was  brought  to 

the  edge  of  the  field,  the  outer  stars  extended  fully  half  a  radius 

beyond  the  middle  of  it.f 

The  appearance  of  this  magnificent  object  resembles  that  shoira 
in  Plate  XXI.  Ji'j.  1,  only  (hat  the  stars  are  much  more  den^'l; 
crowded  together,  and  the  outliuc  more  circuhr,  indicating  a  prcll; 
cxaol  globe  as  the  real  form  of  the  mass. 

33fll.  The  great  nebula  in  Oriun. — The  position  of  this  citn- 
ordiuary  object  is  in  the  sword-handlc  of  the  figure  vchieh  forms  tLc 
constellation  of  Orion.  It  consists  of  irregular  eloud-shapcd  ucliu- 
luus  pat<:iiea,  extending  over  a  surface  about  40'  square ;  that  is, 
one  whose  apparent  breadth  and  height  exceed  the  apparent  diamt'- 
tcr  of  the  moon  by  about  one-third,  and  whose  superficial  magoiiude 
is,  therefore,  rather  more  than  twice  that  of  the  moon's  di,«k. 
Drawings  of  this  nebula  have  been  made  by  several  observers,  abJ 
engravings  of  tberu  have  been  already  published  in  various  works, 

Jq  Plate  XXI  V./y.  2  is  given  a  representation  of  the  central  furt 
of  this  object.  The  portion  here  represented  measures  25'  in  beigbt 
and  25'  in  breadth;  a  height  and  breadth  about  one-sixth  less  Ibua 
the  diameter  of  the  moon.  An  engraving  upon  a  very  large  sctiK-, 
of  the  entire  extent  of  the  nebula,  with  an  indication  of  the  various 
stars  which  serve  as  a  sort  of  landmarks  to  it,  may  be  seen  by  ref^- 

*  Usracliel,  Outlines  of  Astroaom;,  p.  613. 


"-''-- Ui!' ;,■;.; 


..!■;   AND  CLl-STKltJ 


STELLAR  CLUSTERS  AND  NEBULiB.  733 

rence  to  Sir  J.  Herschers  *'  Cape  ObsenratioDs/'  accompanied  by 
tbe  iDteresting  details  of  his  observations  npon  it. 

Sir  J.  Herscbel  describes  the  brightest  portion  of  this  nebnia  as 
resembling  the  head  and  yawning  jaws  of  some  monstrous  animali 
with  a  sort  of  proboscis  running  out  from  the  snout.  The  stars 
scattered  over  it  probably  have  no  connection  with  it,  and  are  doubt- 
less placed  much  nearer  to  our  system  than  the  nebula,  being 
visually  projected  upon  it.  Parts  of  this  nebula,  when  submitted 
to  the  powers  of  Lord  Eosse's  telescopes,  show  evident  indications 
of  resolvability. 

3392.  T?ie  great  nebula  in  Argo. — This  is  an  object  of  the  same 
class,  and  presenting  like  appearances;  it  is  diffused  around  the 
star  fi  in  the  constellation  here  named,  and  formed  a  special  subject 
of .  observations  by  Sir  J.  Ilerscbel,  during  his  residence  at  the 
Cape.  An  engraving  of  it  on  a  large  scale,  giving  all  its  details, 
may  be  seen  in  the  '^  Cape  Observations."  The  position  of  the 
centre  of  the  nebuk  is,  R  A  10°  38'  38",  n  p  d  148°  47'. 

This  object  consists  of  diffused  irregular  nebulous  patches, 
extending  over  a  surface  measuring  nearly  7'  Ttime)  in  right  ascen- 
sion, and  68'  in  declination ;  the  entire  area,  tnerefore,  being  equal 
to  a  square  space,  whose  side  would  measure  one  degree.  It 
occupies,  therefore,  a  space  on  the  heavens  about  five  times  greater 
than  the  disk  of  the  moon. 

A  part  of  the  nebula  immediately  surrounding  the  central  star  is 
represented  in  Plate  XXV.  The  space  here  represented  measures 
about  one-fourth  of  the  entire  extent  of  the  nebula,  in  declination, 
and  one-third  in  right  ascension,  and  about  a  twelfth  of  its  entire 
magnitude. 

No  part  of  this  remarkable  object  has  shown  the  least  tendency 
to  resolvability.  It  is  entirely  compressed  within  the  limits  of  that 
part  of  the  milky  way  which  traverses  the  southern  firmament,  the 
stars  of  which  are  seen  projected  upon  it  in  thousands.  Sir  J. 
Herschel  has  actually  counted  1200  of  these  stars  projected  upon  a 
part  of  this  nebula,  measuring  no  more  than  28'  in  declination,  and 
32'  in  richt  ascension,  and  he  thinks  that  it  is  impossible  to  avoid 
the  conclusion,  that  in  looking  at  it  we  see  through  and  beyond  the 
milky  way,  far  out  into  space  through  a  starless  region,  disconnect- 
ing it  altogether  with  our  system. 

3393.  Magellanic  cloiuls.  —  These  are  two  extensive  nebulous 
patches  also  seen  on  the  southern  firmament,  the  greater  called  the 
nubecula  major,  being  included  between  R  A  4^  40'",  and  6^  0"  and 
N  P  D  156°  and  162°,  occupying  a  superficial  area  of  42  square 
degrees ;  and  the  other  called  the  nti5ecii/a  minor,  being  included 
between  ra  0'  21'"  and  l**  15"  and  between  npd  162°  and  166®, 
covering  about  10  square  degrees. 

These  ncbuUs  consist  of  patches  of  every  character,  some  irre- 
m.  62 


^ 


^t4  AETROKOUT. 

BoWable,  and  others  resolvable  m  nil  degrees,  and  mixed  with  eln»- 
tcrs ;  in  fine,  baving  all  the  ehBracIcrs  alreaijj  explained  in  ilia 
WMS  of  Ihc  largo  diffused  ncbulce  described  above.  So  great  u  tlie 
number  of  distiuct  acbuliB  and  elostcn  crowded  together  ifi  then 
;  tnicla  of  the  Grinainent,  that  278,  besidea  50  or  60  oatlien,  li»\n 
Wn  enumeraled  by  Sir  J.  Hersobcl,  within  iheuMOf  tfa*Bvbcra!> 
major  aloae. 


CHAP.  XXX. 

NOTICES  0¥  RKMARKABI.E  AfiTaoNOMtCAL  IKBTROMEirrH. 

3304.  (^amjimli'/n  <>/ the  in^rvmenU  of  t^amatiOH.  —  In  llie 
nxth  ChapUtr  of  this  buuk,  an  ei))lanalion  of  tL«  priltai^e  of  lh« 
COD  struct!  on,  the  ferm,  and  applicalioo  of  the  mart  Decern^  in»tni- 

,iDeDts  of  so  obserratorj,  is  given,  anch  as  vis  deemed  nffielbiit  to 

.nnder  iotelUgible  tte  sDcceeding  parts  of  the  vod.  Tbs  inttra- 
'  jineota  lelecled  for  that  purptne  were  those  wfcidk  dtoBBfl  best 
-    adapted  to  illuatrnle  tha  theoretical  principles  afterwattls  developed, 

.  aod  to  bbow,  ia  l!ie  Diost  simple  manner,  the  mode  in  which  tbe 
various  data  oa  whieli  tlicse  principles  rest  were  obtained.  It  wu 
thought  more  coeducive  to  the  progress  of  the  student  to  postpone 

,the  exposition  of  other  instrnmeiila  of  observation  until  43»  import- 
ance and  ma^itude  of  the  results  attained  b;  them  ocnJd  be  more 
adequalelj  appreciated,  and  the  principles  of  their  stniotuie  and 
mechauiani  more  clearly  comprehended. 

We  shall  now,  therefore,  conclude  this  volnme  with  a  sliort  nctit.'e 
of  some  of  the  most  generally  useful  and  some  of  the  moat  remark- 
able iuBtrumeDla  of  astronomical  observation,  including  the  mntt 
important  of  those  recently  erected  in  different  eoantriea,  ud  some 
which  have  been  rendered  memorable  by  the  uses  to  which  thcj 
have  been  subeervtent.  If  we  omit  some,  more  especially  those  in 
observatories  erected  and  conducted  at  the  charge  of  prints  iodi- 
viduuls,  it  is  from  no  undue  sense  of  their  value  and  importanct-, 

.nor  from  any  diMoclinatJon  to  sward  the  praise  due  to  the  spirit 
which  has  prompted  such  dorotion  of  lime  and  fortune  lo  tbe  i<J- 
vanccnient  of  the  noblest  of  the  sciences,  but  from  tbe  necesEJij 
under  which  lie  objects  and  purposes  of  this  work  place  US  to  con- 
fine it  within  certaiu  limits  of  bu]i. 

All  astronomical  observaUon  is  limited  either  te  asoeitehi  tbe 
magnitudes,  forms,  and  appearwice  of  celestial  objecta,  or  to 
determine  the  places  they  occupy  at  any  given  moment  on  tbe 
firmament. 

To  attain  l^e  foT<m«  nb^oct,  telescopea  are  constmoted  with  tbs 


RXMABKABLB  A8TB0N0MI0AL  IK8TRUMSKTS.  786 

greatest  practioable  magnifying  and  illaminating  powen,  and  so 
mounted  as  to  enable  the  observer  with  all  the  requisite  facility  to 
present  them  to  those  parts  of  the  heavens  in  which  the  objects  of 
his  observation  are  placed. 

To  attain  the  latter,  it  is  necessary  to  provide  an  apparatus  by 
which  the  direction  of  the  visual  line  of  the  object  of  observation 
relatively  to  some  fixed  line  and  some  fixed  plane  can  be  ascertained. 
The  visual  line  being  the  straight  line  drawn  from  the  eye  of  the 
observer  to  the  object,  at  the  moment  of  the  observation,  and  having, 
therefore,  no  material  tangible  or  permanent  existence,  by  which  it 
can  be  submitted  to  measurement,  it  is  necessary  to  contrive  some 
material  line  with  which  the  visual  line  shall  ooindde.  The  tele^ 
scope  supplies  an  easy  and  exact  means  of  accomplishing  this. 
When  it  is  directed  so  that  the  object  or  its  centre,  if  it  have  a  disk, 
is  seen  unon  the  intersection  of  the  middle  wires  in  the  eye-piecOi 
the  visaal  direction  of  the  object  is  the  line  drawn  from  the  centre 
of  the  object-glass  of  the  telecsope  to  the  intersection  of  the  middle 
wires. 

Now  the  telescope  being  attached  to  a  graduated  circle  is  so 
placed,  that  the  line  joining  the  centre  of  the  object-glass  with  the 
intersection  of  the  wires  is  parallel  to  a  diameter  of  the  circle.  This 
diameter  will,  therefore,  be  the  direction  of  the  visual  line.  If  the 
circle  thus  arranged  be  so  mounted  that  a  line  drawn  from  the 
observer  to  the  fixed  point  of  reference,  whatever  that  point  be, 
shall  be  parallel  also  to  a  diameter  of  the  circle,  and  if  the  circle  be 
so  mounted  that,  however  its  position  may  otherwise  be  changed, 
one  of  its  diameters  shall  always  pass  through  the  fixed  point  of 
reference,  the  angular  distance  of  the  object  of  observation  from  the 
fixed  point  of  reference  will  always  be  equal  to  the  angle  formed  by 
the  two  diameters  of  the  circle,  one  of  which  is  parallel  to  the  line 
joining  the  centre  of  the  object-glass,  with  the  intersection  of  the 
wires  at  the  moment  of  the  observation,  and  the  other  parallel  to 
the  line  drawn  from  the  observer  to  the  fixed  point  of  reference. 

But  this  is  not  yet  enough  to  determine  in  a  definite  manner  the 
position  of  the  object  on  the  heavens.  A  great  many  different  ob- 
jects may  have  the  same  angular  distance  from  the  fixed  point  of 
reference.  If  a  plane  be  imagined  to  pass  at  right  angles  to  a  line 
drawn  from  the  observer  to  the  fixed  point  of  reference,  it  will  inter- 
sect the  celestial  sphere  in  a  certain  circle,  every  point  of  which  will 
obviously  be  at  the  same  angular  distance  from  the  point  of  refe- 
rence. To  render  the  position  of  the  object  of  observation  determi- 
nate, it  is  therefore  necessary  to  know  the  position  of  the  plane  of 
the  graduated  circle,  with  relation  to  a  circle  whose  plane  is  at  right 
angles  to  that  diameter  of  the  celestial  sphere  which  passes  through 
the  fixed  point  of  reference. 
The  plane  of  the  graduated  sircle  may  be  fixed  or  moveable.     If 


ASTBONOHS. 

la  position  with  relation  to  tlio  fiied  poiot  of  reference  in 
ned  oneo  for  all ;  after  which,  the  position  of  the  object  of 
ration  will  be  determined  merely  by  its  angolar  diatanee  froai 
loint  of  reference.  If  moveable,  it  is  necessary  to  provide 
ir  graduated  circle,  tile  plane  of  which  ia  pcrpendicnlar  to  iha 
iDd  upon  nbicb  sotdc  fixeJ  direction  is  maiked.  The  poeitioo 
ne  plane  of  (be  moveable  circle,  which  carries  the  telescope, 
relBtion  to  this  latter  fixed  direction,  is  then  ascertained  by  tba 
f  the  second  Eradoated  circle,  which  is  included  between  the 
eable  i^rcle  and  such  fixed  directkon. 

11  instruments  of  observation  for  determining  the  position  of 
3t8  on.  the  celestial  sphere  &ro  constructed  and  mounted  on  one 
ther  of  these  principles;  and  they  differ  one  from  another  ia 
•wt  to  the  point  adopted  as  the  fixed  point  of  reference,  and  the 
(  at  right  angles  to  the  diameler  of  the  sphere  passing  through 
point  with  relation  to  which  tho   position  of  the  circle,  if  it  he 
liable,  is  delenniued. 
•  be  fixed  point  of  reference  is,  in  all  cases,  either  the  lenitfi  or 
pole;  tm  the  plane  of  refeiiesee,  ooiuequeDtly,  either  that  of 
boriEon  or  the  e<giiator. 
>Vhen  the  plane  of  the  graduated  circle  carrying  the  telescope  is 
filed,  it  is  almost  inrariubly  that  of  the  meridian,  but  in  certain  ie- 
etancea  the  circle  has  been  fixed  in  the  vertical  piano  at  right  angles 
to  the  meridian,  that  is  to  say,  in  the  plane  of  the  prime  vertical. 

It  will  be  obvious  that  the  mural  circle  (2407)  and  the  liansit 
(23i)7)  arc  meridional  instruments. 

When  the  fised  poiot  of  reference  is  the  zenith,  and  the  ^Ju- 
aled  circle  is  moveable,  the  immediate  results  of  the  observations 
made  with  the  instrument  arc  the  zenith  distance  or  altitude  aail 
the  azimuth  of  the  object  observed.  Such  instrumcnls  are,  conse- 
quently, denominated  altitude  and  azimuth  circles,  or  altazi- 

MUTH  INSTBUMESTS. 

When  the  fiicii  point  of  reference  is  the  pole,  and  the  graduated 
circle  is  moveable,  the  immediate  results  of  the  observations  mide 
with  the  instrument  are  the  polar  distance  or  declination  and  the 
right  ascension  of  the  ol^ect  observed;  and  the  motion  of  the  in- 
strument being  parallel  to  the  celestial  equator,  it  is  called  an  EQL"i- 
TORiAi.  (2336). 

These  general  principles  being  understood,  we  shall  give  a  few 
examples  of  each  class  of  instrument,  commencing  with  those  which 
are  adapted  to  the  investigation  of  tho  magnitude,  appearance,  and 
structure  of  the  celesliiil  objects,  without  reference  to  their  exact 
positinn  in  the  drniamcaf. 

3895.  Sir  Yi\  Hrrs>-heri  foTfij.frHrfficoli.T.  —  This  instrument, 
which  is  memorable  as  the  hrst  ever  constructed  iipnn  a  sc.ile  of 
BUch   stupendottft  inagn\l\i4ej  md  still  more  so  for  the  vast  discove- 


THE  BFlv  y~,.^ 


SIR  W.  UERSCIIEL'S  GREAT  TELESCOPE. 


Fwx(  (.,i.,rt  411/    AjHr;ii,-  ij: 


TU£  LESSER  R088E  TELESCOPE. 


Focal  Uiigth  27/    Aperiurt  3/ 


REMARKABLE  ASTRONOMICAL  IKSTRUMENTS.  787 

lies  made  with  it  by  its  illustrious  inventor  and  constnictor,  is  re- 
presented in  Plate  XXYII.  It  will  be  seen  in  the  drawing  that 
the  instrument  is  mounted  on  a  platform  which  revolves  in  azimuth 
on  a  series  of  rollers.  The  telescope  is  placed  between  four  ladders, 
which  serve  the  double  purpose  of  a  framework  for  its  support  and 
a  convenient  means  of  approaching  the  superior  end  of  the  great 
tube.  These  ladders  are  united  at  the  top  by  being  bolted  to  a 
cross  bar,  to  which  the  pulleys  are  attached.  By  one  system  of 
pulleys,  the  telescope  is  raised  or  lowered ;  and  by  another  the  gal- 
lery or  balcony  in  which  the  observer  stands  is  also  raised  or  low- 
ered, so  as  to  enable  him  to  look  into  the  tube.  These  pulleys  are 
each  worked  by  a  windlass  established  on  the  platform  below.  The 
framing  is  strengthened  by  another  system  of  diagonal  ladders,  as 
well  as  various  masts  and  braces  which  appear  in  the  figure.  The 
telescope  is  so  mounted  that  it  can  be  raised  until  its  axis  is  vertical, 
80  that  an  object  in  the  zenith  can  be  observed  with  it.  The  ob- 
server's gallery  rests  in  grooves  upon  the  ladders,  and  slides  up  and 
down  easily  and  smoothly  by  the  operation  of  the  pulley,  so  that 
when  the  telescope  tube  is  elevated,  even  to  the  zenith,  the  observer 
can  ascend  and  descend  at  pleasure  by  signals  given  to  the  man  at 
the  windlass.  A  small  staircase  is  placed  near  the  foot  of  one  of 
the  principal  ladders,  by  which  observers  can  mount  into  the  gallery 
when  it  is  let  down  to  its  lowest  point 

The  total  length  of  the  telescope  tube  is  39  ft.  4  in.,  and  its  clear 
diameter  4  ft  10  in.  It  is  constructed  entirely  of  iron.  The  great 
speculum  is  placed  in  the  lower  end  of  the  tube,  the  apparatus  for 
adjusting  it  being  protected  by  the  wooden  structure  which  appears 
in  the  figure.  The  diameter  of  the  speculum  is  4  ft,  and  the  mag- 
nitude of  its  reflecting  surface  is  consequently  12*566  square  feet 
It  contains  1050  lb  of  metal. 

The  axis  of  the  speculum,  when  placed  in  the  tube,  is  so  inclined 
Co  the  tube  that  its  focus  is  at  about  two  inches  from  the  lower 
edge  of  the  upper  mouth  of  the  tube,  so  that  the  observer,  stand- 
ing in  the  gallery  with  his  back  to  the  object,  and  looking  over  the 
edge  of  the  tube  towards  the  speculum,  can  direct  an  eye-piece  oon- 
Teniently  mounted  at  that  point  upon  the  image  of  the  object  of 
observation  formed  by  reflection  in  the  focus. 

Three  persons  are  employed  in  conducting  the  observations :  the 
observer,  who  stands  in  the  gallery;  his  amanuensis,  who  may 
either  be  in  the  gallery  or  in  the  wooden  house  below,  receiving 
the  dictation  of  the  observer  by  a  speaking  tube;  and  the  person 
who  works  the  windlass. 

3396.  The  lesser  Bosse  telescope. — This  instrument,  with  its 
mounting,  is  represented  in  Plate  XXVIII.  The  arrangements 
are  so  similar  to  those  of  the  Herschelian  instrument  described 
above,  that  they  will  be  easily  understood  from  the  Plate  without 

62* 


I.  ASTEONOKT. 

deBoription-     The  epeeuluni  ii  3  feet  aperture,  and  T'068 

.IB  feet  reflecting  Burfooe.     The  leagtb  of  (he  telescope  U  27 
It  is  creeteJ  upon  ibe  pleaaure-grotrnds  ftt  Porsonstown  Castle, 
.  seat  of  its  illustrious  coaaiructor.     The  weight  of  metal  ia  the 
culum  is  about  13  cwt. 

3397.  Tlie  greater  RosK  tekse/jpe. — This  stapendous  iastmnient 
celestial  iaves ligation,  bj  far  the  largest  and  most  powerful  ever 
istmcted,  is  represented  in  Plates  XXIX.  and  XXX.  from  draw- 
made  for  this  work  under  the  EDpenDt^ndence  of  bis  Lordship 
self.  Plate  XXIX.  presente  a.  North,  and  Plate  XXX.  a 
jih  view  of  tbe  instrument. 

The  clear  aperture  is  (1  ft.,  and  con=pr|ucTitlj'  the  magnitude  of 
refleotiDg  Bur&ce  b  28 '274  square  feet,  being  greater  than  tbat 
Benohel'e  great  teleacope  in  the  ratio  of  7  to  3. 
The   iuBtninient  ia  at  present  used  as  a  Newtonian   telesoope 
15),  that  IB  to  BBj,  the  rsjB  proceeding  along  the  axis  of  the 
jBt  Bpeoulam  are  received  at  an  angle  of  45°  upon  a  second  small 
tcnlum,  b;  which  the  focus  is  thrown  towards  tiie  side  of  the  tuba 
jere  tbe  eye-piece  it  directed  npon  them.     Provision  is,  however, 
ide  to  use  the  instrument  also  as  an  Hersohelian  telescope. 
The  great  tube  is  supported  at  tbe  lower  end  upon  a  massive 
universal  joint  of  cast-iron,  resting  on  a  pier  of  stone-work  buried  in 
the  grouud,  and  is  so  counterpoised  as  to  be  moved  with  great  ease 
in  di^clination.      In    all  such  instruments,  when   it  is  required  10 
direct  them  to  an  object,  they  are  first  brought  to  the  desired  direc- 
tion by  some  expedient  cnpaUe  of  moving  (hem  rapidly,  and  thej 
are  afterwards  brought  cxactl}'  upon  the  object  by  a  slower  and  moro 
delicate    motion.      In  this  case,  the  quick  motion   is  given    by  a 
windlass,  worked  upon  the  ground  by  an  assistant  at  the  command 
of  the  observer.     The  slow  motion  is  imparted  by  a  mccbaoL-m 
placed  under  the  hand  of  the  observer. 

Tbe  extreme  range  of  tbe  telescope  in  right  ascension,  when 
directed  to  the  equator,  b  1  hour  in  time  or  15°  in  space;  but  when 
directed  to  higlier  declinations,  its  range  is  more  cstensive. 

The  tube  is  slung  entirely  by  chains  and  is  perfectly  steady, 
even  in  a  gale  of  wind 

When  presented  to  the  south  the  tube  cin  be  loweri  1  until  it  a 
nearly  horizcntal  towards  the  north  it  can  only  be  depressed  to 
the  altitude  of  the  pole  The  apparatus  of  suspensi  o  is  so  arranged 
that  the  instrumeut  may  be  worked  as  an  equitonal,  and  it  is  even 
intended  to  apply  a  elect  work  mechanism  to  it 

The  horizDutal  avis  tf  the  great  universal  joint,  by  which  the 
lower  end  is  supports  1  carries  an  indcs  pcinting  to  pohr  dislanp{', 
and  playing  on  a  gnduatfd  arc  of  C  fcit  radiu  By  this  mean.', 
the  telescope  is  easily  set  in  polar  di-tanic      The  same  object  i) 


THE  GREAT  ROSSE  TELESCOPE. 


F      11     jt         J       V^^tr,    J 


BEMARKABLE  ASTRONOMICAL  INSTRUMENTS.  789 

also  attained,  and  with  greater  precision^  bj  a  20-inch  circle  attached 
to  the  iDstrument. 

Two  specula  have  been  provided  for  the  telescope,  one  of  which 
contains  3  J,  and  the  other  4  tons  of  metal,  the  composition  of  which 
is  126  parts  in  weight  of  copper  to  57}  of  tin. 

The  great  tube  is  of  wood  hooped  with  iron,  and  is  7  feet  dia- 
meter, and  52  in  length.  The  side- walls,  12  feet  distant  from  the 
tube,  are  72  feet  in  length,  48  feet  in  height  on  the  outside,  and 
56  feet  in  the  inside.  These  walls  are  built  in  the  plane  of  the 
meridian. 

The  observer  stands  in  one  or  other  of  four  galleries,  the  three 
highest  of  which  are  drawn  out  from  the  western  wall,  while  the 
fourth  or  lowest  has  for  its  base  an  elevating  platform,  along  the 
surface  of  which  a  gallery  is  moved  from  wall  to  wall  by  a  meohanbm 
at  the  command  of  the  observer. 

3398.  The  Oxford  heliomfJer.  —  This  class  of  instrument,  which 
derives  its  n<anic  from  having  been  first  applied  to  the  measurement 
of  the  diameter  of  the  sun,  consists  of  a  telescope  equatorially 
mounted,  the  object-glass  of  which  is  divided  along  a  plane  passing 
through  its  optic  axis,  each  half  of  the  lens  being  capable  of  being 
moved  in  its  own  plane,  so  that  the  axes  of  the  two  semi-lensesy 
being  always  parallel  to  each  other  and  to  the  axis  of  the  telescope, 
may  be  within  certain  limits  separated  from  each  other^  more  or  lesSy 
at  the  pleasure  of  the  observer. 

From  what  has  been  explained  in  general  of  the  structure  of  an 
equatorial  instrument  ^336),  and  from  the  drawing  of  this  instru- 
ment given  in  Plate  XaXI.,  the  provisions  for  the  direction  of  the 
telescope  in  right  ascension  and  declination  will  bo  easily  compre- 
hended. The  polar  axis,  round  which  the  instrument  turns  in  right 
ascension,  is  fixed  upon  the  face  of  a  block  of  Portland  stone,  and 
the  graduated  circle  measuring  right  ascension  is  seen  at  the  top 
and  at  right  angles  to  the  polar  axis.  This  circle  receives  its  motion 
in  the  usual  way,  from  clockwork,  which  is  attached  to  the  stone 
pier,  and  which,  with  its  impelling  suspended  weight,  is  seen  in  the 
drawing.  Rods  are  provided  by  which  the  observer  can,  at  pleasure, 
set  the  clock  going,  or  stop  it,  and  connect  it  with,  or  disengage  it 
from,  the  equatorial  circle. 

The  circle  for  indicating  polar  distance  or  declination  is  placed 
upon  the  horizontal  axis  of  the  instrument,  and  also  appears  in  the 
drawing  at  the  side  opposite  to  that  at  which  the  telescope  is  attached. 

The  object-glass  of  this  instrument,  sometimes  called  the  ''  divided 
object-glass  micrometer,'^  supplies  a  very  accurate  method  of  mea- 
suring angles  which  do  not  exceed  a  certain  limited  magnitude. 

It  appears  by  the  principles  of  optics,  that  when  the  image  of  a 
distant  object  is  produced  by  a  lens,  each  point  of  such  image  is 
formed  by  rays  which  proceed  from  every  point  of  the  lens.     If^ 


^  ASTROXOMT. 

,-«  put  of  tbo  Ini  be  corered  by  an  opuiva  bodj  m  eat 
lafk  point  of  the  ini*ge  will  still  be  formed  by  the  nya  which 
4cd  frMI  every  point  of  Ae  Im*  icAirA  it  not  coverrd  or  cut  avag. 
mly  difcfgnce  iriiieh  will  be  obwrved  in  the  image  will  be, 
it  will  be  less  stioi^lj  illmiinated,  being  deprived  of  the  nji 
h  it  MeaTMl  btm  Um  pirt  of  the  km  covered  or  cut  away,  and 
it  will  bs  \t»  distinet  in  cooMqiieDce  of  oeruia  effects  of  dif- 
OB  «Ucii  Med  Mt  benotioed  bm. 

loBove,  tlKralb««,  that  half  a  lena  will  prodtice  at  the  focos  in 

^  of  a  distant  object,  and  if  two  hilves  of  the  same  lens  be 

lad  OMWUitrioidlj,  tt^  will  form  two  iicages,  the  exact  nper- 

(tioa  rf  vbieh  wUl,  in  &ot,  oenatitote  the  image  formed  by  tb* 

iflala  less.     B«t  if  the  two  halves  be  not  oone«iitrical,  the  im- 

I  wiU  not  be  enpwposed,  bat  will  be  sepsnted  by  a  space  cor- 

ending  with,  and  proportiona]   to,  the   distance   between  tlis 

■aa  <tf  the  two  hatf  lenaes.     Thns,  if  the  lenses  be  directed  to 

BMi,  imo  inwes  of  the  aolar  disc  will  be  jnodncod  at  the  focoi 

ke  ieaasa,  and  these  imagea  nay  be  shifted  in  their  podtiocis,  Iha 

cEuires  approaching  to,  or  receding  from,  one  another,  according  u 

the  centres  of  lie  two  half  leoMS  approach  to,  or  recede  from,  each 

other;  and  if  the  angular  distance  tlirr^ugli  which  either  iniige 

moves  can  be  koowo,  it  is  ea<iy  to  fee  bow,  by  this  means,  the  ap' 

psrcDt  diimcler  of  such  an  object  as  the  sun  can  be  measureJ.     Fit 

this  purpose,  let  the  two  half  lenses  be  first  placed  OonecDlricallj,  fo 

that  the  two  images  shall  be  eiaetly  superposed.      Then   let  one  cf 

the  two  lenses  be  moved  (the  edges  of  the  semi-lenses  being  alwijs 

maintaiacd  In  contact),  until  the  im.igc,  formed  bj  the  semi-lcos, 

which  is  moved,  shall   be  rcmoveil  to 

I   such  a  position  that  the   two  images 

shall  touch  each  other  cilemallj,  as  in 

Jig.   879.      In   thai  case  it  is  evident 

that  the  centre  of  the  image  formed  hj 

the  semi-leDS  trhich   has  been  moved, 

must  have  moved  over  a  space  eijual 

■"«■=>"■  to  the  diameter  of  the   image  of  the 

'  disc,  and  if  the  angular  value  of  puth 

apace  he  known,  the  apparent  diameter  of  the  sun  will  be  known. 

This  was  the  application  of  the  divided  object-glass,  from  whicli 
the  heliometcr  took  its  name.  The  instrument,  hnwever,  has  sinee 
been  applied  to  so  many  other  imporiaut  purposes,  that  the  name 
has  ceasi'd  to  express  iLs  uses. 

The  (wo  semi-lenses  forming  the  objecl-glass  of  the  hcliomeler 
are  set  edge  to  edge   in   strong  brass  frames,  which  slide  in  grooves 

which,  by  lUe  inlefseWCvati  ol  co^-VaeAs,  w^  vm.vv.bA  b^  a.  tjair  of 
rods  wbich  pass  o.\o'l\gt,\l6\,li^l%^Jl^^i^^s;VwK.■<{e■    '^^^vi-^-ci'issii.i^. 


PUBLiC  1,1^., 


THE  OXFORD  HELIOHETER. 


TEOCGHTON'S  TRANSIT  CIRCLE. 


KEMABEABLE  ASTBOKOMICAL  INSTBnMENT&  741 

ihe  centres  of  the  semi-IeDses,  and  consequently  the  angular  distance 
between  the  two  images,  is  measured  according  to  a  known  scale  by 
the  number  of  turns  and  parts  of  a  turn  of  the  screw  which  are 
necessary  to  produce  the  separation  or  to  bring  back  the  semi-lenses 
to  a  concentrical  position,  if  they  are  separated. 

It  is  obvious,  that  the  same  principle  will  be  applicable  to 
measure  the  apparent  angular  distance  between  any  two  objects, 
such  as  two  stars,  which  are  so  near  each  other  that  they  may  be 
seen  together  in  the  field  of  view  of  the  telescope.  For  this  pur- 
pose, let  the  semi-lenses  be  first  placed  concentrically.  The  two 
stars  8  and  s'  will  then  be  seen  in  Uieir  proper  positions  in  the  field. 
Let  the  semi-lenses  be  then  moved  so  that  two  images  of  each  star 
will  be  visible.  Let  the  motion  be  continued  untU  the  image  of 
the  star  8  by  one  semi-lens  coincides  with  the  image  of  the  other 
star  s'  by  the  other  semi-lens.  The  angular  distance  corresponding 
to  the  separation  of  the  lenses  will  then  be  the  angular  distance 
between  the  stars. 

In  this  heliometer  a  very  ingenious  contrivance  is  introduced  to 
enable  the  observer  to  read  the  scale  by  which  the  angular  magni- 
tude corresponding  to  the  separation  of  the  centres  of  the  semi- 
lenses  is  indicated.  This  is  accomplished  by  placing  a  scale  behind 
the  object-glass  in  the  interior  of  the  telescope  tube,  so  that  it  can 
be  read  by  means  of  a  long  microscope,  the  eye-glass  of  which  is 
placed  near  the  eye-piece  of  the  telescope.  This  interior  scale  is 
illuminated  by  a  piece  of  platinum  wire  placed  near  it,  which  is 
rendered  incandescent  by  a  galvanic  current  transmitted  upon  it  at 
pleasure  by  the  observer.  This  current  is  produced  by  a  Smee's 
battery  placed  in  a  room  below  that  containing  the  heliometer. 

A  very  splendid  instrument  of  this  class  has  been  erected  at  the 
Pultowa  observatory. 

3399.  The  transit  circle,  hy  Troughton,  —  This  instrument, 
which  is  represented  in  Plate  XXXII.,  unites  the  functions  of  the 
mural  circle  and  the  transit  instrument.  The  telescope  is  fixed 
between  two  parallel  flat  metallic  circles  or  rings,  the  exterior  face 
of  each  of  which  is  graduated  to  5'.  These  flat  rings  are  connected 
with  the  horizontal  axis,  by  two  sets  of  radial  hollow  cones,  so  as  to 
form  two  wheels,  and  they  are  connected  with  each  other  by  various 
bars,  crossing  each  other  so  as  to  form  rhomboidal  fibres,  as  well 
as  by  a  system  of  perpendicular  rods,  which  appear  in  the  figure. 
Each  of  these  rings  is  4  feet  in  diameter.  The  horizontal  axis, 
which  receives  the  spokes  of  each  of  the  wheels,  is  cylindrical  be- 
tween the  wheels,  the  parts  projecting  beyond  them  being  strong 
cones,  which  rest  in  Ys  fixed  on  two  piers  of  solid  stone-work,  5  feet 
6  inches  in  height,  and  a  little  less  than  3  feet  apart.  The  length 
of  the  horizontal  axis  is  8  feet. 

The  faces  of  the  stone  piers  coincide  with  the  plane  of  the  me- 


p  ASTKOHOHT. 

I  Tb  m  proTided  vitb  adjnstments,  one  of  w1iu&  ii 
^wing  3tid  lowering  (ho  Y .  and  the  otiier  of  moving  it 
hrmigb  gmill  spaces.  When  the  inBtrameiit  U  plued 
,.,Kirt«.  the  line  of  collim&tion  of  the  telescope  will  pUy 
ihe  mcndiaa,  utd  it  will  \k  made  to  do  bo  exactly,  {17 
he  adjustments,  BocoTding  to  the  method  cipbuned  in  tlie 
ud  IraONt  iDStroment  (239^),  1^  ttq. 

KTsduatMl  fiwea  of  the  two  circles  are  sttrroimded  bj  foor  or 
■uorosoopt-s,  by  which  the  obeeiratioo  ia  read  off  in  the  soom 
and  subject  to  the  same  conditiooa  as  have  been  alreajj 
1  in  the  ease  of  the  maral  circle  ('2408),  e(  ttq. 
Tft*  ffrfcniricS  trantit  circU.  —  The  great  moral  eireU 
iDsit  tDstrnment  have  latelj  been  Enperseded  at  the  liojil 
— ij,  Greenwich,  by  an  instrument  upon  the  principle  of 
[escribed,  but  conatmcted  npon  a  vast  scale  of  mapniiode, 
ned  with  a  variety  of  accessories  by  which  its  stability  ud 
uwKBBarj  prefflsion  of  its  indications  are  secnred. 
i  perspective  view  of  this   iimtniraent  is  presented   in  Pl»t« 
XXXIII.,  made  from  original  drawings  talieo  by  pcrniLssiiin  of  the 
AstronomcT  Roy  a). 

It  was  found,  by  the  results  of  observations  made  with  the  great 
10-feet  transit  instmmeDt  previously  in  use  at  Greenwich,  that,  1!- 
though  it  was  the  best  of  its  class,  and  bad  been  constructed  vith 
the  greatest  degree  of  artistic  skill,  it  was  nevertheless  so  unstable 
as  t«  produce  errors  in  the  determination  of  time,  wbich  it  was 
possible,  and  therefore  desirable,  to  remove  bj  introducing  improved 
principles  of  construction,  which  will  be  presently  explained  in  rela- 
tion to  another  iustrnment  previously  erected  at  the  Observatory. 

Like  the  transit  circle  of  Tronghton,  already  described,  this  in- 
strument consists  of  a  telescope  filed  between  two  parallel  circles, 
one  of  which  is  gradustcd,  resting  on  horizontal  support.'',  placed 
on  two  stone  piers,  so  that  the  line  of  coUimation  moves  in  the  plane 
of  the  meridian. 

The  telescope  lube,  which  is  nearly  12  feet  long,  cnnsists  of  a 
hollow  cube  of  metal,  at  the  centre  of  which  two  cones  are  bolted 
by  means  of  flanges.  At  the  smaller  end  of  one  cone  is  the  object- 
glass,  and  in  that  of  the  other  the  eje-piece.  E.-tch  of  these  cones 
weighs  1-75  cwt.,  and  the  central  cube  with  its  pivots  weighs  8  cwt. 
The  whole  length  of  the  horizontal  axis  on  which  the  instrument 
rests  is  6  feet,  the  diameter  of  each  of  the  bearings  being  0  inches. 
The  object-glass  is  8  inches  aperture,  its  optical  power  being  suffi- 
cient for  the  observarioo  of  the  faintest  objects  which  are  presented 
in  the  ordinary  course  of  meridional  observations. 

In  erecting  the  instrument  experiments  were  made,  with  the  view 
of  determining  th«  amount  of  drop  produced  by  the  weight  of  the 


"''Top,  (^^  : 


GREENWICH  TRANSIT  CIRCLE. 


PCLTOWA  PRIME  VERTICAL  INSTRtJHENT. 


REMARKABLE  ASTRONOMICAL  INSTRUMENTS.  748 

• 

cones  of  the  telescope,  when  it  was  found  that  Uiis  quantity  did  not 
exceed  the  thousandth  of  an  inch. 

The  parallel  circles  between  which  the  telescope  is  fixed,  are  each 
6  feet  in  diameter,  and  are  firmly  attached  to  cylindrical  bands,  one 
on  each  side  of  the  central  cube  of  the  telescope.  The  clamping 
apparatus  is  applied  to  the  pastern  circle,  and  the  western  circle  b 
graduated.  The  reading-off  is  effected  by  means  of  six  microscopeS| 
each  45  inches  in  length. 

The  mduation  of  the  circle  is  such  as  to  show  approximately 
lenith  distances ;  while  a  pointer  fixed  to  a  block  projecting  from 
the  lower  part  of  the  pier,  directed  to  another  graduated  band  on 
the  outer  or  eastern  side  of  the  circle,  is  used  for  setting  the  tele- 
scope, and  gives  approximately  north  polar  distances.  A  small 
finder,  with  a  large  field  of  view,  is  attached  to  the  side  of  the  oone 
near  the  eye-piece,  as  well  as  sights  for  directing  the  telescope  to 
stars  by  the  naked  eye. 

A  large  gas-light  conveniently  placed  illuminates,  by  means  of 
reflectors,  the  graduated  arc  of  Uie  circle  at  the  points  where  the 
several  microscopes  are  fixed,  and  also  the  field  of  the  telescope. 

A  variety  of  other  provisions  and  adjustments  are  attached  to  the 
instrument,  which  it  would  be  impossible  to  render  clearly  intelli- 
gible without  reference  to  the  instrument  itself,  or  very  detuled  and 
elaborate  drawings  of  its  several  parts^  which  our  limits  do  not 
permit  us  to  introduce  here. 

3401.  The  PuUowa  prime  vertical  instrument. — ^This  instrument 
may  be  summarily  described  as  a  transit,  whose  line  of  oollimation 
moves  in  the  plane  of  the  prime  vertical,  instead  of  that  of  the  me- 
ridian. Nevertheless,  its  astronomical  uses  are  essentially  distinct 
from  those  of  the  transit  instrument  (2397). 

The  first  instrument  made  on  this  principle  was  erected,  in  the 
beginning  of  the  last  century,  under  the  direction  of  the  celebrated 
Koemer,  whose  name  is  rendered  memorable  by  the  discovery  of  the 
mobility  of  light  (2959).  It  was  applied  by  that  astronomer  chiefly 
to  observations  on  the  sun  near  the  equinoxes;  but  none  of  the 
purposes  to  which  it  has  more  recently  subserved  appear  to  have 
been  contemplated,  and  the  instrument  was  allowed  to  feXL  into 
disuse.  Its  revival,  and  the  idea  of  its  application  to  various  im- 
portant classes  of  observations  in  the  higher  departments  of  practical 
astronomy,  and  more  especially  to  replace  the  zenith  sector  in  obser 
yations  having  for  their  object  the  more  exact  determination  of 
^  aberration  and  nutation,  and  for  researches  in  stellar  parallax,  is  due 
to  Professor  Bessel.  Many  of  the  improved  details  of  construction 
exhibited  in  the  Pultowa  instrumA-.t  are,  however,  due  to  Professor 
Struve,  who,  besides,  has  obtained  such  remarkable  results  by  the 
system  of  observations  which  he  has  made  with  it 

The  Pultowa  prime  vertical  instrument  was  constructed,  under 


It  ASTROSOMT. 

rofesBor  Struve,  by  ^Icssn.  RepBoM,  of  Hamborg. 

^.„„w  ^ I  being  erected  in  planes   at  right   angka   to  tbo 

idian,  vertical    chairs   arc  fixed  upon  the    sommila  in  such   a 

tion  that  the  line  joining  them  is  in  the  plane  of  the  raeridian. 

3  chaira  aro  the  supports  of  the  cylindrical  extremities  of  the 

anlal  axis  of  the  insiramcnl,  nbich  is,  therefore,  also  in  the 

o  of  the  meridisa.     The  eitremitiea  of  this  axis  projoct  bejoiad 

chaira  and  the  piers  on  each  side,  and  the  transit  tel««cope  is 

•Kd  on  to  one  of  them,  while  a  oountar-vsight  b  keyed  on  to  the 

■.     The  telescope,  having  its  hoe  of  collimattoD  adjaHt«d  at 

angles  to  tlie  horisontal  axis,  revolves  with  this  axis  outside 

piers,  in   the  same   manner  exactly  as  the   transit  telescope 

-)lves  between  its  piers;  and  as  the  line  of  collimation  of  tbo 

er  moves  in  the  plane  of  the  meridiiui,  that  of  the  transit  tele- 

pe  of  tbo  preseot  instrument  maTcs  in  the  plane  of  the  prime 

^dJustmenU  arc  provided  in  connection  wilh  the  two  cbairs,  one 

vhich  raises  and  Iowcm  the  axis,  and  the  other  moves  it  in  axi- 

tb,  similar  exactly  to  those  described  in  the  case  of  the  trannl 

tmmont  (2399),  et  teq.     By  these  meaiu,  ani]  by  proper  lerdt, 

M.V  axis  is  rendered  truly  horizontal,  is  brought  exactly  into  tbe 

plane  of  the  meridian,  and  the  line  of  collimation  is  brought  to 

coincide  with  ihc  plane  of  the  prime  vertical   Ijy  olber  oTpcdients, 

Nmilar  in  principle  to  those  adopted  in   the  case  of  the  transit 

instrument. 

The  instrument,  moanted  od  the  piers,  is  represented  in  Pints 
XXXLV,,  as  »ecn  from  the  west,  projected  on  the  plane  of  the 
meridiao,  the  telescope  being  on  the  north  eide,  and  placed  so  that 
the  line  of  collimation  is  directed  to  the  zenith.  The  t4.'leseope  bu 
7  feet  7  inches  focal  length,  with  an  object-glass  having  a  clear 
aperture  of  6-25  inches.  The  magnifying  power  commonly  used  is 
270.  In  the  eye-piece  a  system  of  seven  parallel  vertical  micro- 
meter wires  is  fixed,  similarly  to  those  of  the  transit  instmmeDt 
(2396),  and  is  similarly  used  wilh  relation  to  the  clock,  as  already 
aescrihed  in  the  cose  of  the  latter  instrument.  A  lamp  is  placed  at 
a  convenient  distance  from  the  centre  of  the  telescope,  the  light  of 
which,  admitted  by  a  pial«  of  glass  fixed  in  the  side  of  the  tube,  b 
received  upon  a  small  reflector  at  45°  within,  and  reflected  along 
the  tube,  so  as  to  illuminate  the  wires  at  night 

To  enable  the  observer  to  direct  the  telescope  to  any  required 
altitude,  a  small  telescope,  called  a  Jindcr,  is  fixed  to  the  outside 
of  the  great  telescope,  near  the  eyc-pioce,  having  attached  to  it  a 
graduated  circle,  the  piano  of  which  is  parallel  to  the  prime  vertical, 
and  also  a  level-  The  line  of  collimation  of  the  finder  being  parallel 
to  that  of  the  groat  telescope  when  the  former  is  directed  to  any 
altitude  bj  me&ua  ot  l.lkQ  UveL  and  graduated  circle,  the  former  will 


BSMAREABLE  ASTRONOMICAL  INSTRUMENTS.  746 

lie  fllmilarly  directed.     This  finder  appears  in  ihe  drawing  outside 
the  telescope,  and  a  counterpoise  to  it  is  represented  on  the  inside. 

The  process  of  reversion  of  the  horizontal  axis,  which  in  the 
transit  instrument  is  only  used  for  the  purpose  of  adjustment  (2400), 
eonstitutes,  in  the  case  of  the  prime  vertical  instrument,  an  essential 
part  of  every  observation.  It  was,  therefore,  of  the  greatest 
importance  that  an  easy,  expeditious,  and  safe  apparatus  for  rever- 
sion should  be  provided.  This  was  contrived  with  great  ingenuity 
by  the  makers,  and  attended  with  the  most  successful  results — results 
to  which  M.  Struve  ascribes  a  great  share  of  the  advantage  obtained 
by  this  instrument.  A  part  of  this  apparatus,  by  which  the  hori- 
lontal  axis,  with  the  telescope,  counterpoise,  and  their  accessories, 
is  elevated  from  the  chairs,  is  represented  in  the  drawing  above  the 
instrument.  The  two  cords  of  suspension  being  attached  by  hooks 
to  two  points  on  the  axis  at  equal  distances  from  its  centre,  so  as  to 
maintain  the  equilibrium,  the  instrument  is  elevated  by  means  of  a 
windlass  established  on  the  floor  below  it  and  between  the  piers. 
When  raised  to  the  necessary  height,  it  is  turned  through  half  a 
revolution  in  azimuth,  so  that  the  ends  of  the  axis  are  brought 
directly  over  the  chairs,  into  which  they  are  then  let  down.  So 
perfect  is  the  performance  of  this  apparatus,  that  notwithstanding 
the  magnitude  and  weight  of  the  instrument,  the  whole  process  of 
reversion  is  completed  in  sixteen  seconds;  and  the  interval,  from 
the  moment  the  observer  completes  an  observation  with  the  tele« 
•cope  on  the  north  side,  to  the  moment  he  commences  it  on  the 
south  side,  including  the  time  of  rising  from  the  observing-couch, 
disengaging  the  clamps,  withdrawing  the  key  from  the  micrometer, 
reversing,  directing  the  instrument  on  the  south  side  to  the  object 
by  means  of  the  finder,  closing  the  clamps,  returning  the  key  to  the 
micrometer,  and  placing  himself  on  the  observing-couch,  is  only  80 
seconds. 

How  essential  to  the  practical  use  of  the  instrument  this  celerity 
is,  will  be  understood  when  it  is  stated,  that  the  same  object  which 
has  been  observed  on  one  side  must  be  also  observed  on  the  other 
in  ihe  $ame  transit.  The  reversion,  therefore,  must  be  completed 
in  less  time  than  that  which  the  object  takes  by  the  diurnal  motion 
to  pass  over  the  space  commanded  by  the  field  of  the  telescope  in 
the  two  positions. 

To  comprehend  the  method  of  applying  this  instrument  to  the 
purposes  of  practical  observation,  it  is  necessary  to  remember  that 
it  is  only  applicable  to  objects  moving  in  parallels  of  declination 
which  intersect  the  prime  vertical.  Such  objects  must  have  northern 
declination  (the  instrument  being  supposed  to  be  established  in  a 
place  having  a  north  latitude),  and  a  polar  distance  greater  than  that 
of  the  zenith  of  the  observatory,  that  is  to  say,  greater  than  its  co- 
latitude.  The  parallels  over  which  such  objects  are  carried  by  Uie 
m.  63 


I  tnteraect  the  prime  vertiinl  at  two  pointa  of  «qiMl 

iB  etitem,  and  tbe  other  OQ  tbe  western,  qiMdranl 

paasiDg  from  tbe  east  point  of  iDlerseclion  to  the 

aiiit,  iUB  ubjiwt  passes  oyet  tixe  tneriiiiiio,  and  it  is  evident 

ae  momeot  of  ita  mcridionat  traoFit  is  predselj  tbe  middle 

interral  between  ita  two  prime  vertical  tranaila.     If,  tbero- 

oe  exact  times  of  the  latter  be  observed,  the  time  of  the  tsut' 

al  traoBit  can  be  deduced  by  a  simple  arithmetical  prooeu. 

treparo  the  instrmont  f — ■•— rvation,  let  the  polar  diatanea 

object  about  to  be  obser        ja  taken  from  tbe  Tablei.     I>ct 

iipTeesed  by  «;  let  the  uu-latitade  of  tbe  obserratorj,  or, 

IB  fha  same,  tbe  polar  distance  of  tbe  xeoith,  be  ^;  and  let  tha 

u  distance  which  the  object  must  have  when  it  comes  on  tbe 

Tertical,  be  z.     These  three  arcs,  e,  >■,  aod  «,  form  a  right- 

1  spherical  triangle,  tbe  nght-anglo  being  included  \>j  x  and  i. 

le  angle  at  the  pole,  or  the  hour  angle,  be  k.     We  eball  thep, 

e  elcmentar}!  principles  of  trigonometry,  have 

COS.  J  =  '^^  (1);  oos.  A  =  ^^^  (2). 

Uy  the  fonnaln  (I"),  the  tenith  distance  of  tbe  poinU  at  wbidi 
tbe  object  will  cross  the  prime  vertical  is  known.  The  observer,  bj 
means  of  the  Qndcr,  nod  the  circle  and  level  attached  to  it,  direcU 
tbe  great  telescope  to  that  tenith  distance  on  the  eastern  quadrsnt 
of  tbe  prime  vertical ;  and,  although  the  exact  position  of  the  object 
is  tbe  thing  sought,  its  approximate  position  is  already  known  witL 
that  degree  of  precision  which  ensnrtis  its  passage  through  the  field 
of  the  ioslrunient  nhen  it  is  set  to  (ho  Eenith  distaDce  given  by  lb* 
oacul;itiiiu  made  from  the  tabular  polar  distance. 

When  the  telescope,  being  on  the  north  side,  ia  thus  directed  and 
clamped  in  its  position,  the  observer  awaild  the  transit,  tbe  time  of 
which  be  ulready  knowii  approximately  by  the  formula  (^),  which 
gives  the  hour  angle  from  the  meridian  when  the  object  is  over  tbe 
prime  vertical,  At  the  near  approach  of  the  transit  he  places  bios- 
self  on  tlie  oh?|ir\ iiig-coiic!),  and,  seeing  lie  olycct  ealcr  ibe  field, 
notes  the  moments  by  tbe  clock  of  ils  transits  over  the  seven  wires 
of  tbe  micrometer.  Let  these  timea  be  expressed  by  t„  Tj,  t«  t„ 
T»,  T„  and  T,. 

The  moment  the  transit  over  the  seventh  wire  has  been  observed 
he  rises  and  performs  all  that  ia  necessary  for  the  reversion  of  the 
iristrumeot,  which  being  completed,  be  again  places  himself,  and 
observes  the  transita  over  tbe  seven  wires  on  the  south  side;  but  in 
this  case,  owing  to  the  change  of  position,  the  order  of  the  transits 
is  reversed.     Let  the  times  of  transits  be  eipresaed  by  C„  t,,  /„  („ 

14ow,  it  U  e^«fit.  \\M.'k  ^  tna  moment  of  the  transit  over  tfaa 


RSMARKABLE  ASTRONOMICAL  INSTRUMENTS.  747 

prime  Tertioal  will  be  found  by  taking  a  mean  between  tbe  times 
•f  ihe  transits  over  all  the  wires  at  both  sides.  K  this  time  be 
tspressed  by  i!j  we  shall  then  have 

.         T,  +  T,  +  .  »  »  +  Tt  +  ^  +  ^6  +  .  .  .  +  <i 

^= n • 

These  observations  being  completed,  the  observer  awaits  the  transit 
of  the  object  over  the  western  quadrant  of  tbe  prime  vertical,  when 
he  makes  a  similar  series  of  observations  on  the  transits,  first  with 
the  telescope  on  the  south  side,  in  the  position  it  had  at  the  last 
observation,  and  then,  after  reversion,  at  the  north  side.  The  true 
moment  of  the  transit  is  found,  in  this  case^  in  the  same  manner  as 
in  the  former. 

By  taking  a  mean  of  these  two  means,  or,  what  would  be  equi- 
valent, a  mean  of  the  tiroes  of  all  the  twenty-eight  transits^  the  time 
of  a  meridional  transit  will  be  obtained. 

The  total  length  of  the  interval,  necessary  to  observe  the  transits 
over  the  wires,  north  and  south,  in  each  quadrant  of  the  prime  ver- 
tical, is  found  to  be  about  eleven  minutes,  less  than  1^  minute  of 
which  is  employed  in  the  reversion  of  the  instrument  and  attendant 
arrangements. 

The  time  which  elapses  between  the  observations  on  the  eastern 
•nd  western  quadrants  of  the  prime  vertical,  will  necessarily  vary 
with  the  polar  distance  of  the  object,  and  will  be  less  in  proportion 
as  excess  of  that  distance  above  the  co-latitude  is  less.  Tbe 
observations  which  have  been  made  with  this  instrument  at 
Paltowa,  have  been  chiefly  confined  to  stars  whose  polar  distanoo 
exceeds  the  co-latitude  by  less  than  2°.  In  that  case,  the  interval 
between  the  observations,  east  and  west,  would  be  less  than  three 
hours. 

Professor  Struve  notices,  in  strong  terms,  the  advantage  which 
this  instrument  possesses  over  others  in  respect  to  the  errors  arising 
from  the  variation  of  the  inclination  of  the  line  of  collimation  to  the 
axis  of  rotation.  In  the  prime  vertical  iDstrumcnt,  the  deviation 
of  the  line  of  collimation  from  true  perpendicularity  to  the  axis  of 
rotation,  is  assumed  to  be  invariable  only  during  the  short  interval 
of  a  single  observation,  whereas,  in  other  instruments,  its  invaria- 
bility is  assumed  for  twelve  hours,  and  in  some  cases  for  months, 
and  even  years.  It  has  the  further  great  advantage,  that,  by  rever- 
sion in  each  quadrant,  cast  and  west,  all  optical  imperfections  which 
affect  the  precision  of  the  image  of  the  star  are  absolutely  annihi- 
lated.* 

*  For  a  detailed  account  of  the  Pultowa  prime  Tertlcal  instrument,  see 
Description  de  I'Observatoire  Astronomique  de  Pultowa,  par  F.  G.  W. 
Strave.     Also  Astronom.  Nachriohten,  No.  468,  e<  mj. 


ASTROSOMT. 

II      9v't  ahiluile  and  axinaUh  ctrda.  —  The  form  of 

■rfcm,  adapted   to  render  the  principle  of  altitude  tad 

-u  ...atniniento  in  gpneral  intelligible,  is  that  which  ia  rfpre- 

.J  in  Plnle  XXXV.     TliJa  citulo  was  originally  ranatrucled  bj 

nghtpu  for  tbe  Kojal  Academy  of  St.  Petersburg;  but,  at  the 

1)  of  the  invasion  of  Rueain  bj  the  French,  the  fear  that  Pelers- 

■oi"*-*      1  eiposed  to  the  Kime  disasters  as  Moscow,  induced 

I".  •horitiea  to  relinquish  their  claim  on  the  instrumeut, 

into  the  banda  of   Dr.  Pearson,  at  wboi^e  prirate 

Kilworth,  it  was  erecied.     Owing  to  tbe  indispo- 

1t        ton,  tho  graduation  of  tbe  limbs  was  eiccated  by 

le  drawing  presents  tbe  circle  ao  that  all  the  important  parts 

"i  visible.     The  instrument  ia  sapported  on  the  capstone  of  a 

Btone  pedestal.     Upon  this,  the  fixed  parts  of  the  instni- 

jpon  which  it  revolves  in  ozimutb,  are  firmly  established, 

!"— 'ist  of  a  solid  vertical  cone,  terminating  below  in  an  heia- 

1  mass  of  metui,  each  vertical  face  of  which  me&snres  3 

-arc.     From  this  proceed  four  radial  cooea,  three  of  which, 

ingtes  of  120"  with  each  other,  are  aapported  on   tbe  stone 

j.^jeBtal  by  feet  supplied  with  ailjtisting  screws,  by  nieana  of  which 

the  iu.slniment  is  levelled.      Tbe  fourth  radial  cone,  wbicb  forms  an 

angle  of  60°  with  two  of  tbe  others,  carries  a  clamp,  which  will  be 

presently  noticed. 

Tbe  moveable  part  of  the  inslmment  termiuales  at  the  lower 
part  in  a  hollow  cone,  which  appears  in  tbe  figure  between  the  two 
Tcrtical  pillars,  with  which  it  ia  connocled  by  a  metallic  collar. 
This  hollow  cone  rests  upon  and  conceals  Ibe  solid  cone  already  de- 
ECribed,  and,  turning  freely  upon  it,  gives  to  the  instrunicnt  its  azi- 
muth motion. 

A  horizontal  circle,  3  feet  in  diameter,  is  connected  by  cooical 
spokes,  in  the  usual  manner,  with  (he  lower  ends  of  the  two  vertical 
pillars  and  tbe  intermediate  hotlnw  cone. 

To  the  throe  radial  cones  of  the  fixed  hase  of  the  appamtus,  at 
angles  of  ISO'',  are  attached  three  pieces,  which  rise  vertically 
outaide  tho  circle,  and  support  three  micra»copes,  hy  wbicb  the 
aiimutbal  angles  are  read  off.  This  position  for  the  microscopes 
gives  some  practical  advantage,  inasmuch  as  the  observation  is  read 
at  six  different  points  of  the  limb,  when  the  observation  is  repealed 
by  turning  the  circle  180°  in  azimuth.  To  the  fourth  radial  arm 
of  the  fixed  base  a  clamp  is  attached,  by  which  tbe  position  of  the 
instrument  is  maintained  in  the  position  it  has  at  the  moment  the 
observation  is  made.  This  clamp  appears  in  the  drawing  with  iis 
tightening  screw  above  it,  and  its  tangent  screw  for  giving  the  ar.i- 
muth  circle  a  alow  motion  to  bring  the  instrument  to  its  exact 
JKWilJoD.      Thia  UTijen*.  witq"«  ^ftimmiteB  in  a  square,  which  can  be 


I 


rt  •  >  -  »  ■      >  •  w 

I       1  :     , 

,1  \j  L^  L^L\y   JL^.-t.. 


TROUGIITONS  ALTITIDK  AXD  AZIMCTH  CIRCLE. 


GREENWICH  ALTAZIMUTH  INSTRUMENT. 


BBMARKABLB  ASTBONOMICAL  IKSTBUMBNT8.  749 

inserted  in  a  square  hole  of  corresponding  magnitndey  connected  by 
an  universal  joint  with  a  rod  of  convenient  length,  which  the  ob- 
server holds  at  the  moment  of  the  observation^  and  by  turning  which 
the  whole  instrument  is  moved  slowly  in  azimuth. 

The  vertical  circle  consists  of  two  parallel  limbs,  having  the  tele- 
scope between  them,  constructed  and  connected  in  a  manner  exactly 
similar  to  the  transit  circle  already  described ;  and  this  circle  is  sup- 
ported on  the  two  vertical  pillars  in  the  same  manner  exactly,  as 
already  described  in  the  case  of  the  transit  circle  (3399). 

One  only  of  the  two  vertical  circles  is  graduated,  being  divided 
as  well  as  the  horizontal  circle  to  5'.  The  clamp,  with  its  tangent 
screw,  is  placed  on  the  side  not  graduated.  The  focal  length  of  the 
telescope  is  44-4  inches,  and  its  aperture  3}  inches. 

The  observations  of  altitude  are  read  off  by  four  microscopes,  the 
supports  of  which  are  shown  in  the  figure.  Two  are  supported  by 
arms  attached  to  the  vertical  pillar  on  the  graduated  side  of  the 
circle,  and  the  other  two  to  a  hoop  screwed  on  the  pillar  and  to  the 
arms  which  carry  the  two  former. 

The  instrument  is  provided  with  a  plumb-line  and  four  levels,  by 
which  its  proper  position  with  relation  to  the  vertical  direction  can 
be  always  verified. 

.  3403.  The  Greenwich  alt-<izimuth  instrument  —  This,  ks  the 
name  imports,  is  an  altitude  and  azimuth  circle  in  principle  similar 
to  that  just  described,  but  in  its  construction  and  application  dif- 
ferent from  any  instrument  of  its  class  hitherto  constructed.  The 
purpose  chiefly  to  which  it  b  applied,  and  with  the  view  to  which  it 
was  conceived  by  the  Astronomer  Royal,  is  the  improvement  of  the 
lunar  theory  by  multiplying  in  a  large  ratio  the  observations  which 
can  be  made  from  month  to  month  on  the  moon,  without  in  any 
degree  impairing  their  precision.  Such  observations  were  always 
made  with  the  mural  circle  and  the  transit,  until  this  instrument 
was  brought  into  operation,  and  they  were  consequently  confined  to 
the  meridional  transits  of  the  moon.  Now,  these  transits  cannot  be 
observed,  even  when  the  firmament  is  unclouded,  for  four  days  be- 
fore  and  four  days  after  the  new  moon,  in  consequence  of  the 

{>roximity  of  that  body  to  the  sun  ;  an  interval  amounting  to  little 
ess  than  one-third  of  the  month.  Besides  this,  it  happens,  in  this 
climate,  that,  at  the  moment  of  the  meridional  transits  at  other 
parts  of  the  month,  the  observation  is  frequently  rendered  imprac- 
ticable by  a  clouded  sky.  It  was,  therefore,  highly  desirable  to 
contrive  some  means  of  making  the  observations  in  extra-meridional 
positions  of  the  moon. 

This  could  obviously  be  accomplished  by  means  of  an  altitude 
and  azimuth  circle,  such  as  that  described  above ;  but  such  an  in- 
strument, however  perfect  mieht  be  its  construction,  is  not  sus- 
ceptible of  the  necessary  precision.     The  Astronomer  BA^al^  t]^ftge%» 

6E* 


■   7M  A8TR0N0MT. 

fore,  oonoeived  tho  iiloa  of  on  iDstramcnt  on  Lho  Esmc  principle, 
Khich,  vbile  il  would  be  cnpable  of  BUifiing  its  aEimutli,  noald  etilt 
be  susceptible  of  as  uiucb  prerieioD  in  each  vertical  ia  wbicb  it 
might  bo  pluccd,  as  the  niDml  circle  has  in  the  roeridiuD.  He  4C- 
00I^lingly  proposed  to  attaia  this  object  hj  adoptjug  adequate  eagi- 
neoriDg  expedients  to  produce  tho  necessary  solidity  and  invariability 
of  form.    He  adopted,  ae  funJamontat  priooiplea  of  ounstraetioii, — 

1.  To  prodooe  aj;  many  parts  aa  p<is3ible  in  a  aingla  casting ; 
*    ,    2>  To  use  no  small  screns  for  oombiaing  the  parLa; 

3.  To  alloiT  DO  poner  of  adjuBtmenl  anywhere.  , 

FollowiDft  out  these  principles,  Uio  instninient  represoDt^d  in 
Plate  XXXVI.  was  constructed,  andcr  Uis  superintendence,  by 
HesaiB.  Rausome  and  May,  engineers,  of  Ipswich;  the  eraduatioo 
iMing  executed  by  Messrs.  Troiighton  anil  9imnis:  and  the  Gral 
observation  with  it  was  made  by  Mr.  Hugh  Dreeu,  jun.,  one  of  tb4 
u^stants  at  the  Observatory,  on  the  I6th  of  Slay,  1847,  whicb  WW 
found  to  W  as  good  as  any  succeeding  observation.  . 

The  inalmmeiil  ia  mounted  in  a  tower,  raised  to  snob  a  height  u 
to  command  the  horizon  in  all  directions  above  the  other  buiMiogs  ' 
of  the  (.)b.^crvatorv,  csci']il  on  the  sido  I'f  the  soutb^.'ast  dome  sml 
tbe  octagon  room.  The  foundation  of  the  iDstnimcut  is  a  three- 
rayed  pier  of  brickwork,  carried  up  nearly  to  the  level  of  the  floor 
<d  the  room  ippropriated  to  the  instrument.  UpoD  thia  pier  it 
placed  a  cyliDdrieal  atone  pillar,  3  feet  in  diameter,  which  appean 
in  the  drawing,  and  on  which  the  iDstrument  is  placed.  Thia  pillar 
and  the  pier  upon  which  it  reposes  are  quite  independent  of,  and 
unoonneoted  with,  the  tower  within  which  it  is  erected,  and  do  not 
even  touch  the  floor  of  the  room  through  which  they  pass. 

The  fixed  borizonUl  usimutb  circle  ia  solidly  csUbltKhcd  upon 
this  stone  pillar.  It  is  a  circle  3  feet  in  diameter,  tbe  rim  being 
connected  with  the  centre  in  the  usual  nay  by  apokes.  The  whole 
ia  couatruoted  of  hard  gun-metal.  In  the  upper  surface  of  the  rim 
a  circular  groove  is  left,  which  is  filled  with  a  band  of  Eilver,  on 
which  the  divisions  are  engraved.  This  oircle  is  divided  into  arcs 
of  6'  continuously  from  0°  to  360°.  It  is  sot  with  the  aero  towardi 
the  north  and  the  numbering  of  the  divisions  runs  from  north  to 
east,  south  and  west.  This  amnuthal  circle  was  cast  in  a  single 
piece,  and  weighs  441  lbs. 

Attached  to  this,  and  concentric  with  it,  is  another  fixed 
horizontal  circle,  having  teeth  on  tho  inside  edge,  in  which  the 
pinions  work  by  which  the  azimuth  molion  is  given  to  the  in£tni< 

There  are  four  microscopes  placed  at  equal  distances  over  the 
graduated  aro,  which  are  provided  with  micrometers,  by  which  the 
obseryatioQ  iu  humutkuio^  u%.    '\Wn«,  \nkco&co[iF'jt  are  atiached 


REMARKABLE  ASTRONOMICAL  INSTRUMENTS.  751 

to  ihe  inslraiDeiit  so  as  to  revolve  with  it.     Their  reflectors  are 
illaminated  by  a  lamp  properly  placed. 

The  lower  pivot  on  which  the  instrument  turns,  is  supported  on 
a  point  in  the  stone  pillar  at  the  centre  of  the  azimuthal  circle.  To 
Bupport  the  upper  pivot,  an  iron  triangle  is  established  on  the  three* 
rayed  pier.  On  each  side  of  this  is  erected  another  iron  triangle, 
whose  plane  is  vertical,  and  whose  sides  unite  in  a  vertex  which 
furms  one  of  the  angles  of  a  corresponding  triangle  above.  This 
upper  triangle  supports  three  radial  bars,  which  carry  at  their  point 
of  union  the  Y  in  which  the  upper  pivot  plays.  The  bars  of  the 
lateral  triangles,  which  are  apparent  in  the  drawings,  pass  the  holes 
in  the  floor  without  touching  it. 

The  frame,  revolving  in  azimuth  and  carrying  the  instrument 
with  it,  consists  of  a  top  and  bottom  connected  by  vertical  cheeks, 
all  of  cast  iron.  The  supports  of  the  four  microscopes  for  reading 
off  the  azimuth  on  the  lower  circle  are  cast  in  the  same  piece  with 
these  vertical  cheeks. 

The  vertical  circle  carrying  the  telescope  is  3  feet  in  diameter, 
and,  like  the  azimuth  circle,  is  made  of  hard  gun-metal.  The 
aperture  of  the  object-glass  is  3f  inches.  The  top  and  bottom  of 
the  instrument  each  carries  two  levels,  parallel  to  the  plane  of  the 
Tertical  circle. 

The  dome  over  the  instrument  is  cylindrical,  with  double  sides, 
between  which  the  air  passes  freely.     Its  diameter  is  10  feet. 

The  drawing  represents  the  instrument  as  in  use.  The  ladder 
revolves  in  azimuth,  with  the  instrument,  round  the  central  pier, — 
to  facilitate  which  motion,  rollers  are  placed  under  it.  Two  boards 
are  attached  to  the  revolving  frame,  having  their  edges  in  a  plane 
parallel  to  that  of  the  vertical  circle.  The  eye  being  directed  along 
these  to  view  the  object,  the  instrument  is  placed  very  nearly  in 
the  proper  azimuth,  and  the  telescope  is  then  accurately  directed 
to  the  object  by  the  ring-finder.  These  boards  are  omitted  in  the 
drawing. 

The  drawing  has  been  reduced  from  an  engraving  prefixed  to  the 
''  Greenwich  Observations  for  1847,"  which,  however,  was  originally 
published  in  the  ''  Illustrated  London  News." 

The  results  of  the  observations  made  with  this  instrument  are 
stated  to  have  fulfilled  all  the  anticipations  of  the  Astronomer 
Royal,  as  well  as  to  the  number  of  observations  as  to  their  excel- 
lence. At  least  twice  the  number  have  been  made,  and  of  equal 
goodness  with  those  formerly  made  with  the  meridional  instru- 
ments. Some  have  been  made  even  with  a  day  of  conjunction ; 
and  Mr.  Main,  the  chief  assistant  at  the  Observatory,  has  expressed 
his  conviction  that  in  a  few  years  observations  with  this  instrument 
will  remove  all  the  deficiencies  which  still  remain  in  the  lanar 
theory. 


sr^: 


MM.  Tit*  SafAta^^hnd  bkteape —  CambriJgt  ohaerMtorj. 
■^n*  hM  Dnk*  of  SorUmmbeliaail,  who  filled  dnrin^  the  UlUi 
|pri  «f  Ua  Bit  tha  V\A  utd  hoiwimble  offios  of  Cbknceilar  of  Ihe 
fai^^^iy  df  CMfan^g^  prawBted  lo  that  oniTeiKt;  this  initni- 
BMti  vkM,  wameumni]  in  tbs  kaods  of  tb«  Astrononicr  Bopl 
■■1  PndMHT  CWfii^  MB  ooBiobated  ao  eflecto^l;  ut  tbe  idnnce- 

TW  hlmpwl,  of  vfaieh  >  penpcctire  riew  is  girea  b  Plate 
XXXTH,  lae^hiC  with  *  nev  oT  the  boildiog  in  wbidi  it  i« 
MMfl.  OTWiaM  of  •  n&iieliag  telescope  of  19|  feet  foed  leii|ih, 
mad  111  ittcfcw  BfOTtiire  cqomtoreallj  DtNuited.  Tbe  poUr  uit,  u 
mamimn  io  th«  dnvine,  oovnits  of  a  sjrrten  of  &«mtag  compce^ 
«■  «x  gapBg  dckl  |MM,  kttaebed  kt  tbe  ead*  to  tao  bexi^oil 
fc«KM  of  CMt  lnB>  1^  eentiea  of  wbieii  anpport  the  upper  tod 
loBif  pmta  M  vUch  lb«  teleacepe  revolrca.  Tbcae  poll*  tX  the 
■MJIt  n  Inetd  bjr  tnosTtne  iron  baad),  lad  b;  a  (jtten  <^ 
J  ro&  of  tel  kUtthig  nnr  tbe  niddle  of  iIm  poles.  TleM 
ibiM  to  tbe  flnlin  Ensiing  of  tbe  poUr  axis.  Mid  maiDlain 
«  b«npoaa1  &mBie*  aqmra  to  il.  ESnent  means  are  proriilfd  to 
gite  eIuu<[Ev  ti:  the  -spf^iU  of  the  F>irot9  and  amoolbaced  to  the 

Tlie  tnbe  of  the  teleseope  u  made  of  well-oeaaooed  deal,  tod 
attached  to  one  lide  of  it  is  a  flat  l«asa  bar,  6  feet  long,  canjiog  a 
■mall  gndnaled  are  at  right  aoglea  to  it  at  one  end,  and  tnmiDg  tt 
the  other  oo  a  pin  fixed  in  tbe  tekaoope  tnbe  at  a  distance  of  30 
iacbca  from  the  axia  of  reTolntion.  This  are,  which  is  called  the 
deelinatioa  sector,  serves  to  meaaore  small  difierenoes  of  deelias' 
tion,  and  i<  ttad  bj  a  micrtHneter  microacopo  fixed  to  the  telescope 
labe. 

The  hour  cirele,  which  inaunires  the  eqoatoreal  motion,  is  5} 
feet  dtameto',  and  is  so  airanged  that  it  can  be  clamped  to  ths 
telescope,  or  dinngaged  finm  it,  at  pleasore.  It  has  two  iodexes 
with  Temieis,  one  fixed  to  the  support  of  the  lowet  pivot,  and  the 
other  to  the  hexagonal  frame.  Bj  setting  the  latter  to  a  certain 
angle,  detennined  bj  an  ofaeertatioD  c^  a  star  of  Jniown  right  aiceo- 
tioD,  the  telescope  on  be  directad  to  anj  proposed  right  ascension 
bj  means  of  the  other  index.  Obaerrationa  ot  right  ascension  can 
be  made  to  1  second  of  time.  The  onter  rim  of  the  circle  is  cat 
into  teeth,  which  are  acted  on  bj  an  endless  screw  connected  st 
pleasure  tj  a  tMan  tod  with  a  la^  clock,  b;  which  a  motion  can 
be  given  to  the  teleaoope  conet|ionding  with  ue  diomal  motioa  of 
the  heavens. 

The  how  circle  is  clamped  to  tbe  fnme  of  the  axis  bj  a  tangent 
anew  damp  fixed  to  (he  frame  itself,  bj  means  gf  which,  with  the 
aid  of  a  handW  ex\eTt4\n^  Vo  ^«  ^^kca  tit  \^i«  >^V]hu^qt,  he  cao, 
when  the  en4\e»  screw  Sa  »t^\wA,  »">«  ms^iKm.  >&  •^-  -— 


xobthumb::rland  equatorial. 

CAMBRIDGE  ouehvatost. 


u 


RBMARKABLE  ASTRONOMICAL  INSTRUMENTS.  758 

through  a  limited  space  upon  the  hour  circle.  The  rate  of  motion 
given  to  the  hour  circle  hy  the  clock  is  not  affected  hy  this  move- 
ment. The  hour  circle,  therefore,  going  according  to  sidereal  time, 
small  differences  of  right  ascension  can  be  measured  by  reading  off 
the  angles  pointed  to  by  the  moveable  index  before  and  after  the 
changes  of  position. 

The  dome  which  covers  the  instrument,  and  which,  as  well  as  the 
other  details  of  its  erection,  was  constructed  under  the  direction  of 
the  Astronomer  Royal,  who  was  then  the  Cambridge  astronomer,  is 
supported  so  as  to  revolve  on  free  balls  between  concave  channels, 
holdfasts  of  peculiar  construction  being  provided  to  obviate  the 
eventuality  of  the  dome  being  dislodged  or  blown  off  by  wind  or 
any  other  unusual  disturbance.  The  winch  which  acts  on  the 
machinery  for  turning  the  dome,  is  carried  to  the  observer's  chair, 
so  that  he  can,  while  engaged  in  a  long  observation,  turn  the  dome 
slowly  without  removing  from  his  position. 

The  magnitude  of  the  instrument,  and  the  consequent  extensive 
motion  of  the  eye-piece,  rendered  it  necessary  to  contrive  adequate 
means  by  which  the  observer  could  be  carried  with  the  eye-piece  by 
a  common  motion  without  any  personal  derangement  which  might 
disturb  the  observation.  This  is  accomplished  by  means  of  an 
ingenious  apparatus  consisting  of  a  frame,  of  which  the  upper  edge 
is  nearly  a  circular  arc  whose  centre  is  the  centre  of  the  telescope, 
which  frame  travels  horizontally  round  a  pin  in  the  floor  exactly 
below  the  centre  of  the  telescope,  the  observer's  chair  sliding  on  the 
frame.  The  observer  can,  by  means  of  a  winch  placed  beside  his 
chair,  turn  round  the  frame  on  which  the  chair  is  supported,  and 
by  means  of  a  lever  and  ratchet  wheel  he  can  raise  and  lower  the 
chair  on  the  frame.  He  has  also  means  of  raising  and  depressing 
the  back  of  the  chair  so  as  to  give  it  the  inclination  he  may  at  the 
moment  find  most  convenient. 


INDEX. 


Note.— Tbi*  Indeji  refert  to  the  numbers  of  tbe  parafrapbs,  and  not  to  the  p«fee,  and  it 
ct>iupri«es  ibe  entire  contents  of  the  three  courses  which  compose  this  Hand-book.  It 
may  be  convenient  to  the  reader,  who  uses  tbe  work  for  the  purposes  of  reference,  to 
renieuiber  that  tbe  second  course  begins  at  paragraph  1304 ;  and  the  third,  at  paragraph 
S160. 


A. 

Aberration,  spherical,  1048;  longitudinal, 
1049:  lateral,  ib.;  chromatic,  1078;  of 
light,  'i440.    Bee  Light,  £y«,  Lnu. 

Absorption  of  heat,  15A8. 

Achromatism.  1078, 1081.    Bee  LigkL 

Action  and  reaction,  305,233;  bow  mo> 
difled  by  elasticity,  21S. 

Adams's  researches  as  to  Neptune,  8880. 

Adherenu,  effect  of,  370. 

Adhesion,  attraction  of,  351 ;  of  solids,  365 : 
examples  of,  366 ;  of  wheels  of  locomo- 
tives to  rails,  367;  between  solids  and 
liquids.  37^2. 

Affinity,  chemical,  353. 

Agonic  lines,  16tii;  American,  1669;  Asi> 
atic,  ib. 

Aggregation,  states  of,  13. 

Air,  momentum  of,  llh2;  retiiwtance  of, 
affects  projectiles,  Stil ;  resistance  of,  to 
falling  bodies.  554;  mechanical  properties 
of,  701 ;  atmospheric,  the  type  of  all 
elastic  fluids,  ib. ;  impenetrable,  703 ; 
has  inertia.  703 ;  compres«ible.  705 ;  elas* 
tic,  706 ;  has  weight.  707;  conipreseihility 
and  elasticity  of.  70rt;  diminution  of  vo- 
lume of  proportional  to  compressing  (hrcc, 
ib.;  weicbt  of,  701);  rarefied,  a  non-con- 
ductor of  electricity,  1718;  variations  of. 
at  sea  and  on  land,  S03;  changes  in  at- 
mospheric pn^ssure,  3321. 

Airy,  (Professor.  Astronomer-Royal),  ob- 
servations of  solar  eclipse  of  1851,  2930. 

Alloys,  liquefaction  of,  1453. 

Altitude,  3t<45.  and  aziuiuth  circle  (Trough- 
ton's),  3402;  (Greenwich).  3403 

Almanac  (Nautical)  preUicts  phenomena 

of  eclipses,  2958. 
Amptre.  method  to  reverse  galvanic  cur- 
rent, 1911;  apparatus  ibr  supporting 
movable  currents.  1915;  method  of  ex- 
hibiting revolution  of  galvanic  current 
round  a  magnet,  1933;  electro- magnetic 
rectanalc,  3003. 
Angle,  or  incidence  and  reflection,  317. 936 ; 
of  refhiction,  902;  of  total  refl«>ction. 
996;  refk^acting,  1004;  visual.  1117;  of 
polarization,  I^ ;  measurement  of, 2393; 
oomptement  of,  8361.    Bee  Stund,  UgUt 


Animals,  motion  of,  governed  by  centre  of 
gravity,  388;  wool  and  Air  of,  their  uses, 
1527. 

Animalcules,  minuteness,  organiaation, 
and  functions  of,  49. 

Annealing,  136;  use  of,  1433. 

Anomaly,  2607. 

Anode.  3054. 

Aphelion, 2605; distance. 2986.  See  Planett, 

Apojove.    Bee  Jovian  tfttem. 

Apogee,  2472. 

Apsfdes,  2472,  2607,  3303,  3807,  3308,  3810. 
3315.    See  Lunar  (iksery,  Ptrturbaliont, 

Aqueous  humour,  1086.    See  £y«. 

Arago,  electro- magnetic  researches,  1984; 
on  coating  of  sun,  3547. 

Archimedes,  anecdota  of,  658;  screw, 
700. 

Area,  visible,  1183. 

Arc,  linear  and  angular  magnitude  of,  8893; 
complement  of,  2361. 

Armatures,  1691. 

Armstrong,  hydro-electrical  machine,  1730. 

Awension  (right),  2405. 

Astatic  needle,  1695. 

Astrsa.    See  PUnHoidi. 

Astronomy,  2383. 

Astrometer,  Uerschel's,  3320;  Lardner's, 
3336. 

Athermanous  media,  1563. 

Atmosphere,  low  temperature  of,  superior 
strata  of,  1433;  non-conductor  or  elec> 
tricity,  1717 ;  dimensions  of  earth's,  8333; 
of  sun,  353G;  phenomena  of  eclipae  evi- 
dence of  solar,  3938. 

Attraction,  350;  capillary,  353;  between 
plane  eurfkces,377 ;  examples  of  capillary, 
378;  magnetic,  1619;  electric,  1696. 

Atwood's  machine  for  illustrating  falling 
bodies,  346. 

August's  hygrometer,  3346. 

Aurora  borealis,  SSifN);  influence  of,  on 
magnetic  needle,  2338. 

Austral  fluid,  1634. 

Axis,  principal,  342.948,  1096;  secondary, 
948;  of  lens,  1030;  of  double  refraction, 
1348;  magnetic,  1632;  of  circulating 
galvanic  current,  1936 ;  of  ellipse,  3460, 
9606;  of  rotation  of  earth,  3357 ;  of  moon, 
2475 ;  of  sun,  2553.    Bee  PsrlartelkiM. 

Atloiutli  83441  coBpassy  1650. 


■■bkut,iilKtKi-iii>ta*tK  iwinhn,  1WU. 

>  atBUncliniikal  Idafnpn.  1133. 
Be>.i>iBnk  ai  > :  emipmHUon  sC  I  Tit. 
„  (If  6a  Lm,  *c.  »«:  Ot- 


Clm  tiUet,  rouipuuot  m 


•  •I*,  (Mac*  OC  SL 


nov*  iD  conic  KctiaiiN  Son ;  lif  pcrtnUc 
■  □ilfanbnlJc,iiMpehoiUe,mi  ^tllif  br, 

pencidic.  3QI9:  ami}  ncuidi^  («  ok- 

"liplii  tcvolvin*  wiilii'"JuTorS>»»! 
3DI»;  Encke'l.  li.  SOtl:  UUc  of  ck- 
mcnti  sT  arbil,  30IS ;  IndlcalmM  sf  rr- 

■mini  nedinm,  XSOi  oovM  unisuMr 

lulian  Dflliell^  lnioI«,]e9T;  ttjaX 
SOU;  Oe  Vin>x  Mid  Snnu-i,  N»^ 

D'Arn9i'i,3033;(iiipiicDri;M,9W:iir 
i7e6.  naSi  UtiEri'*.  naa^  aiiiijiii  or 

Liplin  applM  lal.eHll'LMS' ;  RiiHi>* 

prncH  <iyiv  biill  idm  ilftcaiioa  nfpttMK, 
may  be  ileci>M,3MI :  inbaMe  I'MDtr  "T 
lie  Vko'i.  •'Iih  Uui  or  ie»,  VO :  BUia 
sua'*,  or  ISt*.  IHS:  PeoiV  of  l«>t^ 


COoroid,  lOse,  IIM.    &e»E»f 


INDEX. 


757 


racttr  ororb}ta,3049 ;  ellipticwliow  nwan 
diiUneet  are  neariy  equal  to  thai  of  Ura- 
nua.  3051 ;  of  long  perioda,  first  recofniaed 
as  penodic  U. ;  H  alley's  research«>«,  3033 ; 
Ualley's.  jft.  3093;  path  and  time  of 
perihelion  of  Halley^s  calculated  by  Clai 
raut  and  Lalande.  3056;  disturbing  action 
of  a  planet  on  a,  exfrfained,  3059 ;  effect  of 
the  perturbing  action  of  Jupiter  and  Sa- 
turn on  Halley*s,  between  Va8i  and  1758, 
3000;  calculations  of  its  return,  3061 ;  ta- 
bular synopsis  of  motion  of  H alley *s,30G3 ; 
Pons*8,  of  1812,  3064;  Olbers's,  of  1815, 
3065;  th  Vico'8,or  1846,  3066  ;  Brorsen's, 
of  1847, 3067;  Westphal's,  of  1853,  3068; 
tabular  synopsis  of  motions  of  these  six. 
3069;  elliptic,  whose  mean  distances  ex- 
eeed  limits  of  solar  system,  3072;  twenty- 
one  elliptic,  of  freat  eccentricity  and  long 
period,  it. ;  hyperbolic,  3074 :  parabolic, 
3075;  distribution  of  cometary  orbits  in 
space.  3076;  relative  number  of  direct  and 
retrograde.  3077;  inclination  of  orbits, 
3078;  directions  of  nodes  and  perilielia, 
3079;  distribution  of  the  points  of  peri- 
helion, 3080;  physical  constitution  of, 
3061 ;  apparent  form,  head  and  tail,  ib. ; 
Aucleus.  3083;  coma.  3083;  mass,  volume 
and  density.  30H8;  light,  3089;  Struve's 
drawings  of  Halley's.  3093;  its  appear- 
ances on  various  days,  3094.  A  »tq. ;  Sir  J. 
Herschel's  deductions  ft^oni  these  pheno- 
mena. 3103;  observations  and  drawings 
of  MM.  Maclear  and  Smith,  3105;  number 
of.  31 16 ;  duration  of  the  appearance  of, 
3117;  near  approach  to  the  earth,  3118. 

Compass,  azimuth,  1650;  mariner's,  1651. 

Compensators,  1306. 

Complement.  2361. 

Component,  and  resultant,  correlative,  150, 
and  resultant  interchangeable.  153:  or- 
thogonal, 3130;  radial  and  traniiversal. 
3132;  tangential  and  normal.  3133;  posi- 
tive and  negative.  3136;  effects  of  the 
radial  of  th<>  disturbing  force,  31.18 :  effects 
of  the  transvemal  of  tho  disturbing  force, 
3153;  effects  of  the  nrihnconal  component 
of  the  disturbing  force,  3158. 

Composition,  of  forces,  144;  of  forces  ap- 
plied to  different  points,  156;  of  motion, 
165 ;  examples  of.  174. 

Conipressionjdiminishes  bulk.  89 ;  augments 
density,  ib. ;  of  wood.  03 :  of  stunu,  93 ;  of 
metals.  94 ;  of  liquids.95 ;  of  water  proved, 
96;  of  gaties,  97;  of  vapour,  1499. 

Compressibility,  89 ;  all  bodies  compressible, 
90. 

Condensation.  1309,  14P5;  of  vapour,  1514. 

Condenser,  electric,  1745;  priririple  of, 
1746;  forms  of  Cuthbertson's,  17.'il. 

Conduction,  1313,  1519;  electric,  1710.  See 
Eltctrieitw. 

Conductibihty,  1313. 

Conductors,  good  and  bad,  1519;  electric, 
1711 ;  connecting  galvanic  elements,  1887. 

Congelation,  1308,  1441 ;  latent  heat  ren 
dered  sensible  by,  1437;  points  of,  1456; 
of  alcohol,  1471. 

Conic  sections.  3611. 

Conjunction,  2573;  superior  and  inferior. 
2576. 

Contraction.  1307. 1360 ;  general  effects  of, 
113;  of  solids,  136S;  of  mercury  in  cool- 
ing, 1464. 

III. 


Copernican  system,  3445. 

Cordage,  strength  of.  596. 

Cornea,  1085.    See  Eyt. 

Corpuscles  of  bl(H)d.  47. 

Coulomb's  eleclroncope.  1756. 

Couple,  defined,  160;  mechanical  efiSsct  o( 
161 ;  equilibrium,  163. 

Couronne  des  taases,  1883. 

Crank  described,  515. 

Crosse's  electro-chemical  researches,  3076. 

Cruikshank's  galvanic  arrangement,  1883. 

Crystals,  uni-axial,  1355;  biaxial,  1357. 

Crystallization,  indicates  existence  of  ulti 
mate  molecules,  60;  process  of,  01. 

Crystallized  stale,  some  bodies  exist  natu- 
rally in,  63. 

Crystalline  humour,  1087.    See  Eyt. 

Currents,  atmospheric,  cause  of,  13(49;  vol- 
taic. lUOl.  See  Etutriciiif.  Rectilinear, 
]!>07;  indcfiDiie.  ib.;  closed,  ib  ;  circular 
or  spiral,  ib  ;  circulating,  190T  ;  spiral  and 
heliacal.  1940;  thermo-electric,  3U37. 

Culhbertson'a  eleoric  condenser,  1751. 

D. 

Dance,  electric  1795. 

Daniel's  constant  battery,  1865, 1895 ;  hy- 
grometer.  3345. 

Davy,  galvanic  pile,  1889 ;  experiments  in 
electro-chemistry,  8083;  method  of  pre- 
serving copper  sheathing,  31U1.  See  Eiec- 
tricity. 

Dawes's  observations  on  Saturn's  ring. 
3813 ;  of  solar  eclipse  of  1851.  3936. 

Day,  civil,  3453. 

Declination,  1655,3453;  in  different  longi- 
tudes. 6C3;  observed  at  Paris,  1067. 

Defla^rator.  galvanic.  1893.  3135. 

Delarive's  floating  electro-magnetic  appa- 
ratus, 1957. 

Dcluc's  galvanic  pile,  1897. 

Density.  74;  determined  by  proportion  of 
mass  to  pores,76 ;  and  porosity  co-relative 
terms,  77;  examples  of.  81 :  effect  of  le- 
latiou  of  different  strata  of  same  liquid, 
1398;  relation  of  specific  heat  to.  1417; 
of  earth,  3373;  of  moon,  3481;  of  sun, 
V53*i;  to  deterniiiie.  3r>4(i.  See  Sun,  Mcon, 
Planett,  the  Motral  Pluntls,  Planttoid$t 
Cometf. 

Dew.  principles  of.  1577,  2348;  point,  2240, 
3344. 

Diameter  of  moon.  3468;  to  determine  real, 
34»33.  See  Sun,  tlie  teveral  PlantU,  Moon, 

Diathcrmanous  media.  1315,  1566. 

Dilaiability.  l»9. 

Dilatation,  1307;  by  temperatiire,  110;  of 
liquids  in  thermometers.  111;  usefbl  ap- 
plication of,  to  metal.  113;  general  f-ffccta 
of,  113;  of  mercury,  rate  of,  i:*38;  of 
solids,  1355;  of  gases,  1374;  of  gases 
differs  wiih  change  of  pressure  and  tem- 
perature, 1381 ;  of  liquids,  1301;  ratea  of, 
of  liquids,  1393. 

Dip,  lines  of  equal,  1658;  local,  1664;  oh* 
served  at  Paris,  1667. 

Dipping-needle,  1653. 

Direction  of  force,  146;  of  motion  in  curve, 
166;  resultant  of  two  motions  in  same, 
171;  in  opposite,  173;  in  different,  173; 
vertical,  338. 

Discharglng-rod,  1742. 

DisUoce,  of  sua,  3456  \  iDOQa>  lUAS  \  vafiAfli 


158 


I 


|HtwMIIH.MiiiiilWMiri.»;n(*iM',»; 
or  BIba  Vidli^  91 :  •mnpln  nr.  N ;  mi- 
MM.  pnvitf  kr  •iil«ir,  SI ;  or  Buiik,  33 1 

.'^^S'-'^JWV**-- ^ - 


Hi  BiunKia  aiuuiiM   sf^   IMS: 
~  ~     '  iiimdlir,  turn,  ami  dlna*- 


•,  A  ftfti  l>B|ili  sr  a 


tnnd  a( 


ta3 :  ul*.  can :  Kiuiiar,  gnlei,  wid  oi 
dliBt.SH;  IwiiiltidKra.  U.;  mia 


iij.assSi 


ir«i(lit.9H;an 
Iha  dlurnil  and 


■  i>r,U»;arMl, 


n|>aqun  ckiW  MIS;  ixniiDibta,  WIS; 
•niar  odrpriii  llnlu.  3M3.  appraraiicei 
■licmjlni  »liir,  leSJ ;  Bairyi  berula,  9»il : 
amarKlimeonui.SVHi  mwiralinni 
ur^>iranoinerRDyalnr,9g3l«nlMrrailniii 
srMM.  Dunhin  and  HumDhriiTi.  «93l; 
or  W,  On*.  «33a!  of  MM.  StFpbtnKo 
(nd  Andrrwi,  u.ia:arHt.Iji»Ht,MS4; 


EKcirKat  attnnioH  aad  »b<iMks«  m*. 

ElHtrK  taiuH.  SIM. 
llitil.  (ftj. 

It.;  »7Rt.  »('««.  l«r):  MJ,  «■! 

Kiu.  tnO;  ■*»  Ouiib.  mi  1  »UiH  ••! 

pBaii^H  ■■«  iH«aU*>  ankuacM.  IMi 

!5r"sr»..'r'-"'?i 

laialaUiw  atonla.  171(1  IndwUin.  n<* 

',-««fi,.'!:^,i'.iti.., — 

r*.?.'?ss4S;riBsa 

i-OIXU  at  ITVB;  if  niltoa  aliKUl>.  Ii» 
MKUic  pMol,  ]a04:  uepoirdB  < 
pHMkid.  IMTi  KFansalry>  ilecliaMB 


-Btu    ot    1*6: 
^ftciioCisa: 


tvpolbxia  sf  Tolla.  IHl, 


aJecin-mulln  (onhiMliDiH,  IBM:  p<>^ 
ilTO  and  niaiivB  pok..  l?Ui  Voluv 
am  combinaiien.iraB;  Wonaalea'Kna- 
binalioa,  ISWi  Haicl  iiBnl  anaiva- 
ncnl,  IMI  :«liadiital  tonUnalKia  via 
oira  Ruid,  ]»3;  wlib  eitd  BiiM^  IM: 
Grora'i  ballcrr,  IMS;  BniusnV  tall«T< 
IHA:    Duller*  cnnManl   ballHT,   I»I'; 

batleir,  1BI0:  WBoaliuine'i'  aiwih 
1P71;  B^rallofi^  ■jracam,  ISTSi  B«& 
qUBtall  lyilcai,  1013:  flcMnbtia'a  no- 
diAcallan   Df   Banarn-a    balltrjr.   int; 


INDEX. 


7«e 


Zamboni*t  pile,  1896 ;  pilM  of  %  liiiKle 
metaK  18!)9;  Kitter*«  iMondary  pil««, 
1900;  voltaic  currents,  19U1 ;  direction  of 
current,  JUO^;  poles  of  pile,  1903;  voltaic 
circuit,  1904;  method  of  coatinf  con- 
ducting wires.  1909;  supports  of  wires, 
1910;  Ampere's  method  to  reverse  current, 
1911;  Pohrsrheotiope,  1919^  electrodes, 
1913:  Ampdrc's  apparatus  for  supporting 
movable  currents,  1915;  reciprocal  in- 
fluence of  rectilinear  currents  and  mag- 
nets, 1916;  electro  magnetism,  1917; 
effect  of  shock  on  bodies  recently  deprived 
of  life.  3150;  on  a  leech,  ib.;  excitation 
of  nerves  of  taste,  S151;  of  nerves  of 
light,  S152;  of  nerves  of  hearing,  8153 ; 
■apposed  sources  of  electricity  in  animal 
organization.  2154 ;  electrical  fishes,  2155 ; 
properties  of  the  torp<*do,  215G;  the 
electric  organ,  9150;  atmospheric,  2959; 
obeervattons  of  Quetelet.  2909;  Romas*s 
experiuidnts,  ^Xi6;  inductive  action  of 
electric  clouds  on  earth,  9274 ,  fulgurites, 
S375. 

Electricity,  thermo-,  2038 ;  thermo-electric 
current,  9037;  Pouillet's  thermo-electric 
apparatus.  S042;  conducting  powers  o( 
metals.  '2044 ;  thenno-elertric  pilos,  2049 ; 
eleciro-chemistry,  9051;  electrolytes  and 
electrolysis,  205*2;  Faraday's  electro- 
chemical nomenclature,  9054;  positive 
and  negative  electrode,  9055 ;  electrolysis 
of  water,  •MSB;  Mitschcrlich's  apparatus, 
SOOO;  compounds  susceptible  of  electro- 
lysis, ^)08;  electro  negative  botlics.  9070 ; 
electropositive  bodifs.  2071 ;  researches 
of  Becquerel  and  Crosse,  9U76  ;  Faraday's 
voltameter.  9079;  Faraday's  law,  90^); 
Bir  H.Davy's Pzperinients/jnA3t  Faraday's 
doctrine,  2087 ;  Pouillet's  ob^rvations, 
2069;  Davy's  experiments  confirmed  by 
Becquerel,  2090:  liquid  electrodes,  9094 ; 
electrolysis  of  the  alkalis  and  earth's. 
2090;  tlM  series  of  new  metals,  9097; 
Sdidnbein's  experiments  on  the  passivity 
of  iron,  2098 ;  tree  of  Saturn,  9100 ;  Davy's 
method  of  preserring  copper  sheathing, 
SIOl ;  calorific,  luminous,  and  physio- 
logical effects  of  voltaic  current,  9134; 
Hare  and  Children's  deflatrators,  91.^5; 
Wollaston's  thimble  battery,  913<t: 
Jaeobi's  experiments  on  conduction  hy 
water,  2140;  combustion  of  the  metals, 
2141;  electric  light,  2143;  electric  lamps, 
SI  46. 

Electro-chemistry,  9051. 

Etoetrodea,  1013,  9055. 

Elertrolysis,  2062;  compoumls  susceptible 
of.  9008. 

Electrolytea,  2053. 

Etactrolyiie  classification  of  the  simple 
bodies,  9060. 

Bleetro-mafnets,  1960. 

Eleetro- magnetism,  1917;  apparatus  to  ex- 
hibit direction  of  force  impressiMl  by  a 
rectilinear  current  on  a  mafrnetic  pole, 
1929;  apparatus  to  measure  intensity  or 
such  force,  1993;  apparatus  to  ilhistratc 

.  electro-mavnctic  rotation,  1930:  Ampdre's 
method,  1933;  reciprocal  influence  of 
circulating  curronts  and  magnets,  1935; 
eirrulating  current,  U. ;  axis  of  current, 
1936;  spiral  and  heliacal  currents,  1940; 
Aaiptre  ami  DeUrive's  apparatua,  1057; 
iaaiabto  eqaiUbriam  of  eurr^al.  im? ; 

.  tigki-baMded  and    leA -handed    bellcea, 


1959;  electromagnetic  induction,  1B59; 
Savary's    experiments,    1965;     electro 
magnets,  1909;   electro-magnetic  power 
employed  as  a  mechanical  agent,  1971 
electro-motive  power  employed   by  M. 
Froment,  1979;  electro-motive  macninea 
constructed   by  him,  1973;  distributor, 
ib.;   regulator,  ib.;   use   of  a   contact 
breaker,    1960;     magneto-electric    ma- 
chines, 1981 ;  effects  of  momentary  in* 
ductivc  currents  produced  upon  revolving 
metallic  disks,  1904;  researches  of  A rago, 
Herschel,  fiabbage,  and  Faraday,  IWi; 
influence  of  terrestrial  magnetism  on  vol- 
taic currents,  19ij5 ;  direction  of  earth^s 
magnetic  attraction,  iA. ;  Pouillet*s  ap* 
paratus  to  exhibit  emcta  of  earth's  mag- 
netism, 1994 ;  Amptee's  rectangle,  2003 ; 
reciprocal  influence  of  voltaic  currents, 
9004 ;  voltaic  theory  of  magnetism,  2025 ; 
rbeoKopes  and  rlieometera,  S030 ;  differen* 
tial  rheometer,  9094. 
Electro-magnetic  induction,  1959. 
Elect ro-roetallurgy,  SI  10;    production  of 
metallic  moukh,  2121 ;  production  of  ob< 
Jects  in  solid  metal,  2199;  reproduction 
of  stereotype  and  engraved  plates,  9123; 
metallising  textile  fabrics,  9124 ; 'glypho- 
grapby,  2195;  reproduction  of  daguerreo- 
type, 9196. 
Electro-motive  force,  1846. 
Electro-negative  bodies,  9070. 
Electro-positive  bodies,  9071. 
Electrophorus,    1745,  1752. 
Electroscopes,  1753;  pith-ball,  1754 ;  needle, 
1755;  Coulomb's,  1756;  quadranL  1757; 
gold  leaf,  175H;  condensing,  1759.^ 
Electro- telegraphy,  9127;  conducting  wiree. 
2198;  earth  best  conductor,  9198;  tele- 
graphic   signs,  9199;    Morse's    system, 
9I.')9;  electro-chemical  telegraphy,  2133; 
Hain's  telegraph,  ib. 
Element- positive,  9056;  negative,  i^;  va* 

riable,  3195. 
Ellipse,  method  of  describing,  2460;  Awl, 
axis,  and  eccentricity,  ib. ;  major  and 
minor  axea,9(ilG:  instantaneous,  3195; 
paralactic.  3996. 
Elongation,  9571. 
Endosmose.  98ti. 
Engine  (.fire-).  752. 
Equator,  ma|:netic.  1614.  1658. 

,  thermal.  9172;  celestial,  9346»  9363; 

terrestrial,  9.158. 
Equatorial,  9:130. 
Equation,  annual,  3193;  of  the  centre,  3190; 

of  the  diuinoxes,  3986. 
Equilibrium,  of  couples.  162;  stable,  un- 
stable,  and   neutral,  9iW;  examples  of, 
309 :  power  and  weight  in,  rest  not  ne- 
cessarily implied,  400;  infers  either  ab- 
solute restorunifbrm  motion,  401;  stable, 
of   floating    body,  679;    unstable,  673; 
neutral,  U74. 
Equinox,  vernal  and  autumnal.  9431 ;  pre- 
cession of  the,  3975  ;  equation  of.  3986. 
Erard's  piano,  example  of  complex  leverage 

in,  440. 
Eunomia.    See  Planetoids. 
Evaporation.  I4H5;   mechanical   force  de- 
veliiprd  in,  1494;  heat  absorbed  In,  1511. 
Eye,  10P9. 
Eccentricity,    Bee  Lsaer  TlkMtni^  P««vikv* 

batiens.  Orbit,  PUiitU. 
ExoamoB««  ^K^ 


Kallini  buly,  vcJocJly  oC  mupiw-u   n 
l>m...llllll.S.I, 

FWft  Haiiaui.  IWO. 

FttmuBU,  antouai,  ulnutcogu  gt  ill 

FiHnllMi,  Si. 

Flnwwun,  ftua  of.  ripldneii.  lai  I. 

rU*-»tattt,  imnpla  ot  puUbv,  tug, 

rin  Hmm,  dm. 

PlnuiMil,SN8)  raFn  ud  motionior, 

•■iwct  or  ik.;  iQuiioa  or.  su^  n: 

wUeb   waipoH   TuiUc,  33)19:   (iIil 

Iki  nu\UJ  wj.  Xtni  praLubla  foi'm 
■inidim  or  lun  M  wtaicb  Um  im 
piKKd.  ma. 
ruiw*.  uioilani  of,  In  lla<i>ib.  179;  irii 
MiiM  or  (caln  eipluuid.  laX;  tIki 


F«m,  of  eJliiw-,  34W ;  einpiji,  3WI6. 

F"(«.3-iSl, 

Fonr. dlilurbinr, 31 II),  Mttm. 

Forcu,  clMlrica).  Iiw*  of.  IM 

FouHsli'i  ilcH>Diia(n[ion   of  rolauoD 

Fiwnlaf  uililurea,  MD7;  ■Bpanliu,  14 
Fn^Dch  niFiiiul  aynnn,  iwl. 
Friction.  SIS. 

FHUI  (hour),  WIS;  ptinelplnar,  1577. 


itiiH.  siDwi  of.  im 


of,  m.  ■«;  •ptclBe.  W: 

a, 

:liBf  LtlCKOpe,  1113. 

.pp.r.l'M>,  iSS.             "^ 

EI««.ll04,13ie;HnalUa,  IWS;  in 


na;ii;ien 

of  All  Ion.  ht:; 

nporalinn 

psraluni.  nil )  mil  alio 

Df.lM3;nll«- 

isS'S- 

as-'ss. 

i'ssi; 

■lunrpiliw. 

tllon     of,   1370: 

of.   i*.;  qi 

v'ii.u'S  sr 

Kl^b,™ 

Waimrwt 

™« of  *;«*»- 

■MAIoruii 

nal.  1G04:  i 

■  ntii.al.«pl 

tocdbrchc 

'aS'Is^vH' 

■tBHitnn  ot 

JMenoiich 

,9I<W:  UkibiU 

of  heat.  IMS,  '      "      1  1'    "       BabT'sM  ?lmi«<tt 

0]«a».  nimulenm  M  ft\»nwn»*  ot.  W-,  ai-    I    H.ithU.  Allan  Ihrnuah.  nnalyai.  nf.  s 

Globe' i™wi'ui),aaas.  "  \     »ot  oT'wS^'ib^oilii  «v"'^\°'9 


INDEX. 


791 


irMch  body  fttllB  in  a  feeond,  949; 
why  All  from  great,  not  so  detiruciive, 
8S4. 

Heliacal,  galTanic  pile  of  Paris,  1885. 

Helicia.    Bee  EUctrititf. 

Heliometer  (Oxford),  3397. 

Hemispbere  (ct* lesiial),  S330. 

BenderMD  (ProfeasorV,  discovery  of  pftral- 
lax  of  a  Centauri,  3303. 

Berscliel,  Sir  John,  electro-magnetic  re> 
Bcardies.  1984;  observations  of  moon. 
S491 ,  observations  and  drawings  of  clus- 
ters  and  nebula,  3388;  observations  and 
drawings  of  spots  on  sun,  3543 ;  hypo- 
thesis to  explain  solar  spots,  S5S2;  tele- 
scopic drawings  of  Jupiter,  3754;  deduc- 
tioiis  from  phenomena  of  H alley's  comet, 
3103;  astrometer,  3330. 

— — ,  Sir  William,  observations  of  Venus. 
9687 ;  of  Saturn,  3810 ;  observations  of 
dcMible- stars  to  discover  stellar  parallax, 
3355 ;  telescope.  331*5. 

Bind,  observations  of  solar  eclipse  of  1851, 
9935. 

Bodgkinson's  experiments  on  strength  of 
timber.  (>00. 

Horizon.  3331. 

Humboldt,  researches  as  to  snow-line,  9188. 

Humphrey's  observations  of  solar  eclipse 
of  185i.  3931. 

Hurricanes,  3328. 

Hunter's  screw,  501. 

Hydraulic  press,  Britannia  bridge,  casting 
of,  1538. 

Hydrostatic  balance,  771. 

Hydrometer,  773. 

Hygeia.    See  Planttmdt. 

Hygrometer,  Daniel's,  3345;  August's,  9346 ; 
Saussurit's.  3347. 

Bygrometry,  3339 ;  dew  point,  9340  9344. 

I. 

loe,  method  of  preserving,  1533;  production 
of  artifirial,  14(i8.  1579. 

— — ,  polar,  33n5;  extent  and  character  of 
iceflelds.330(>;  fabrication  of,  ifci5U. 

Icebergs.  3307. 

Impact  of  elastic  body,  316. 

Impenetrability,  93. 

Inactivity.  114. 

Incandescence,  1310. 

Incidence,  angle  of,  317. 

Inclination,  moon's,  3390.  See  Lunar 
tktorjf.  Orbit,  Perturbation. 

Induction.  1633;  magnetic,  1630;  electric, 
1738;  effects  of  electro-magnetic,  1959. 

Inequalities,  3184 ;  lunar.  See  Lunar  tkeary. 
Oeneral  summary  of  lunar,  333t>;  long, 
3355 ;  secular,  3364.    See  Parturbationa. 

Inertia,  114;  defined,  115;  astronomy  sup- 
plies proof^  of  law  of.  110;  examples  of, 
180;  supplies  means  uf  accumulating  force, 
534. 

Inflection,  1930. 

Influence  of  terrestrial  magnetism  on  vol- 
taic currents,  1985. 

Infusible  bodies.  1475. 

Inlaying,  metallic,  1368. 

Insects'  wings,  thinness  of,  43. 

Insulating  stools,  1714.  1741. 

Insulators.  1713. 

Instruments  ^remarkable  astronomical), 
3394.  Sir  Willian  Uencbal's  fbrty -ftet  re- 


fleeting  teleacopc,  7SM ;  lesttr  Rosse  tele- 
scope,  3396 ;  greater  Rosse  telescope,  .3397 ; 
Oxford  heliometer.  3396;  Troughton'a 
transit  circle,3399 ;  Greenwich  transit  cir- 
cle, 3400;  Pultowa  prime  vertical,  34U1; 
Troughton's  altitude  and  azimuth  circle, 
3403;  Greenwich  alt-azimuth,  3403; 
Northumberland  telescope,  3404. 

Intensity  of  force,  144. 

Interference.  836,  1330,  1941. 

Irene.    See  Planataidt. 

Iridescence  of  fish-scales,  4bc.  explained, 
1339. 

Isogonic  lines,  1663. 

Isothermal  lines,  3160;  isothermal  zones, 
3170. 

Ivory  balls,  elasticity  of,  105;  rebound  o£ 
315. 


J. 

Jacobi's  experiments  on  electric  conduction 
by  water,  3140. 

Jovian  system,  elements  of,  9999 ;  theory  of, 
3338;  analogy  to  terrestrial  system,  ib.; 
mutual  perturbation  of  satellites,3330;  re- 
trogression  of  lines  of  conjunction  of  first 
three  satellitea.  3331 ;  effects  of  their  mu- 
tual  perturbations  upon  their  orbits.3836; 
motion  of  apsides,  3337;  positions  of  peri- 
Joves  and  apjovea  of  the  three  orbits, 
3339;  value  of  eccentricity,  3340;  efl^s 
of  the  eccentricity  of  the  undisturbed 
orbit  of  the  third  satellite,  3943;  pertur- 
bations of  the  fourth  satellite,  3343 ;  com- 
plicated perturbations  of  this  system, 
3344.    See  P»rturbati»n». 

Juno.    See  Ptanetnda. 

Jupiter,  3739;  Jovian  system,  ib.;  period, 
3730;  heliocentric  and  synodic  motions, 
373l;distance,  37.13;  orbit,  3733;  annual 
parallax,  3734;  distances  fh)m  earth, 
3735;  orbital  velocity,  3736;  intervals  be- 
tween opposition,  conjunction,  and  quad- 
rature. 3737;  no  sensible  phases.  3738; 
appearance  in  firmament  at  night,  8739; 
stations  and  retrogression.3740 ;  apparent 
and  real  diameters,  3741 ;  relative  splen- 
dour  of.  and  Mars.  3743;  surflice  and  vo. 
lume,  3743;  solar  light  and  heat,  3744  ; 
rotation  and  direction  of  axis,  3745;  Jo- 
vian years,  3746:  seasons,  3747 ;  telescopic 
appearance.  3748;  belts,  3750;  telesrnpie 
drawings  of,3754 ;  obseivations  ofMiidkr, 
3755;  spheroidal  A>rm,  3756;  satellites, 
9757;  phases.  3758;  elongation  of  satel- 
lites, 3759;  dintanees  firum  Jupiter.  8760; 
harmonic  law  observe<l,  3761 ;  relation  be- 
tween motions  of  first  three  satellites, 
9763;  and  their  longitudes,  3763 ;  orbits  of 
satelliteo,  3764 ;  apparent  and  real  magni- 
tudes, 3765;  parallax  of  satellites,  3767; 
apparent  magnitude  of,as  seen  Horn  satel- 
lites, 97(«;  satellites  visible  ftt>m  cir- 
cumpolar  region,  3769 ;  rotation  on  their 
axes,  3770;  mass,  3771 ;  mutual  perturba- 
tions. 9773;  density,  3773;  masses  and 
densities  of  satellites,  3774 ;  superficial 
gravity,  3775;  centrifugal  force  at  equator, 
9776;  variation  of  superficial  gravity  fVom 
equator  to  pole,  3777;  long  Inequality  of 
3356.  Sea  Jovian  tffoUm,  PUnata,  Par 
turbtinu. 


[>(tiiH|«i1UF.I|!»)  (qoMlnanfai 


X«U(r>.  UDI. 


TMialtnn*  ef  OlIMie  m _.  ._ 

□rb.i.  xni  1  wgkctM  Dttke  tMHUiii  ma 


id  Itiu.  40:  clKWial.  IIS 
1. ;  HuuiBOa  CI  ti  ndiicat,  tTX;  H 


Mm) w  (irf  enlW^  dnMMi  □/  RtfiT^ 

unnet.  3im. 

Jup.lEr,  2754. 

pul'iiiin.   luao:   iinl   lUt;  bscnl  u4 


vnriilion  nfdip,  lasS;  (iaa  ofeqinl/i*. 

li'ja; kical dip,  iM4ip»)itoaarBifB«ie 
pDlri.li><U:  iuleir '— _i-.  i™i. 


».;  mMhnl  or  wiiflF  inneb,  IW«:  oT 
I«k;;   Iliufi   of  maineiic   Kim,    l«W; 


ilsincu.  natiinl,   iniS:   BiitSFial,   ICtTJ] 

rmi.pnmiii,  Iii4»:  Willi  »nw<|neBlWiiu 


INDEX. 


763 


IT:  Iwlineentrir  and  »yno(lir  inotionn. 
ail6tf;  orlMi,  aitiV;  divivioii  u(  fytioilic 
period,   37flO;   aitpnrenl    uiolioii,   tJTUI ; 
•iaii«»na  and  reir(»Krenioii.  tntri :  phayirv, 
snuCi;  apparent  and  real  dittmriei,  'J7(M; 
volume.  'iTUS;  niaaa  and  deniiiy,  t^titi; 
Bupn^ial  giaviiy,  S707;  Milar  light  and 
JbeaL  diU8:    rotation,  mu9;   days   and 
ni|[bta,  :t7IO ;  aeaaoni  and  climates,  S7I 1 ; 
obaervationa  of  Ucer  and  Miidler,  <i7l'J; 
areographk  character,  371:1;    teUicopic 
▼iewa  of,  971-1 ;  areugraphic  charts  nf  tlie 
cwu  heiuispheres,  i*. ;  polar  snow,  1715; 
poaaible  aaicllite,  2717. 
Maim  of  earth,  :l3'ii :  of  moon.  2481 ;  ofiun, 
1532;  to  determine  maw.  %33;  of  Mercury. 
9ti3*J:  of  Venus.  U.;  of  Jupiier,  *J77I;  of 
Saturn.  Stl37:  of  Tranns.  ^M&i.    See  tliK 
BtT«rm4PlaHtts,Plamel*.Planeioidt,Comets. 
MasMilia.    See  J'lmMtioidt. 
Materialn.  struiiKth  of,  ^7. 
Matting  on  ej[«>iics.  its  uso.  I.'i.ll. 
Blelloni.    tlirruiOMTopir.    iipparatiiN,    15<i^ ; 

tbernio*elertric  pik.  -Jtijd. 
MelptMucne.    f>vv  Plnuttetas. 
Meniscus,  l(i->f. 

Mercury  (nielal).  nintliixliinf  piiriryinL'.7l.> ; 
pr^pB ration   nli  for   tlM>riiioiiii?|i.'r,    \'.\'1'.\; 
iiiirtiiliirtioii   in  tiilto,  \.\'i>\\  rule  of  «lil:i- 
tatiou  nf,  iJ.'tf':  <pialiiii-s  \%liich  rendfr  it 
aconvenieiil  IherinoMopic  tliiiiJ,  VM'l 
— — .  (//aiir/),  2i».'>3:  niaM  of, 'JU;i*.>;  iivriod. 
9653;  lielioceniric  and  synodic  motions. 
9i»S4;  distance,  ^iti&5;orbit.'Ji*5e;  apparent 
motion.  Sti5!t;  apparent  diameter,  'Jtj4il: 
n>al  diameter,  3t)4)2:  volume,  Siitj.l;  mass 
and  density.  *^^i4:  superficial  yraviiy, 
'SenS;  solar  lifht  and  lieat. 'Jtjti6 ;  moun- 
tains,  2lMiU;  corrected  estimate  of  mara, 
30*24. 
Meridian,  magnetic,  1654. 1650;  true,  l(i54  ; 
tcrrpstrial.  ih.  XUb;  celebtial,  2342 ;  fixed, 
S3>iO,  mark,  S 101. 
Metals.  Cfmipression  of.  04 :  vibratory,  131  ; 
banhiHM  and  ela!>ticityof.tiy  rombiiiation, 
]3'i;  table  of  tenacity  of.  141 :  wcldablc. 
146<i;  ignition  of.  by  cl(.>rtririty,Ir'0-2;  elec- 
tric ciuiducting  power  of.  *J044  ;  new.2uW7. 
Metallic  bars,  useful  application  of  dilata- 
tion and  contraction  of,  11*2. 
Heleorolofy,  3l(>ti;  diurnal  thormoinctric 

period.  *Jlii*2 :  annual,  21b3. 
Metis.    See  PlmmetcidM. 
Microsrope.  simple,  l'iU3;  compound.  1307, 

^4011:  siilar.  I'ill. 
Bficnnvopic  phenomena,  40. 
Micmiiifter.   <:W-2;    parallel    wire,    SUM); 

wiri's,  240;!;  (|H>sitiou),  33Uj. 
Miiliiielit.  S45-J. 

Mill-stunem  method  of  forming,  383. 
Mirage.  KMK). 
Mirrfirfi.  silvering,  371. 
Mil!<cherliLh's  electro  clicmical  apparatus, 

'JOiiO. 
M<M^turf.  defiosit  of.  on  windows.  lo7(i. 
Mole<-.iiles,  ultimate,  may  be  inti;rr«;d.  (i'J; 
t«>o  miiinte  for  obATvation,  (i7 ;  indeotriic- 
tiblo,  ii(| :  coiM|imieiir  of  n  btwiy  not  in  con* 
tart.  74 ;  wniglit of  ncgregnlu  of,  its  w  eiuht 
of  h<idy,3ti:Z;  eflVriof  I'olir-Kion  on  gruviiy 
of.  ^<;  resultant  of  gravitutiiit{  forrcs  of. 
8ii4:  method  of  determining   rusuliunt. 
9i>5. 
Moment,  of  power,  defined.  400. 
— — .  of  weight,  defined,  409. 
Moawatam,  otwolid  mutma,  J 90 ;  of  liquids. 


101 ;  of  air,  1!K2:  arithmetical  expression 
for  comiiiunicatioii  of.  198. 
Month,  nioiin  temperature  of,  SlfiS:  of  mean 

temperature. '21(17;  lunar, '2480. 
Moon.  2405 ;  apfK'arance  of,  when  riving  or 
setting:  oval  form  of  disk,  S4*JC;  dintuncc, 
24<i(>;   linear  value  of  \"  on,  S-|t'i7:  a|>- 
parcnt  and  real  dioineter,  S4t')8;  apparent 
am]  real  motion.  2409;  orbit,  2171  ;  ap- 
sides. 2472 ;  apogee  and  {leiigce,  ib  ;  pro- 
gri'HHion  of  aiwides.  ib.;  nodes.  2473;  ro- 
tation. 3474  ;  inclination  of  axis  of  rota- 
tion, S475;  libration  in  Intiiucle.  247(}; 
phases,  247!):  synodic  perioil.  24H) ;  mass 
and  density.  24HI,2li4fl  ;  no  air  up<in.  24t<2; 
nKKinliglit.  24)r'4;   no   liquids  on,   24b5; 
dink.  21f*a;  surface.  24^0:  plains.  24l»0; 
mountains,  ib.;  influence  of  on  weather, 
21113;  other  influences.  2404;  red.  24M5; 
lideA  and  trade  winilti,  2513:  nmiparison 
of  liisiK'  (»f  full  moon,  with  sun,  3323. 
S'e  Lunar  thtorjf. 
MoniiliL'lK,  21H4. 
Morsi-'i*  elect  lie- telepraph,  2132. 
'    Aliili<:n.  144:  why  rein  I  (Uf  I  and  destroyed, 
llr;  how  afferieil  by  forre,  144;  resolu- 
tion of.  Iii5;  direction  of.  in  curve,  116; 
'        priiiriples  of  ronl|x>^ition  and  resolution 
oifiirreappliriible  to.  \',{i:  of  two  in  fame 
direriioii,  re-iiltniit  of.  171;  in  opp*isite, 
172:  ill  difll-rent,   173;  coni|»ositinn  and 
refidution  of.  examples  of.  174  :  of  fishes, 
birds.&c,  17H ;  absolute  and  relative.  185 ; 
lans  of,  210;  always  same  quantity  in 
world  explained,  221  ;  of  falling  body  ac- 
celerated, 238;  of  falling  bcnly,  analysis 
of,  240;  uniformly  accelerated,  242;  of 
boflies  projecteil  upwards  retarded.  254; 
down   inclined   plane,  255;  on    inclined 
Inne.  uniformly  accelerated.  256 ;  of  pro- 
eel  ill's.  257 ;  causes  of  irregular,  504 ;  eye 
has  no  perception  of  any  but  angular, 
1174.    See  Mm,  Moon,  PlaneU,  and  the 
tfreral  Ptanftg. 
Mould><,  for  casting  metal,  13G4;  electrO" 

metailurgic.  2121. 
Multiplier,  electric-maenetic,  2033. 
Musical  sounds  or  notes.    See  Sovnd. 


N. 


Nadir,  2.341. 

Nairiie's  cylinder  electrical  machine,  1737. 

\a|Hileon'H  {.'alvaiiic  pile,  leOO. 

Nebnl».     S«'e  Cluster. 

Needle,  niacnetic,  li>30;  dippinc.  irt.52;  di- 
urnal variation  of.  lli75;  influenco  of 
aurora  iMirealisi  cui.  Hi77 ;  .^sialic,  1M»5. 

Neptune.  2^r3 ;  difcoverv  o(i  ib. ;  reisearches 
tif  Le  Verrier  and  'Adamn.  2r<Hi ;  its 
predicted  and  olrtwrveil  places  in  near 
proximity,  2f*J<H ;  ijrbit.  2rlil):  rompanwui 
of  the  etriTti*  of  tlK'  real  and  predicted 
pIanot.v  2Ki:i:  p.riod.  2.'*ti4 :  relative  orbits 
of.  and  earth,  ^M\^:  apparent  and  real 
diameter.  2Ki7;  satellite.  2rti»*;  mans  and 
density.  2Hy'*:  apparent  niacnitud'j  of 
sun  at*.  21-110,  snuKTteil  rinir,  2i"0l. 

Newton's  laws  of  motion.  210. 

Newtonian  iele!<co|)e,  1215. 

Nobili's  reomeier,  2033;  tlicrnioolectrlc 
pile.  2<i5(l, 

Nodal  lines  or  points.    See  Sound. 

Nodes,  of  moon.  24r.t,  3221 ;  ascendinc  and 


t 


Cm  KlMt,  OhhCi,  !■«••  O-m.  I 


DeHli»><n.tll>iFL«>Hi,»M.    Sh  &'■*». 

i>.fliiKd.a»H:fc»U»HioDii.»i«Biluiiii- 

Br  iMIkilllr  of  tui  ullw  eo«MM"*t- 
I  or.SRWi  wtiMiid  anUMIMiti  of 
mar  OMBHtUCHa  U  tMiIni  dnubM  attt, 

tarn  I  hr  (Wdi*'*  mm*,  oito. 

(Mk.  OMftlMto*  oC,  Jlii. 

OiiUril  iMlnawiW,  lia^^ 

6rUl,  Ibunrjr  or  nrl*U*,  1119;  prnHihi- 
linai  ■uddinnrMui  linrH,  am ;  nwllvvl 
or  nnaU*  t4uMU,ilw  iminauiwnH 

Mili^iiiU  aMcra  IndlnUloH  Uul  nattm, 


Oxygci'i,  ila  i| 


E; 

nil. 

™; 

Bk 

if 

r"' 

'■" 

pS;; 

n 
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riHiKd  th>i  of  •elltitK,  MM;   pMcMtr 

fiLiiM.a«aiaiiuituu.>ft«;*«uu«><' 


1  :R;4ih;  jifr--'ii^  ii|riftvfnn' 


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.     Sh  JE4Hlriii/r-     ' 


pjiiH^i"iJi.3;rt':>iiKovn]>  nrotH.  ntsi 

fionllBl  pliiiti',  «ai :  dlmwry  «f  Jut.* 
S72-J:  "f  Vmw.  9^3 ;  o(  1I«  «1Iw  pl.~?^ 

Flaneii.  ;U1B:  prlmuTind  Kcnndtiy,  M  .- 

prclor.  a3U3 1  period!,  iSM :  »BciiUe  mn- 
llan.  iSiiii  (HJonirli:  Knd  MlnsairH 

■lan'ci  i'db.  UT  I ;  Hfllu'nciiHni .  SST^'qiixl^ 

■  <iri  infrrlw  ennJiiBHIoB,  9ST«:  ■noRAl 
moHanDri'ifctJatpIi  nri^aSTF.UOi;  «»t* 

Wnn.wTi  ■ppKRiUDMliwi'df  u^rtw 
planri.SSi^l.  SSM:  dinci  und  nlncm)* 


,1*«l%'».»y«f  •V««i>«fO,'- 


IHDXX. 


765 


of  orbitf.  node*.  ?634;  xndiac,  9GS0; 
methods  ofdctermininK  distance  from  sun, 
:i«)'<!7  ;  to  deieriiiine  real  diameters  and 
volunie8/2():t-i;  to  determine  ma«e8,3ii33; 
of  iMars.  "iuM:  of  Venus  and  Mercury, 
Sr>3U ;  nf  the  moon.  2640;  to  determine 
the  densities,  '2t>4ti:  to  determine  super- 
ficialgravity,!2(>47;classification  in  groups, 
iit>50.;  terrestrial,  ib;  planetoids,  2651: 
major,  'J(k>-2;  Mercury,  2Qi3;  method  of 
a^rertaiiiing  diurnal  rotation.  2667;  data 
which  determine  the  magnitude,  fnrm.and 
position  of  the  planetary  orbits,  397  J  ;data 
to  determine  the  place  of  the  planet,  2983 ; 
sidereal  period,  2984;  equinoctial  period, 
ib. ;  extreme  and  mean  distances  from  sun 
and  earth,  2985;  perihelion  and  apbelion 
distances,  2986;  conditions  aflbctin^  the 
physical  and  mechanical  state  of,  inde- 
pendently of  its  orbit.  2987;  distancea 
from  the  sun  and  earth  in  millions  of 
miles,  2988;  surfaces  and  volumes,  2969 ; 
masses,  2990;  densities,  2991;  intensity 
of  solar  light  and  heat.  2994  ;  superflcial 
gravity,  2995;  orbital  velocities,  2996; 
superficial  velocity  of  rotation  ,2997 ;  solar 
gravitation,  2998.  See  Ss/ar  tyscsai,  S»' 
UUites,  Ptrturbationt   Earth. 

Platinum  rendered  incandeacent,  1593. 

Plumb-line,  2*27. 

Pohrs  rheotrope,  1912. 

Points,  cardinal,  2343;  equinoctial.  2430. 

Point,  working,  defined,  390;  standard,  in 
thermometer.  1328;  freezing,  1332;  boiling, 
ib.  1504;  of  fusion,  1448;  of  congelation, 
1456;  consequent.  1648,  1962;  electric 
conductors  with,  1777;  electro-maguetic, 
1962. 

Pointers,  3333. 

Polarization,  beat,  1570;  light,  1366. 

Polariscopes,  12(i8. 

Polar  regions,  2177;  cold  of,  3313. 

Pole-star,  2333. 

Poles,  magnetic,  1614,  1656;  position  of 
magnetic.  1665;  (electric),  positive  and 
negative.  1853;  of  galvanic  pole,  1903. 

of  earth,  2358;  galactic,  3369. 

Pores,  defined,  75;  proportion  of,  to  mass, 
determines  density,  76;  differ  ft-om  cells, 
79;  sometimes  occupied  by  more  subtle 
matter.  80;  the  densest  substances  have, 
84 ;  of  bodies,  region  of  molecular  forces, 
349. 

Porosity  and  density  correlative  terms,  77; 
examples  of.  81 ;  of  wood.  82 ;  of  mineral 
substances,  87;  of  mineral  strata,  88. 

Power,  moving,  defined.  389 ;  when  it  mor^ 
than  equilibrates  accelerated  motion  en- 
sues,  402;  when  too  small  to  equilibrate 
motion  retarded,  405;  moment  of,  defined, 
409. 

powers,  mechanic,  classification  of,  424. 

Potassium,  3U97. 

Pouillet's,  modification  of  DanieFs  battery, 
180R;apparatU8  to  exhibit  eflfects  of  earth's 
magnetism.  1994;  thermo-electric  appa* 
ratus,  2042. 

Precession  of  the  equinoxes,  ^75.  See 
Sphenndal  ptrturbati^ng. 

Pressure.  1375.  1492,  1382, 1383,  1488.  Bee 
FmperiztUun. 

Prime  vertical,  8343. 

Prism.  1004.    See  Lir  Al. 

PriHnatk  speelrum,  1058.    BtUgkL 

Prqjeeiil*.  357;   shoe  Aorisonufijr, 
maovm  in  ptnhoUc  earveB,  900-  conelu- 


I  slons  as  to,  modified  by  resisUnee  of  air. 
361. 

Projection,  oblique,  5250. 

Proof  plane,  1770. 

Props  or  points,  effects  of,  in  machinery,307. 

Ptolemaic  nysteui,  2444. 

Pulley,  4U1. 

Pusilism.  collision  in,  311. 

Puinp,  ro\}e,  373;  air,  743 ;  lifting,  748;  sue> 
tion,  749 ;  forcing,  750. 

Pyramid,  stability  of,  281. 

Pyramids,  remarkable  cireumstanee  con- 
nected with,  3;t84. 

Pyrometer,  1313, 1350;  graduation  of,  1351. 

Pyscbe.    Bee  Fimntuidt. 


Quadrature,  8574 ;  line  of,  3188L  See  Lmnar 
tketrf. 

Quetelet.  observations  on  atmoepbenc  elec- 
tricity, 3863. 

R 

Radiation,  1314, 1543;  rate  of,  1554 ;  Inten- 
sity of.  1555;  influence  of  surface  on, 
1556;  radiating  powers,  1550. 

Railway  carriage,  object  let  fkll  from,  183 ; 
trains,  collision  of,  210. 

Rain,  2252 ;  gauge,  2253 ;  quantity  of,  3354. 

Rays,  diverging  and  converging,  903.  Bee 
UfkL    Solar,  3553. 

Reaction  and  action,  305, 333;  how  modified 
by  elasticity.  313. 

Reaumer's  scale,  1336. 

Red-hot,  1310. 

Reflection,  817,  936;  and  incidence,  817; 
laws  of,  explained,  1334. 

(beat),  1316,  1553,  1573;  reflecting 

powers,  1559.    See  LigkU  Htat, 

Reflector,  941,  948.    See  Light. 

RefVaction  fheat).  1317.  1570;  0>gM),  97P; 
index  of,  980 ;  rocus  of,  1036 ;  laws  of,  ex- 

Elained,  1824 ;  double.  1843;  laws  of  dou- 
le,  1349;  of  thermal  ravs.  1549. 

Regnault*8  tables  of  speciilG  heat,  1430. 

Regulator,  509 ;  general  princifrie  of  action 
of,  ik.;  governor,  510;  pendulum,  511; 
balance-wheel,  ib.;  water,  512;  fusee, 
513;  fly-wheel,  516;  electro-magnetic, 
1973. 

Rheoroeter,  8030 ;  diflferential,  8034. 

Rheoscope.  2030. 

Rheotrope.  PohPs,  1913. 

Repulsion,  354;  mutual,  of  atoms  of  gas, 
360;  mutual,  ascribed  to  action  of  lieat, 
363;  between  solids  and  liquids,  372; 
magnetic,  1619;  electric,  1696. 

Resolution,  of  forres,  154;  of  motion,  165; 
examples  of.  174. 

Resultant,  of  forces  in  same  direction,  148; 
of  opposite  forces,  149;  and  component 
correlative,  150;  of  forces  in  different  di- 
rectionn,151;  and  component  interchange- 
able, 153;  of  any  number  of  forces  in  any 
directions,  155;  of  parallel  forces.  157; 
condition  under  which  two  forres  admit  a 
single,  163;  of  two  motions  in  same  direc- 
tion, 171:  in  opposite,  172;  in  different, 
173 :  of  gravitating  force  of  molecules,  264. 

Retina,  1089.    See  Rf€. 

Ritter's  secondary  galvanic  piles,  1900. 

Rod,  diseliaT%\\^,  Vl\^  _^ 


m-iric,  1337  ■.rtniltn^.aO: 


1,  VW; 


■ntem.  (k.*  I»- 

e   inaiiDii,   n«; 
dMunea,   VTMl 


pLaan,  CM :  ■laUonl  nnd  nl»|rBII«WM> 

>utrg'«  ^ITnUina.'sTn.SSU:  ^urnJ 

■nd  auwdihva,  SlWi  antat  li|hi  bihI 
b<!a[.IT«tl;iti|>,B)Mip»llK>B<irnodn 
of  itDI  aail  <neJiiaUan  in  HUplic,  ilMWi 
ob1iqu<l]riirili>|  K  BlaiHri«bii.9Mili 
pliaaH  of  lUoWMi  bmiwbm  iwl  »■! 


£   probably    iriplfl:   otuflrTaltonj 
uell  ind  Dawu,  «ei3;  raearclH 


3p"/^?».'rr,  ''.'"hI^Iiw,  »»£l™«nl- 
luj:iu|uni^ini(al  fiweatjvtiaiar.tSWi 


■  DP||T>ph)'n(.aMl! 


K:l»«»«ii-i  nadilhlUiHi  of  Bdii»i 
vrrt.  Vf!*:  .ipMimeoH  «■  ine  pa 


DOilllilw  oCtltT;  <fe|U<l 


Bwbu,  a»  or,  1 
nlh.w 


fllnM,BM. 

flMll|>«BB>l 


dFBWIBfm  at  BBllBft 

IwnvlilBl  I'm  oC  IMt.  »l% 


ihini-intii«inr,aM7;» 


asaihliBW^  lUI 
Sodiorn.  Vm. 


SpmBchsBl,  ItOfl;  n 


BiaHhv,  nr  tiodj.  eomtjllona,  9»:  nfp 
Biar«,'(llir-'d).3334;(ii>rul»rpar»11«i.p«ni- 


irv  33IB;  HanrMI'i  BMroiiMUr.  mt; 
ini'nnnilTB  lu«n  oT  ■   Cealnri  Willi 

RiiaBure'ahvRTnmelai.^lVI.  V       <\«\  Vkm.SMI'.  BoniNiriBBBsr  liMnar 

SB»«r['annHjmeBH.inofll»>lJutton«KV(J  \      ti\\»Mm-ft>^.teo.-,y  «.>.Bj>I 


INDEX. 


767 


of  Mm  and  flxad  tlv,  333S;  aitrometrie 
taWe  otf  IttO,  2339;  um  of  telescope  in 
Mellar  ob»ervation»,  3330;  teleicopic 
3332;  stellar  nomonclature,  3333;  use  of 
poinlers,  3334;  of  star-maps,  3335;  of 
celestial  globe,  3X)6:  proper  motion  of, 
33(i3;  cffiact  of  sun's  supposed  motion  on 
apparent  places  of,  3365.    8e«  FtrmamnU. 

Biars  (periodic,  lempiirary,  and  niiiltiple), 
333d:  missiu9.3:i45 ;  Stru  ve's  classification 
of  double,  3J6U;  coloured  double,  335*2; 
attempts  to  discover  stellar  parallax  by 
double,  3354 ;  observations  of  Sir  William 
Herschol.  3355;  extension  of  law  of  fra< 
▼flat  ion  to,  33S7;  orbit  of  star  round  star, 
^58;  magnitudes  of  stellar  orbittf,  33til ; 
masses  of  binary  stars  determined  by  their 
parallax  and  period,  33(il. 

Star  (polo),  2333;  eflect  of  annual  parallax, 
f{44ii;  mornins  and  evening,  35H<},  3679; 
singular  visibility  of,  aAer  commence- 
Djent  of  occultation,  21*66;  suggested  ap* 
plication  of  lunar  oocultations  to  resolve 
double,  3969;  pole  star  varies,  3^83. 

Bteain,  high  pressure,  expansion  of,  1438. 

Steam-boats,  collision  of,  310;  expedients 
adopted  in,  to  counteract  effect  of  aide 
wind,  677. 

Steel,  tempering,  1484. 

Sieel-springs,  elasticity  of,  107. 

Stellar  clusters  and  nebule.    See  Qiuttn, 

—  universe,  3384. 

Stone,  compression  of,  93. 

Stools,  insulating,  1714.  1741. 

8toves,l386;  unpolished,  advantage  of,  1574. 

Stratingh's  galvanic  deflagrator,  1803. 

Structures,  metallic,  1306. 

Struve's  drawings  of  Hal  ley's  comet,  3093. 

Strychnine  dissolved  in  water,  55. 

Substances,  magnetic,  1630. 

Sulphur,  fusion  of,  1455. 

Sun,  3539;  appearance  of,  when  rising  or 
seltins.  1170,  heat  emitted  by.  3414,3316  ; 
oval  form  of  disk.  3436;  distance.  3456; 
apparent  motion,3458 ;  efibct  of  attraction 
on  tidea.  8517;  apparent  and  real  mag- 
nitude, 3539 ;  surface  and  volume,  3531 ; 
mass  and  density .3538;  (brm  and  rotation, 
8533;  axis  of  roution,  ib.;  spots,  2534; 
atmospheres,  3536;  Capocci'a  observations 
and  drawirigs,3540 ;  Fastorff^s,  3541 ;  Sir  J. 
HerschePs.  3543 ;  coating  of,  8546.  3549, 
test  proposed  by  Arago,  3547 ;  rays,  calo- 
rific, 3553;  probable  cause  of  solar  beat. 
8554 ;  distance  determined  by  transit  or 
Venus,  3963;  comparison  of  lustre  of 
with  full  moon,  3333;  of  light  with  that 
ofa  Centauri.  3384 ;  of  intrinsic  splendour 
of.  and  fixed  star,  3385;  not  a  fixed  centre, 
3364 :  efl*eci  of  supposed  motion  on  places 
of.  the  stars,  3365;  velocity  of  solar  mo- 
tion, 3367 ;  probable  centre  of  solar  mo- 
tion, 3368. 

Surface.  See  the  »evtral  PUntts^  Atn, 
Planets. 

Swimming,  175. 

Syringe,  exhausting,  730 ;  fire,  1418. 

Sjzygy,  line  of,  3187.    See  Lmnar  tkecrf. 


Telescope.  2304.  1312:  Newtonian,  with  mi- 

crometric  wires.  8303;  use  of.  in  stellar  ob- 

•ervations,  3330 ;  Uersebers,  3395 ;  earl 

of  Roaae'iL  3386^3397;  Nortliufflberitiid, 

J404, 


TMiperatnre,  I3S0,  1374;  dilaUtion  by. 
110;  affects  malleability,  135;  methods  of 
computing,  acroiding  to  different  scales, 
1337;  of  greatest  density,  1396;  method 
of  equalization  of.  1413;  in  liquids  and 
gases,  15.'3;  of  globe  of  earth,  1540,  ne- 
cessary to  produce  combustion,  1588;  of 
blood  in  human  species.  1596;  of  blood  in 
animals,  1598.    See  /feat. 

,  local  variations  of,  3161;  mean  di- 
urnal. 3164;  mean  of  month,  3165;  of 
year,  2166 ;  month  of  mean,  3167 ;  of  the 
place,  3168 ;  table  of  Paris,  3182 ;  extif^iie, 
3183;  depending  on  elevation,  S1H5; 
stratum  of  invariable.  8190,  et  teq  ;  of 
springs,  3196;  of  seas  and  lakes,  3197; 
variations  of  air  at  sea  and  on  land,  33C.) ; 
of  celestial  spaces.8318 ;  received  by  earth 
from  celestial  space,  3319. 

Tenacity,  140;  table  of,  of  metals,  141 ;  of 
fibrous  textures,  148. 

Terrestrial  magnetism,  1649;  infiuence  of, 
on  voltaic  currents,  1085. 

Thulia.    See  Fiantt^idt. 

Thaumatrope,  1156. 

Thermal  unit,  1405. 

Thermo-electricity,  8036.    See  Eltctrieitff. 

Thermometer,  1313;  mercurial,  1333;  tube, 
1384;  bulb,  1335;  self-registering,  1344; 
spirit  of  wine,  1345;  air.  1346;  differen- 
tial, 1349 ;  effect  of,  on  refraction,  8434. 

Thermometry,  1380. 

Thermoscopic  bodies,  1 381 ;  apparatus,  1564. 

Tlietis.    See  Planetoid: 

Thunder,  8868 ;  tubes,  8275. 

Tides,  8513;  lunar  influence,  8514;  waxCn 
attraction,  8517;  spring  and  neap,  8518: 
priming  and  lagging,  8580;  researches  of 
WheWell  and  Lubbock.  3581 ;  diurnal  in- 
equality, 3533;  local  effects  of  land,  3534 ; 
velocity  of  tidal  wave,  8585 ;  range,  3586; 
effect  of  atmosphere,  S587. 

Timber,  strength  of,  595. 

Time,  sidereal,  833i3,8453;  mean  solar  or 
civil,  3451 ;  apparent  solar,  3455 ;  equa- 
tion, ib. 

Torpedo,  electrical  properties  of.  8156. 

Torricelli.  anecdote  of,  710;  celebrated  ex- 
periment of,  711. 

Torsion,  elasticity  of,  109. 

Trade  winds,  3528. 

Transit.  3397,  2902,  3950.    Bee  £e/lpss. 

,  of  the  inferior  planets.  8961;  condi- 
tions, ih.;  intervals,  8968;  sun's  dis- 
tance determined  by,  of  Venus.  3963. 

Transit-instrument.  3397;  Troughton'a 
circle,  3399;  Greenwich,  3400. 

Tread-mill,  440. 

Tredgold,  table  of  transverse  siiength  of 
metals  and  woods,  609. 

Tree  of  Saturn.  8100. 

Tropics,  8436. 

Tube,  properties  of  capillary,  375;  thermo- 
metric,  1324. 

Twilight,  3435,  8693.  See  the  ssrera/ 
PUnUs. 

a. 

Undulation,  theory  of.  7P9. 

Unit,  ihermonietric  13.'M:  thermal.  1405. 

Uraiiography  of  Saturn,  prevailing  errors 

as  to.  3843.    See  te/ara.  LarduT. 
Uranus,  8865;  disonver^ . ift. ;  ^UQd^^t8fi&\ 


Mm  Vltiun  fiMn.  Rnfi. 


?;«:e 


p&tllAtMar 


M,  lOM;  HiiUHil,  sT  oadle,  ins. 
mineu.  SbS)  iwo-iiliiT^  of  BriOee, 

ui,9u7a:  niaa  iif.  90^:  pniBd,an70: 
■uim,  w;j;  iirbii,MiiSi  ippannt  ■»■ 

M;  muu  ■HddEiuill)'.  SuSiiuiwiSciit 
■  til)'.  MM;  Klir  lifbl  iBil  beii,  9u8£: 

.  h  on  "<'<r  Caul  a  l!HM»ct«l.  and  St'm  ler. 
RT^DrBnrandMSrlJiir.a^iBHiinil 


?y: 


9(  buiiiiiiiii.  isas.  iiet.  itR. 

Ktidillciiti'jD.lUI  ;ii4«MlrlnrV, 
piBvian,  lcnperalar«,  aaaitiB 
I  Tipcmr  Di;  I1IS;  «afW|ii>iiil 
•till  MDipgniiins.iiaiiBMM' 


«ini  niUiai  u4  MKlac  lai«>i 
U.,'  sUlll>  oT  ftkltiM  I^  Ml. 
WKigniArbudlo  proounwiial  mob 
of  maiwr,  337 1  or  bob  BaRtN 
DiDlKulei. »»;  deSoi^  3SI :  an 


wmnini-nblc,    la   lllunnie  a 

rorec,  Sie. 
Wbi>pcriu(-(al(ertca,  B63. 

1J9.'        '  "        °    ""  "' '"«  " 

Windless. 


;.  38i  r>1">nh;  Mnha 


h.  Xai.Zltl:  diiiina.  i 
iMtbenual,  ai  j^  «  MI. 


CATALOGUE 


BLANCHARD  &  LEA'S  PUBLICATIONS. 

CAMPBELL'S    LORD-CHANCELLORS.    New  EdiUo^i.    (Joftlsnud.) 

LIVES  OF  THE  LORD  CHANCELLORS 

AXD 

KEEPERS  OF  THE  GREAT  SEAL  OF  ENGLAND. 

rROM  TDK  BABLIIST  TIIIE8  TO  TUS  BlIGN  OP  KIHG  OEORGE  IT. 

BT  LORD  GUIEF-JUSTIOB  CAMPBELL,  A.M.,  F.R.8.E. 

Second  American,  from  the  Third  London  Edition. 

Complete  in  seven  handsome  crown  8to.  Tolames,  extra  cloth,  or  half  morocco 

This  has  heen  reprinted  from  the  author's  most  recent  edition,  and  embrac?c 
hia  extensive  modifications  and  additions.  It  will  therefore  he  fonnd  eminentlj 
worthy  a  continuance  of  the  great  favor  with  which  it  has  hitherto  been  received. 

Of  the  solid  merit  of  the  work  our  Judfpnent  mtj  be  fathered  ftom  what  has  already 
been  nJd.  We  will  add  that,  flrom  Its  Inflnito  fUnd  of  aneedote^  and  liappj  variety  of  style, 
tba  book  addres5C8  Itself  with  equal  claims  to  tho  mere  general  Deader,  as  to  the  legal  or 
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■onndng  It  entitled  to  a  distinguished  place  on  the  shelves  of  every  scholar  who  Is  fiMunate 
eBOogfa  to  possess  itv— /Voter's  Magaxim. 

A  work  which  will  take  Its  place  in  our  libraries  as  one  of  the  most  brilliant  and  valuable 
eontributions  to  the  literature  of  the  present  day.— ^Mauntm. 


BT  THE  SAME  AUTHOR— TO  MATCH  —  (Now  Ready). 

LIVES  OFTHE  CHIEF-JUSTICES  OF  ENGLAND, 

From  the  Nomun  Conqneit  to  the  Death  of  Lord  ¥aTigfleld. 

excoNS  BDmoH. 

In  two  very  neat  vols.,  erown  8vo.,  extra  eloth,  or  half  morocco. 
To  match  the  "Lives  of  the  Chancellors*'  of  the  same  anthor. 


MEMOIRS  OF  THE  LIFE  OF  WILLIAM  WIRT.— By  Jobv  P.  KBRirxDT, 
Esq.  In  two  handsome  royal  ISmo.  volumes,  extra  doth,  with  a  Portrait. 
Also,  a  handsome  Library  Edition,  in  two  octavo  rolnmes. 

URAnAM'S  HISTORY  OF  THE  UNITED  STATES;  From  thb  Fuundivg 
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vised  Edition,  from  the  Author's  MSB.  With  a  Portrait,  and  a  Memoir  hy 
President  Qcnrcr.    In  two  large  and  handsome  octavo  volumes,  extra  cl.ith. 

WILLIAM  PENN,  is  Historical  Biograprt.  With  an  Extra  Chapter  on  tin- 
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volume,  extra  cloth. 

OiriZOT'8   GLIYBB   CBOXWBLL. 
HISTORY   OP  OLIVER   CROMWELL  AND   THB  ENGLISH   COMMON- 
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BV8BBLL*B   LIFB   OF   FOX. 

MEMORIALS  AND  CORRESPONDENCE  OF  CHARLES  JAMES  FOX. 
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BtTitcd,  with  Additlona, 


YOUATT   AND   SKINNER  ON   THE 

TAB  nOR3E.-BT  Wilu*i<  Yoditt.  A  Mew  SditioD, 
tioDi.  ToMtbcr  with  k  Oensnl  Hiftarj  of  tbt  Hdim 
Annlnti  TrotttiiE  Hone;  how  Tnlnod  and  Jocktjti 
toitkable  PnformuiHi;  uid  in  Etuy  OD  tha  Au  > 
BKimtii,  Aluatut  P«tiiiu(ir-G«ii*nl.  kod  Sditot  al 
•no  hmodHma  osUro  tolDma,  utn  eloth. 
Thli  edition  of  Yoiutl'*  well-known  ind  (tudwdwa 
DliWMi,  and  TrNLtDiant  of  tb«  Qorw,  auhodjini  tha  ti 
SkiiHMr,  hu  ilnady  o"  ■      '         •  ■      ■      ■ 


YOUATT  AND  LEWIS  ON  THE 
THE  Tt90.    Bj  WrLLUK  Yowrr.    Ediled  by  R  J.  I 
meraoi  uai  beiatUkil  DlBrtraUmi.    In  one  1*17  haadx 
crinnon  «latli,  gilt 

ADVICE  TO  YOUNa  SPORTSHEiT  in  ill  thit  i 
gHeotiiM.  By  LiKUT.-Col.  F.  UiwiBi.  Seoond  Am 
London  Edition.  Edited,  with  nnnarooa  Addiliani  im 
PoHTEB,  Editor  of  tha  New  York  Spirit  of  ibo  linoi. 
octara  Tolame,  extra  tnaiBo  oloth,  with  plitei. 


Tetj  luge  rojil  llmi 
eolamned  pagei.     Tbii  work  11  sow  offered  at  a  verj  1( 

THB  YOUNS  HILLWRIOHT  AND  HILLBR'B  aUID 
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HBW  Atf D  IMFBOVED  BDITIOK. 

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COBDBMIOAL  TEOHHOLOGT ; 

OR.  CHEMISTRY  APPLIED  TO  THE  ARTS  AND  TO  MANUFACTURES. 
By  Dr.  F.  Knapp.  Edited,  with  numerous  notes  and  additions,  by  Dr.  Ed. 
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GRAHAM'S  ELEMENTS  OF  CHEMISTRY; 

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lu   one  retj  Uigt   mil  baadjooio   ocLito  Toluiae,  nilli   tnonlr-eEglit  Uiulifi 
PUtci,  and  t*a  U&pi. 


aMu-Siliyi  i 


,  Tolgm',  csUu  cloUi, 


DON  QUIXOTE  DE  Li  MANCUA.  Tranililed  from  Ibo  Spanuh  or  Mibcil 
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mfnai  UluitnlJosi,  hj  Too;  Jobnnnot.  la  tiro  beitaliftilly-priDtcd  TolBDif, 
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TUE  LANGUAGE  OP  FLOWERa,  wllb  niuBlmliTo  Poetry.  To  -bisb  m 
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me-NoL"  In  ona  elrgant  rojal  18mo.  rolumo,  eitra  criniioa  dolh,  K'tt.  illi 
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DANA  ON  ZOOPHTTES.  Being  part  of  lbs  pobllcaUoDi  of  (b*  Unrni  StaiU 
BirLORrKo  EirBDmas.  On*  Inrgs  royal  quarto  Tolums  of  Isttsr-prwi,  aait 
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(ilcly  engrared  on  eMtl,  and  colonred  after  nature. 

JOHNSTOH'S  PHTSICAL  ATLAS. 

THE  PHYSICAL  ATLAS   OF  BATOKAL  FHBNOUEKA,  roK  m  Uai  or 

L'oLLiaBS.    ACADEHIEB,    AND     FaHII.111.        By    AbCIAIIDBa    KeITB    JaBS9T«5, 

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beet  »lyle,  togolber  witb  over  ons  hundred  pagei  of  deicrlptiTa  letter-pnn. 

DE   LA  BECHE'S    GEOLOGY. 

THE  OKOLOGICAL  OBSERVER.    By  Sm  HeifBi  T.  Ds  tl  Bbcbi,  r.R.8,, 

ic.     In  one  large  nnd  bandBoms  oetaio  Tolunie,  FJtli  OTer  SIO  illiutiaUoni. 

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A   IIANB-BOOK.  0?   CnUli\S.tWl,'SBLft»iaETICAI*   PBACTICAL,  AKB 

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BLANCHARD  k  LEA'S  PUBLICATI0NS.^iSbieiil(/2«.)  6 

Lately  PnblUlied, 

PRINCIPLES  OF  COMPARATIVE  PHYSIOLOGY. 

BY  W.  B.  CARPENTER,  M.D.,  P.R.S.,  etc 

A  new  American,  from  the  fourth  and  reyiscd  London  edition.  In  ono  large  and 
handsome  octaro  Tolnmo  of  750  pages,  with  309  beautiful  illustrations. 
The  present  edition  of  this  work  will  be  found  in  every  way  worthy  of  its  high 
repntation  as  the  standard  text-book  on  this  subject.  Thoroughly  rcTiscd  and 
broagbt'ap  by  the  author  to  the  latest  date  of  scientific  investigation,  and  illus- 
tmtcd  with  a  proftision  of  new  and  beantiftil  engravings,  it  has  been  printod  in 
the  most  careful  miuiner,  and  forms  a  volume  which  should  bo  in  the  posses^iun 
of  every  student  of  natural  history. 

IT  THi  SAVH  AVTHOR.    (Now  Ready.) 
THE   MICROSCOPE   AND  ITS  REVELATIONS.     With  an  Appendix  con. 

talning  the  Applications  of  the  Microscope  to  Clinical  Medicine,  etc.     By  F. 

G.  Smith,  M.D.    Illustrated  by  434  beautiful  engravings  on  wood.    In  one 

large  and  very  handsome  octavo  volume  of  724  pages;  extra  cloth,  $1.00, 

leather,  $160. 

Br.  Carpenter's  position  as  a  microseopist  and  physiologist,  and  his  great  cxpe- 
rieoee  as  a  teacher,  eminently  qualify  him  to  produce  what  has  long  been  wanted 
— a  good  text-book  on  the  practical  use  of  the  microscope.  In  the  present  volume, 
bia  object  has  been,  as  stated  in  his  Preface,  ''to  combine,  within  a  moderate 
eompass,  that  information  with  regard  to  the  use  of  his  'tools,'  which  is  most 
cesential  to  the  working  microscopijit,  with  such  an  account  of  the  objects  best 
fitted  for  his  study,  as  might  qualify  him  to  comprehend  what  he  observes,  and 
might  thus  prepare  him  to  benefit  science,  whilst  expanding  and  refreshing  his 
own  mind."  That  he  has  succeeded  in  accomplishing  this,  no  one  acquainted 
with  his  previous  labors  can  doubt. 

The  great  importance  of  the  microscope  as  a  means  of  diagnosis,  and  the 
ooraber  of  miseroseopists  who  are  also  physicians,  have  induced  the  American 

fabUshcrs,  with  the  author's  approval,  to  add  an  Appendix,  carefully  prepared  by 
'rofessor  Smith,  on  the  applications  of  the  instrument  to  clinical  medicine,  toge- 
ther with  an  account  of  American  mioroscopea,  their  modifications  and  accesso- 
ries. Tliis  portion  of  the  work  is  illustrated  with  nearly  100  wood-cuts,  and,  it  is 
hoped,  will  adapt  tho  volume  more  particularly  to  the  use  of  the  American  student 
Every  eare  has  been  taken  in  the  mechanical  execution  of  the  work,  which  is 
eoofidently  presented  as  iu  no  respect  inferior  to  the  choicest  productions  of  the 
London  press. 

IT  TBR   SAm  ArTBOR.      (Just  IsSUCd.) 

ON  THE  USE  AND  ABUSE  OF  ALCOHOLIC  LIQUORS  IN  HEALTH  AND 
DISEASE.    In  one  neat  royal  12mo.  volume,  extra  cloth. 


BIJSHNAN'S  POPULAR  PHYSIOLOOY. 
THE  PRINCIPLES  OF  ANIMAL  AND  VEGETABLE  PHYSIOLOGY,  A 
PoprLAR  Trsatibe  ov  the  FuNcnoivs  AND  Phekombna  of  Oroanic  Life. 
To  whioh  is  prefixed  an  Essay  on  the  Great  Departmenti  of  Human  Knowledge. 
By  J.  Stbveesoe  Bdshxan,  M.D.  In  one  handsome  royal  12mo.  volume,  with 
over  100  illustrations. 


OWEV  ON  THE  SKELETON  AND  TEETH.    (Now  Beady.) 
THE  PRINCIPAL  FORMS  OF  THE  SKELETON  AND  OF  THE  TEETH. 
By  Professor  R.  Owen,  author  of  "Comparative  Anatomy,"  etc.    In  one 
handsome  royal  12mo.  volume,  extra  cloth,  with  numerous  illustrations. 

PRINCIPLES  OF  PHYSICS  AND  METEOROLOGY. 

By  Professor  J.  Miiller.  Revised,  and  illustrated  with  over  500  engravings 
on  wood,  and  two  handsome  colored  plates.  In  one  large  and  beautiful  oetaTO 
Tolame  of  neariy  060  pagei. 


Sow  Caiiri;.ETe. 

HANDBOOKS  OF  NATURAL  PHILOSOPHY  AND  ASTRONOMY.       .' 

BY  PIOXYSIUS   LARDSEll,  I»,C.L.,  I 

rsrnwFl}  I'n.ftUDC  U  XlItLrkL  rbllMOplif  snj  Ailrunom;  la  CntTSTill;  CaiXrft,  Uiadiia. 

Ttis  valBftWe  Series  in  no"  complclc,  coa-«lilinE  uf  ihrce  Conraes,  u  follatu:—     ] 
FIRSTCOUNSE. 

MECHANICS.  HYOHOSTATICS.  HYDRAULICS,  PNEUMATICS.  SOUND.  Si  OPTtC^    1 

la  one  Urge  rojul  Hmn.  voluine,  of  TaO  pngea,  will  HI  niniLnliinu. 
SECOND    COURSE, 

HEAT,  MAGNETISM,  COMMON  ELEDTBICITY.  AND  VOLTAIC  ELECTRICITY. 

In  on*  lOjii  l!ma.  vulamr,  of  450  ixge*,  nitb  SM  IllBitraliinic 
THtnO     COURSE, 

ASTRONOMY  AND  METKOUOLOGY. 

la  ona  r»ry  Urge  tojiJ  ISmo.  folume,  of  otirly  8iiO  pigcj,  witli  37  FUM,  Md 

TheB«  Tolnmei  can  behadfUhsr  leparatcl;  sr  id  luiforra  aela,  pod  tale  taj  iboil 
lODO  pAgn,  ud  DCaH;  1000  tllatutiang  «n  aUicl  ud  woai. 

To  •eeommoilita  tboia  irbo  deiire  Bcpual*  trcntuu  on  the  ItndiDg  >k|i»rtmiiiiU 
of  Kutui*!  Philoiopb/,  Uio  Fint  Cuuns  majr  oJia  be  liid,  difided  la  Ihrag  foi- 


It  nUI  thus  be  ii'en  Ibtt  thi>  work  ruroiibcs  cUhi^r  a  eamploU  eonn e  nf  inttrae. 
ti'in  iiti  lhe?e  sulijirt'.drpfpnrntc  Ircnli^pJ  un  nU  Ihi^  diffiTcnl  branches  of  rhyticiil 
BclenFo.     Tbo  object  or  th«  aatbor  hai  been  lo  prepare  a  wort  eni'led  eqaallj  tor 
tbe  collegiate,  academieal,  and  prlrate  itadenl,  who  maj  deeir«  to  aeqaainl  fata- 
><-  leir  nith  tbe  preient  ital*  of  icienee,  in  Its  most  adranced  condition,  wlthoat  par- 

(uIde  it  thrDD|;b  ita  malhemalieal  conaeqaeDcri  and  delalli.     Great  Indnitry  hai 
been  maaifeated  Ihronghont  tbe  work  to  elncidals'tha  principlei  adranced  b;  their 

Bieticnl  HppliealiODI  to  the  wanta  and  porposel  of  ciTiliied  tife,  a  Uik  to  whirh 
r.  Lardoer'a  immeniB  and  varied  knowledge,  and  hti  ■Jngnlai  feticllf  and  elear- 
HFBs  of  illaitratloQ  render  him  admlnbly  Sited.  Tkii  peenliaritj  of  the  ««k 
recommesdi  it  eipcciallj  as  tbe  leit-book  for  a  prnctical  age  and  coanlrjr  lach  u 
oura,  u  it  interegta  tbe  iludenC'i  mtnd,  bj  (bowing  him  the  ntilit?  of  bit  itudiff. 
while  it  direct!  hie  atlenUon  lo  the  fartbtr  eilcniion  af  that  ntilitj  b;  the  fulneti 
of  ila  example).  Tta  eitenilT*  adoption  in  mtiny  of  onr  moat  diatiQguiihcd  coU 
logea  and  iciuiiiaries  la  tnfflcient  proof  of  (he  aklU  with  which  ths  adUior*!  ialcO' 
liuai  bava  been  carried  out. 

BIRD'S   NATURAL  PHILOSOPHY. 
BLBMENTS  OP  NATURAL  PHILOSOPHY;  bki-io  m  Exi-aiilHeirrAL  Limo-  ^ 

Di-CTiojTo  TBE  Pnvsic*!.  SoisBcBB.  Illoilrated  wiih  orer  300  Tfood-col«.  Bj 
Got-nixd  Bird,  U.D.,  A»!atant  Phjiidan  (o  Qut*!  Hospital  From  the  Tbiid 
London  edition.     In  one  neat  volnme,  rojal  12mo. 

phjalai  lul^i^irt^- — Xoritt  Jivriran  Rntfto, 

kind  wllb  uhlcli  I  am  aoinalntcd.— AV*.  JoAo  lolMlon,  Iftilfjiaa  Onti,  MiikUtUimi,  a. 

ABBOT'S  EISKSKTB  OF  FHTSICS. 

ELEMENTS  OE  PHYSICS-,  or. fATunAL  Philosopbt,  Qmau.  aib  H■DIBlt^ 

written    tur   VmieitaV  Ua«  W  'e\i!»i  oi  'S«l-\h\avuL  Langnan.     fij  Hilt 


BLAKCHABD  A  LEA'S  PUDLICATI0N8.'-(^ifcalKrmil.)  T 

A    COMPLETE    COURSE   OF   NATURAL   SCIENCE.    (Jmt Uraod.) 

THE   BOOK   OF   NATURE 

An  Elementary  Introdnction  to  the  Sciences  of  Physics,  Astronomy,  Chemistry, 
Mineralogy,  Geology,  Botany,  Zoology,  and  Physiology.  By  Frederick 
ScocEDLER,  Pn.  D.,  Professor  of  the  iNataral  Sciences  at  Worms.  First  Ame- 
rican Edition,  with  a  Glossary,  and  other  Additions  and  ImproTements.  From 
the  Second  English  Edition,  translated  from  the  Sixth  German  Edition,  by 
Ubnrt  AIedlock,  F.C.6.,  Ac.  Illustrated  by  679  engravings  on  wood.  In  one 
handsome  volume,  crown  octavo,  of  abont  700  large  pages,  extra  cloth. 

To  accommodate  those  who  desire  to  use  tho  separate  portions  of  this  work,  the 
pnblishers  have  prepared  an  edition  in  parts,  as  follows,  which  may  be  haa 
singly,  by  mail  or  otherwise,  neatly  done  up  in  flexible  doth. 

NATURAL  PHILOSOPHT lU  pages,  with  U9  lUnstrations 

ASTRONOMY 04  "  51  " 

CHEMISTRY 110  "  48  " 

MINERALOGY  AND  GEOLOGY 104  "  167  " 

BOTANY 98  "  176  " 

ZOOLOGY  AND  PHYSIOLOGY 106  "  84  « 

INTRODUCTION,  GLOSSARY,  INDEX,  Ac.    96 

As  a  work  for  popular  Instruction  in  the  Natural  and  Phyflcal  Sciences,  it  certainly  Is 
unriTalled,  so  far  as  my  kuowled^  extenda  It  admirably  combines  perspicuity  with  br» 
Titr ;  while  an  excellent  Judgment  and  a  rare  discrimination  are  manifest  In  the  selection 
and  arrangement  of  topics,  as  well  as  in  the  deserlption  of  ol^ects,  the  iUustratioa  of  phe> 
nomena,  and  the  statement  of  principles.  A  more  careftil  perusal  of  those  departments  of 
the  work  to  which  my  studies  havo  been  particularly  directed  has  been  abundantly  suffldent 
to  satisfy  mo  of  its  entire  reliableness  —  that  the  oc;iert  of  the  author  was  not  so  much  to 
amuK  as  really  to  instruct, — Prof.  Allen,  OberfAi  htdUute,  Ohio, 

I  do  not  know  of  another  book  In  whkdi  so  much  that  is  Important  on  these  subjects  can 
bo  found  in  the  same  space.— iV^.  JohMton,  Wedeyan  Uhiverttly,  Conn. 

Though  a  very  comprehensiTe  book.  It  contains  about  as  much  of  the  details  of  natural 
science  as  general  students  in  this  country  hare  time  to  study  in  a  regular  academical 
course;  ana  I  am  so  well  pleased  with  it  that  I  shall  reoMnmend  its  use  as  a  toxt-book  in 
this  institution.— Tr.  //.  AOtn,  rretidenl  qf  Oirard  CbOtge,  PhOaddphia, 

I  am  delif^hted  with  Dr.  8ch(xdler*s  **Book  of  Nature;"  Its  tone  of  healthful  piety  and 
reverence  for  God's  word  add  a  charm  to  the  lesming  and  deep  research  which  the  volume 
e?erywhere  manifests.— /Vt;^.  /.  A,  Spenotr,  N.  Y. 


BROWNE'S    CLASSICAL   LITERATURE.    (Now Complete.) 

A  HISTORY  OF  GREEK  CLASSICAL  LITERATURE. 

BY  THE  REV.  R.  W.  BROWNE,  M.A., 

Professor  of  Classical  Literature  in  King's  College,  London. 

In  one  reiy  handsome  crown  ootaro  rolume. 


By  the  laniA  Author,  to  auiteh.    (Now  ready.) 

A  HISTORY  OF  ROMAN  CLASSICAL  LITERATURE. 

In  one  rery  handsome  crown  octaro  rolume. 

These  two  volumes  form  a  complete  course  of  Classical  Literatore,  designed 
either  for  private  reading  or  for  collegiate  text-books.  Presenting,  in  a  moderate 
compass  and  agreeable  style,  the  results  of  the  most  recent  investigations  of 
English  and  continental  scholars,  it  gives,  in  a  succession  of  literary  blograpbies 
and  criticisms,  a  body  of  information  neeessary  to  all  educated  persons,  and  whieb 
eaanot  elsewhere  be  found  in  so  condensed  and  attractive  a  ibava« 


BLANCHAKD  *  LHA'E  PTTBUOATIOKfi.— (»iuiiAi»L| 

Haw  and  maeib  Imprarel  EdiliDn. — (laUlj  lanMd.) 

PHYSICAL     GEOGRAPHY. 

BY  MART  SOMBRVILLE. 

A  new  Ameriflm,  {rora  lbs  tbinl  »ai  tfriied  LondiH)  tdilion. 


BV  W.  8.  W.  BrSCHEMBBRGKR,  M.D.,  U.  S.  Sitt. 
Ib  out  large  ro^nl  lEmo.  va)uiti«,  nt  nearly  ftii  bgndrtil  !<*£«. 
_     Gnln^it  BDiiecccMiywIlh  rcgBrd  to  •  work  Ulie  the  pKMnt,«bteb  ku  ,_     . 
■ttrangta  Ibrta  editiont,  on  e«h  sidt  of  t)>«  Atluittf^  wilbio  lbs  rpu«  of  k  Br*    { 
^Mtf*.     Tt»  pnUliihcn  tlfrfftira  only  eomider  it  necWMry  (a  iU/-  *'■-'  "*-  '— 
LodJod  Edilion  rcotixd  ft  IhDrongh  reiiiiaD  at  the  binda  of  tht  ■ 
Iroduced  irh»lar«  imprDVfmculi  uid  comctioDi  tha  ftdTuiec  of  ta 
tnlnMe;  and  thkt  tbepreunt  iuat.  laaddltlou  to  thii.  bu  bad  • 
Salion  oo  tbspul  of  tbe  editor,  to  adapt  !l  more  eipedal);  lolbu  e 

«are  bai  been  eiercined  in  botb  tbs  text  and  (be  gteHBi^  to  obtaii.    , 

M  eaieotiai  lo  a  Hatk  of  thii  nalnre  j  and  tn  it*  preteot  improTcd  and  Mkqad 
Mate,  wiib  no  eotTFiponding  Ipctwae  uf  priee,  It  ii  eoafidcoUj  prttnlmlt  u  to 
erer;  ws;  woithj  of  a  sonliiiuiUJOD  of  lb*  ttrlkiug  tarot  witb  vbiebUM*  bii 

bi;tler"s  ancient  atlas. 

AN  ATLAS  OF  ASCIENT  GEOURAPHY.  Ry  fiHriL  Brrfceii.  B.P,  lit> 
Lord  Bbhoji  of  Litchfiold.  In  one  bandeomt  octavo  TolBine,  contaiainj;  twmlj 
one  eriourtd  qnarlo  Hspr,  and  an  accODtDiled  Indei. 

TEXT-BOOK  OF  SCRIPTURE  GEOGHAPHY  AND  HlSTOflY.    (JoUlaut.!) 

OUTLINES  OF  SCRIPTUREGEOGRAPHY  AND  HISTORY; 

niDBtrating  the  Hiiterical  Peitioni  of  the  Old  and  Sew  Testunestt. 

BT  EUWARD  HUGHES,  FJt.A.S.,  F.Q^, 
Head  Master  of  the  Bojal  Kavnl  Loiter  Scbool,  Greenw 


With  twain  hindaow  Calond  Kap*.  I 

In  cue  rer;  neat  rojU  llmo.  Tolnma,  extra  elotb. 

The  intimate  eotmection  of  Sacred  Hbtorj  with  Iba  ftognphj  and  pb^iinl 
features  of  the  vuioni  landi  oocupied  by  tba  IiTMlilea,  renden  k  voil  like  Itt 
preient  en  almost  neceaiwj  companion  to  &]1  who  de<ire  to  read  the  Striplirr,' 
Dnderetandingtj.  To  the  j'onnf!,  eipeciallj,  a  elear  and  connected  namiiie  nt 
the  evcnte  recorded  in  the  Bible,  ii  BMeedingly  de>ir«b]e,  partieularlj  wtm 
illutirntcd,  ms  io  tbe  preient  lolume,  with  inccioct  bat  oopioni  aeeounit  of  iba 
neighbuiing  natlona,  and  of  tbe  topajfrHphy  and  political  diiirions  of  ifar  cDDnlnii 
mcDticned,  coopled  with  Ibe  reioUi  d  lbs  latest  inTettigations,  b;  wbieh  Mtan. 
l«<rnrd,  Ljnob,  Olin,  Durbin,  Wilton,  Stepbene,  and  otben,  have  noeeeded  in 
throwing  light  on  ea  mnnj  obienre  portioni  of  tbe  Scriptorei,  Terifying  itl  Mca- 
faoj  in  minute  particulors.  Foir  more  iDtareeting  elaw-booke  coold  Ibcrefore  be 
found  fur  echooli  where  the  Bible  forme  a  part  of  edHcatioD,  and  Boae,  pcibap), 
more  liliolj  to  prore  of  permanent  benefit  lo  the  aehoUr.  Tbe  inflaenee  which 
tbe  pbjTBiaal  gcograph j,  olimata,  and  produclioni  of  Paltitine  had  apoB  tha  Jewiih 
.people  ni\lbe  [aan'iEaUi  h^. ti>i\:&, ii'ti\\« -Oiui uikhq^v -idu^ ^nuat  ihi  Tarisat 


BLANOHABD  A  LEA'S  PDBLIGATI0N8.^1Uti«o(Kmai.)  9 

Now  COHPLVTK. 

SCHMITZ  AND  ZUMPrS  CLASSICAL  SERIES. 

By  the  completion  of  this  series,  the  classical  student  is  now  in  possession  of  a 
thorough  and  uniform  coarse  of  Latin  instmction,  on  a  definite  system.  Besides 
the  advantages  which  those  worlcs  possess  in  their  typographical  acearacy  and 
careful  adaptation  to  educational  purposes,  the  exceedingly  low  price  at  which 
ihey  are  otTered  is  a  powerful  argument  in  faror  of  their  general  introduction,  as 
removing  a  harrier  to  tho  general  diffusion  of  classical  education  in  the  size  and 
eosUiness  of  tho  text-books  heretofore  in  use. 

The  seriea  consists  of  the  following  volumes,  clearly  and  handsomely  printed, 
on  good  paper,  in  a  uniform  large  18mo.  siie,  strongly  and  neatly  bound,  and 
aeeompanied  with  notes,  historical  and  critical  introductions,  maps,  and  oUier 
lUnatrationf. 

Sghxitz's  Elimevtary  Latin  Grammab  and  Exbrcisks,  extra  cloth,  price  $0.50 
Kaltschicidt'8  School  Lati5  DicrioNARr,  in  two  Parts,  Latin-English, 

and  English-Latin,  nearly  000  pages,  strongly  bound  in  leather $1.30 

Part  L,  Latin-English,  about  500  pages,      «  «'  '<      00 

Part  ir.,  English-Latin,  nearly  400  pages,  "  "  "      75 

8cHMiTz*8  Advahckd  Lati.h  GRAMMAR,  318  pagcs,  half  bound,      .00 

Adtancrd  Latist  Exercises,  with  sblectioss  for  Beadiitq,  extra  cloth,      .50 
CoRSBLii  NEPons  LiBBB  DE  ExcELLEXTiBUS  DuciBUB,  Ac,  cxtra  cloth,      .50 

CiBBARis  DB  Bbllo  Gallico,  Libri  IV.,  232  pages, extra  cloth,      .50 

O.  C.  Sallustii  Catiliha  et  Juourtba,  168  pages, extra  cloth,      .50 

Bxcerpta  XX  P.  OviDii  Nasoxis  CARMiinBUS,  246  pages, extra  cloth,      .60 

Q.  CuRTii  RuFX  DB  Albxahdri  Hagmi  Qd^  Sdpxrbuiit,  326  pp.,  ex.  cloth,      .70 

P.  ViROiLii  Haroxis  Carmixa,  438  pages, extra  cloth,      .75 

EcLOGJB  rx  Q.  Horatii  Flacci  Poematibus,  312  pages, extra  cloth,      .60 

T.  Livii  Patayixi  IIistoriabum  Libri  L  IL  XXL  XXIL,  350  pp.,  ex.  cloth,      .70 

M.  T.  CicBROffis  Orationes  Sblectjb  XIL,  800  pages, extra  cloth,      .60 

Also,  uniform  with  the  Series, 
Baibd'b  Classical  Manual  or  Ahciert  Geoqbapht,  Axn- 

quiTiBS,  CHROBOLOCir,  Ae., extra  cloth,      .50 

The  volumes  in  cloth  can  also  be  had,  strongly  half-bonnd  in  leather,  with  cloth 
sides,  at  an  extra  charge  of  five  cents  per  volume. 

The  very  numerous  recommendations  of  this  series  from  classical  teachers  of  the 
highest  standing,  and  their  adoption  in  many  of  our  best  academies  and  colleges, 
sufficiently  manifest  that  the  efforts  of  tho  editors  and  publishers  have  not  been 
nnsuccessful  in  supplying  a  course  of  classical  study  suited  to  the  wants  of  tho 
age,  and  adapted  to  the  improved  modem  systems  of  education. 

With  your  Clawdcftl  Series  I  am  well  acquainted,  and  hare  no  hef  Itancr  in  recommending 
th«m  to  all  mr  frieads.  In  addition  to  your  Tirgil,  which  we  use,  we  shall  probablr  adopt 
other  books  or  the  serlei  as  we  may  have  oecauoa  to  introduce  them.— iV(/.  /.  J.  Oweiif 
If,  Y.  Fret  Academjf. 

I  regard  this  series  of  Latin  text-books  as  deddedly  superior  to  any  otliers  with  whlrh  I 
am  aoqnalnted.  The  Uvy  and  Horace  I  shall  Immediately  introduce  for  the  use  of  the 
oollej;e  claasesw — Pro/.  A.  koQinif  J>daioar9  CcOtgt, 

Having  examined  several  of  them  with  eome  decree  of  care,  we  have  no  hesitation  In  pro- 
nouncing them  among  the  very  best  extant^-iVq/l  A.  C  Knoxj  Hanover  OMeffe,  Indiana, 

I  can  give  yon  no  better  proof  of  the  value  which  I  set  on  them  than  by  making  nra  of 
them  in  my  own  elassea,  and  recommending  their  use  in  the  preparatory  department  of  our 
injititutlon.  I  have  read  them  through  careftilly,  that  I  might  not  speak  of  them  without 
due  examination ;  and  I  flatter  myMif  that  my  opinion  is  tally  borne  out  by  fact,  when  1 
prononnee  them  to  be  the  most  umAiI  and  the  most  eorreet,  as  well  as  the  dieapent  editions 
of  Latin  Claovlca  ever  introduced  in  this  eountry.  The  Latin  and  Knirliah  Dictionary  con> 
taios  as  much  as  the  student  eaa  want  in  the  earlin  years  of  his  course;  it  contains  more 
than  I  have  ever  seen  oompreMed  into  a  book  of  this  kind.  It  ought  to  be  the  student's 
constant  companion  In  his  redtattons.  It  has  the  extraordinary  recommendation  of  being 
at  onoe  portable  and  oomprehenslvew— Atj/".  M,  N.  Newett,  iloMonic  OJOegt,  Ibm. 

That  Invaluable  little  work,  the  Clamleal  Manual,  has  been  used  by  me  ibr  some  time.  J 
would  not,  on  any  aoooant,  be  without  it.  Ton  have  not  perhaps  been  informed  that  It  has 
recently  been  Introduced  in  the  Hlftfa  School  of  this  plaea.  Its  typographical  aeeuracu  Is 
remarkaUcH— JS^^iiMiU  H,  ChaUt  Bartard  OkANErsflj^ 


[  Shaw's  English  Literature— Lately  Published. 

OUTLINES  OF  ENGLISH   LITERATURE.       I 

f  Bf  TnaMAs  B.  SraW,  Pivfejinr  of  Engliih  Lkerslnre  id  the  Idi|wiu1  Aliiuifai 

\  IiTcoBin,  SU  raiortburg,     Suc-ood  Acntriean  £diLan.     Willi  ■  fckettt  of  Aili- 

'  riCM  Lltunlmo.  bj  atxiit  T,  Tcobbmas,  Eeq.     In  odb  laisa  ud  tued-inu 

i  <rulain«,  igjiU  lima,  of  ktont  Art  handred  pagu. 

Ih«  oljoot  of  Ihit  woik  !■  lo  present  to  tin  tUidest,  within  >  modenl*  «iDt«nf 

1  ft.dtiu  and  oanneeted  tIcv  oC  th«  hinMrj  uid  prodacliaiu  of  Euglidb  Lilcnun. 

f  To  BeciimpUab  Ibia,  tbe  author  bu  foUowad  iu  caune  trum  the  uriint  limn  It 

'  ||*ir  rauui  Bud  efTiicli,  isd  leleotiag  tb«  mors  celebniad  utbon  u  (nbJMU  M 

I  b^  tiOgciiphlKal  nod  oriliirmi  sketcbM,  »j)ftl;iing  tbair  but  woiki,  lod  ihu  pn- 

,     HBtlng  W  Ibe  (tudenliidcflnite  riow  of  tho  d«i-e!opmp—  -'  ■•■-  '- —  --* 

1    UUniture,  wltb  luccind  deicripUom  of  Ihoie  boaki  mJ  i . .  , 

I  M»aa  (hoidil  be  tgaoranL     Ha  hu  Ihui  nat  ddI;  aupplled  Ih*  ■cknowMpi 

Vftnt  of  n  mRDusI  OD  thli  lubjoet,  but  b;  tlwIiTelineXf  and  ponu- ofhii  ilfl*.lif 

I  tton>ii|:h  knoif1«dge  ha  ditpU;*  or  hU  tuple,  uid  Iha  itrietj  of  hii  cntoMU,  b< 

I  lU  lucFCfded  in  pradaciog  a  moM  •.^'eeable  [Mdiog-book,  wtudi  will  eipDnU 

[  $«  mind  of  Ibe  tcbalftr,  uid  relieie  iha  010001007  "f  drier  itudiet. 

L  111  merit!  I  b*d  not  now  Itv  the  flnt  Ua*  Id  iHra.  IbuemlUi 

■  MA,  «nb  (he  tntlatt  laliidMUai.    It  VM  k  hiiPT  UBUrtlon,  oOhI 

I  AualBHit-teok  DB  raeh  a  eaVtct  sB  or  Boal  be.  ismpTWa(  >. 

I  8lliii1'l^n^lyi»teB»*hirt]f«RiatM.    The  ar"  -  — — — 

'  •fldnwwaJlaUtlialheatleoiptai  •-'"■-■— • 

^m.  of  eenLM  .nd  fu  - ■■  ■' 

Of  "  Shaw'.  EogUi- 

BOLHAE'S  COHTLi^  FKEHCH  SEHISS. 

Blaocbaid  and  Lea  now  puhllab  the  wbok  of  Bolmar'a  Edueaboiul  Werki,  form- 
ing a  coDipkle  neriFi  for  the  aoqnlfition  of  the  French  tnogvago,  ai  follovi: 

BOLM.^R'S  EDITION  OF  LKVIZAC'S  TIIEOKETIOAL  AKD  PRACTICAL 
OKAMMAll  OP  THE  FKEKCIl  LANGUAGE.  With  DUmerou  Coneilimi 
and  ImprorcmcDt^,  and  the  addition  of  a  enuplete  Troatiae  dd  the  GeDdireof 
Kroncb  Noum  aod  the  Conjugation  of  the  French  Verb],  Kegulat  aod  l[n[0- 
lar.     Thirtj-lirth  odition.     Id  one  ISmo.  Tolumc,  leather. 

BOUtAR'S    COLLECTION    OF    COLLOQUIAL    i'URASGS,  od    cterj  to|^a 

jnerouB  reinailia  on  the  pe™linr  proonncuition  and  use  of  Tarioua  words.    Tka 
wholo  fo  ill  j  ■    ■  1  ■  ..l.li-  to  fncillLalo  the  acquiiilion  of  a  cirrcot  pro- 

BOLMAlrs   I  Mll.OS'S  AVEKTOKES  UB   lELEMAQLK, 

BOLMAR'S  KEY  TO  THE  FIRST  EIGHT  BOOKS  OF  TBLEIUQUB,  Da 
the  literal  and  free  IraDtlaliou  of  Franeh  Inio  EDgllili.  In  OBO  llaao.  toIdof, 
hiilf  bound. 

BOLMAR'S   SELECTION    OF   OSB   HUKDBBD   OF  PBRRIH-8    FABLER. 

accompanied  nith  a  Kej,  containing;  lh»  text  and  a  Itteral  and  a  ftre  traoiilii- 
tbn,  arranf^ed  in  >ucb  a  inanner  ai  to  point  ant  tho  difftreDCa  beliieen  tlir 
French  and  the  Engligh  Idiom  j  alio,  aflgiired  pronnneiatlon  of  the  Fnnch. 
Tbe  whole  preceded  1>;  a  abort  treatiao  on  the  Souoda  of  the  French  langaagF 
as  compared  «ith  tboae  of  English.  In  on*  ISmo.  TaluiM,  half  bmnd. 
BOLMAU'S  BOOK  OF  FRENCH  VBRBS,  therein  the  Uodal  Verba,  and  t*T(~ 
ral  of  the  meal  diffieoll,  are  conjogaled  AfftnnkllTeHr,  NegaKTilj,  lDten«ga- 
llTcly,  ond  Kegalively  »nd  InlerrogatiTely.  conlaJnine  also  nnmeroDi  KelM 
and  Directions  00  the  Different  CoDJogationi,  not  to  bo  foand  in  toy  other  be4 
published  for  the  use  of  Engtiib  acboUrs ;  to  irbich  ia  added  «  oompleta  list  of 
all  the  Irreguhu-  verbs.  In  one  Uma.  Totame,  half  bsund. 
The  long  and  eilended  sate  with  whioh  Ihc.e  works  ba»«  beta  faroimd,  ud 

the  coBitsBtlj  Incraaiiug  demand  which  eiiite  (br  then,  reoden  nsBONBar*  bbt 

ezplBoalion  or  recoTDmeDdalVoii  at  Caea  m«i\\a. 


BLANCHARD  A  LEA'S  PnBLIGATI0N8.--<^<'Mcaf>biia£.)  11 


HERtCHELL'8    ASTRONOMY. 


OUTLINES    OF   ASTRONOMY. 

BY  SIR  JOHN  F.  W.  HBRSCUEL,  Babt.,  F.R.S.,  Ac. 

A  New  Ameriemn,  from  the  Fourth  tnd  Rerised  London  Edition. 

In  one  handsome  crown  octavo  Tolame,  with  numerous  plates  and  wood-cuts. 

The  present  work  is  reprinted  from  the  last  London  Edition,  which  was  caro- 
lUly  rorised  by  the  author,  and  in  which  he  embodies  the  latest  ioTCstigations  and 
discoveries.  It  may  thercfuro  be  regarded  as. fully  on  a  level  wiUi  the  most  ad- 
vanced state  of  the  science,  and  even  better  adapted  than  its  predecessors  as  a 
ftill  and  reliable  teit-book  for  advanoed  elassea. 

A  few  commendatory  notices  are  inbjoined,  from  among  a  large  number  with 
which  the  publishers  have  been  favored. 

A  rich  mine  of  all  that  is  most  valuable  in  modem  AstronoB^.<— iV^afor  2>.  ObiuUad, 
Tate  (UUffe. 

As  a  work  of  reftrenoe  and  studj  fi>r  the  more  advanoed  nuplls,  who  yet  are  not  preparod 
to  aynil  them^elvo*  of  the  higher  mathematloB,  I  know  of  no  work  to  be  oompsrcd  with 
it.— l*ro/.  A.  QuweBf  Bro¥m  UHiverntf,  R.  I, 

This  treatise  is  too  well  known,  and  too  highly  appreelaied  In  the  sdentWc  world,  to  need 
orw  praiM.  A  dtstinKulshiBg  nerit  In  this,  as  in  the  other  prodncttons  of  the  author,  is, 
that  tlw  language  in  whidi  the  proftrand  reasonings  of  science  are  conveyed  is  so  perspicuous 
that  the  writer's  meaning  can  never  he  misunderstood.— iVt/.  Ssanud  Jona,  Jrfftntm 

I  know  no  tnatise  on  AMraDomy  eomparable  to  **  Hersdiers  Outlines."  It  is  admirably 
adapted  to  the  necessities  of  the  student.  We  have  adopted  It  as  a  textrbook  ia  our  Ooi- 
legey— JVy)/.  J.  F,  Gt^dcer,  JlfcuUion  QfUtge,  I\u 

As  far  as  I  am  aUe  to  iudgB^  U  |a  the  best  work  of  Its  dass  hi.  any  language^— Pit/.  Jawta 
CurUy,  Georydotot^  CbtUffe, 

It  would  not  become  me  to  speak  of  the  scientific  merits  of  sudi  a  work  by  such  an  author ; 
but  I  may  be  allowed  to  sayt  that  I  most  earnestly  wish  that  it  might  sopwsode  CTery  book 
used  as  a  text-book  on  Astronomy  in  all  our  institutions,  exeept  perhaps  thoae  where  it  Is 
studied  mathevatleally^/V^.  N.  imnffkad,  BriOgtvaUr^  Man. 

CHEMICAL    TEXT-BOOK    FOR    STUDENTS.    (Just Isnied.) 

E  L E  B E N  T  A  RT~0  H K B I S T  R T , 

THEORETICAL    AND    PRACTICAL. 

BY  GEORGE  FOWNES,  Ph.  D.,  Ac. 

.  With  VnnMnras  Illiiitratloiis. 

A  !£▼.  AlllltlCAH,   rnOM  THB  LAST  AKD  RnyMBB  LOKIKUI  ■DITIOI.     SDIT^n^ 

wrre  additioiis, 

BY  EOBBBT  BRIDGES,  M.D. 

In  one  large  royal  13mo.  volume^  containing  over  650  PJ^get,  clcArly  printed  on 

anall  type»  witJi  181  Illuitrations  on  Wood. 

We  know  of  no  better  text-book,  esperially  In  the  dilllcuU  department  of  Organic  Chemistry, 
upon  which  it  Is  partlcalarly  ftall  and  «atisflietory.  We  would  recommend  It  to  preceptors 
aK  a  capital  **  ofHea^iook*'  for  thefar  students  Who  a*e  hegtmseni  in  Chemistry.  It  is  eoplonsly 
illustrated  with  axeallent  wood^nti,  and  altofsther  admirably  **got  up."— JVl  J.  Jiedieal 
Bfpffrttr. 

A  standard  manual,  wbfeh  has  long  enjoyed  the  reputation  of  embodying  murh  know- 
ledge in  a  small  i^ara.  The  anther  has  achieivad  the  dilBenlt  task  of  condenaation  with 
vaiitorly  tact.  His  hook  Is  eouelse  without  bring  dzy,  and  brief  without  being  too  dog 
matical  or  general.— riiyMa  JMBctotfnnd  9i&gioaiJrmmul, 

The  work  of  Dr.  Vownes  has  long  been  beltoe  the  publico  and  its  merits  have  been  flilly 
appredated  an  the  best  text-book  on  Chemistry  now  In  eoistsaee.    We  do  not,  of  rouise^ 
place  it  In  a  rank  superior  to  the  works  of  Brands.  Graham,  Toracr,  Gracovr^  «t  a«M!AaL. 
but  we  say  that,  as  a  work  te  atndsnts^  it  la  prateattUtA  ivj  «ft  lOfeMm.— ImwIii^  ^tMorMik^ 


II  BLANCHAKD  A  LBA'5  PCBUCATtOSB.—fSOacmUaaat.) 

A  VKW  iUni  COXPIETB  OLASSIOAX.  ATLAS.— (lut  Bvady.l 

AN  ATLAS  OP  CLASSICAL  GEOGRAPHY. 

Oonrnncrxo  IT  WILLIAM  nUOUBS,  isn  bpitbd  ir  QHORGI;  LO.VQ. 

Wltk  B  Ui«lch  or  Anoisnt  Ueographr,  Kod  other  A4ditioa«. 

BT  THE  AKERICAS  EOIKIB. 

Canlaining /^fh/laa  C-lorrJ  Ifapt  and  P/nnr,  or.  /.irrnlj.m  laryt  imftritl  f*»tl 


LIST  OF 
1.  THR  GEOORAPIIT  OP  THE  AK 

CIENT!!.— TimffoaLBAcooMBiif 
c.  000).— Thb  WoblD 


1   lUc 


^  [.bou 


■■aDOTCg  (liiaal  a.c  440). — Tse 

bout  B.c^.  3D0|.  — Tns  WantB 
nni>n      to      EniT03T[rE<<E9 
n*Bo  [fr^tn  BbonI  B.C:.  200  (o 
1.— WE9TCBII    Gl-ropi 

-TnK  WoRtn 

r(ol)oiil*.D.  IBI,.     

—  Biiitiiit 


0  PrULEll 


iccoitDiKO  TO  Prei-Riir. 
J,  TUB  WORLD  AS  KNOWN  TO 
TUIi  ANCIENTS,  vrrn  ths  Boui. 
Dtnr  or  the  Perjiix  Eupirc  i;^deh 

S.  EMPIRE  OF  ALEXANDER  THE 
OREAT,  ivETH   ras  ADJOinno  Re- 

4.  TIIB  PROTINCES  OP  TUB  RO- 
MAN EMPIItB  (A.D.  IIS}, 
i.  BRITANSrA. 
B.  GALLIA. 
T.  IllSPANIA. 

a.  ITALIA  (NoBtBnH  PiKt), 
>.  ITALIA  (SoDrnEDM  Fikt).— Cos- 


ia.  PII'ILIA. 

J3.  8irRACU?-B.— THE  BAY  OF  NA. 
PLUS  M-D  tPitcBirr  Pini  or  ~ 


p.phie«l  pTiiBii.  an  nn  ent^r^fd  tale, 
,,  WBj*  pifiagti  in  ih«  Diuilul  wrlterj. 

kutilon  at  Mi«ita^UaM(]< 


FAKla.  —  Tae  nro  Pamn  or  Burv- 

U.  MACEDONIA,  THBACI*.  lUT- 

RICUM,  AID  mi  PRonicci  orm 

UiDDu  iRD  Lown  Dttvai. 
IS.  ORABCU.  INCLUDIKO  KPIRM 

AND    TIIBS6ALIA,  WITH    PAXT 

OP  MACBDONIA. 
!C.  PART  OF  ATTICA,  WITH  EOEfl. 

TIA,  PK0CIS,LOCRIfl,MKiiARIS. 

tte..  on  *a  enUrged  italc 
IT.  PLAN  OF  ATHENS.  — ATHENS 

AND  ITS  HARBORS. 
19.   PELOPONNESCS,    wnH    Amct 

IB.  THE  COASTS  AND  isLANDS  OF 

THE  AEGEAN  6BA. 
2tl,  APIA  MINOR  AND  THB  NORTH. 

KRNPART  OF  SYRIA. 
;i.  PALAESTINA,  WITU  PART  OP 

STRIA.— Pl*-!  or  jEiir»iLE>. 
22.  ASSYRIA  AND  TQB  ADJACEKT 

COUNTRIES. 
33.  MAURITANIA,  NDMIDIA,  AND 

AFRICA.— Tn«ArBic»i<CouT"o« 

Tm  Stiith  Misor  to  Eotpt.  — Eii- 

I-tKSID  PL:IH   or  TKM  CAiTanaisui 

24.  Arabia' PETRABA  and  part 

OF  EOYPT.  i^cicniSB  TBI  Dilti.     I 
15.  OERMAKIA   MAGNA,  niio  rm 

Photisces  or  twb  rppiK  Dasi-bb. 
IB.  Tboji.- TwiRMOPTLiii.  — Mm- 
!t.  —  Plataei.  —  Mi^:<ej|.  -  ' 

I  Ulcus — I»DB. — AUILA. — TbU 

f  Bosronoi. — ALKiANDitiA. 
a  k  T«r;  Ihnrangh  wriu  of  map*  of  ill  | 
Atlu  conuini  ■  l*rgt  DDDibiTr  of  ujt- 
plsr«i,  elaridiiln;  in  ibaii} 
ner  it  li  beXtrtd  ibit  nati    | 
re*  to  obtain  m.  cliir  mupra- 


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